P-value correction

Given a list of p-values, adjust the p-values for multiple comparisons. This is done in order to control the false positive, or Type 1 error rate. This is also known as the "false discovery rate" (FDR). After adjustment, the p-values will be higher but still inside [0,1]. The adjusted p-values are sometimes called "q-values".

Task

Given one list of p-values, return the p-values correcting for multiple comparisons

   p = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
        8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
        4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
        8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
        3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
        1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
        4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
        3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
        1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
        2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03}

There are several methods to do this, see:

Yoav Benjamini, Yosef Hochberg "Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing", Journal of the Royal Statistical Society. Series B, Vol. 57, No. 1 (1995), pp. 289-300, JSTOR:2346101
Yoav Benjamini, Daniel Yekutieli, "The control of the false discovery rate in multiple testing under dependency", Ann. Statist., Vol. 29, No. 4 (2001), pp. 1165-1188, DOI:10.1214/aos/1013699998 JSTOR:2674075
Sture Holm, "A Simple Sequentially Rejective Multiple Test Procedure", Scandinavian Journal of Statistics, Vol. 6, No. 2 (1979), pp. 65-70, JSTOR:4615733
Yosef Hochberg, "A sharper Bonferroni procedure for multiple tests of significance", Biometrika, Vol. 75, No. 4 (1988), pp 800–802, DOI:10.1093/biomet/75.4.800 JSTOR:2336325
Gerhard Hommel, "A stagewise rejective multiple test procedure based on a modified Bonferroni test", Biometrika, Vol. 75, No. 2 (1988), pp 383–386, DOI:10.1093/biomet/75.2.383 JSTOR:2336190

Each method has its own advantages and disadvantages.

C

Version 1

Works with: C99

Translation of: R

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses.

This work is a translation of the R source code. In order to confirm that the new function is working correctly, each value is compared to R's output and a cumulative absolute error is returned.

The C function p_adjust is designed to work as similarly to the R function p.adjust as possible, and is able to do any one of the methods.

This program, for example, fdr.c, can be compiled by

gcc -o fdr fdr.c -Wall -pedantic -std=c11 -lm -O4

or

clang -o fdr fdr.c -Wall -pedantic -std=c11 -lm -O4.

Link with -lm <lang C>#include <stdio.h>//printf

include <stdlib.h>//qsort
include <math.h>//fabs
include <stdbool.h>//bool data type
include <strings.h>//strcasecmp

unsigned int *restrict seq_len(const size_t START, const size_t END) { //named after R function of same name, but simpler function size_t start = START; size_t end = END; if (START == END) { unsigned int *restrict sequence = malloc( (end+1) * sizeof(unsigned int)); if (sequence == NULL) { printf("malloc failed at %s line %u\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } for (size_t i = 0; i < end; i++) { sequence[i] = i+1; } return sequence; } if (START > END) { end = START; start = END; } const size_t LENGTH = end - start ; unsigned int *restrict sequence = malloc( (1+LENGTH) * sizeof(unsigned int)); if (sequence == NULL) { printf("malloc failed at %s line %u\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } if (START < END) { for (size_t index = 0; index <= LENGTH; index++) { sequence[index] = start + index; } } else { for (size_t index = 0; index <= LENGTH; index++) { sequence[index] = end - index; } } return sequence; }

//modified from https://phoxis.org/2012/07/12/get-sorted-index-orderting-of-an-array/

double *restrict base_arr = NULL;

static int compar_increase (const void *restrict a, const void *restrict b) { int aa = *((int *restrict ) a), bb = *((int *restrict) b); if (base_arr[aa] < base_arr[bb]) { return 1; } else if (base_arr[aa] == base_arr[bb]) { return 0; } else { return -1; } }

static int compar_decrease (const void *restrict a, const void *restrict b) { int aa = *((int *restrict ) a), bb = *((int *restrict) b); if (base_arr[aa] < base_arr[bb]) { return -1; } else if (base_arr[aa] == base_arr[bb]) { return 0; } else { return 1; } }

unsigned int *restrict order (const double *restrict ARRAY, const unsigned int SIZE, const bool DECREASING) { //this has the same name as the same R function unsigned int *restrict idx = malloc(SIZE * sizeof(unsigned int)); if (idx == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } base_arr = malloc(sizeof(double) * SIZE); if (base_arr == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } for (unsigned int i = 0; i < SIZE; i++) { base_arr[i] = ARRAY[i]; idx[i] = i; } if (DECREASING == false) { qsort(idx, SIZE, sizeof(unsigned int), compar_decrease); } else if (DECREASING == true) { qsort(idx, SIZE, sizeof(unsigned int), compar_increase); } free(base_arr); base_arr = NULL; return idx; }

double *restrict cummin(const double *restrict ARRAY, const unsigned int NO_OF_ARRAY_ELEMENTS) { //this takes the same name of the R function which it copies //this requires a free() afterward where it is used if (NO_OF_ARRAY_ELEMENTS < 1) { puts("cummin function requires at least one element.\n"); printf("Failed at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } double *restrict output = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (output == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } double cumulative_min = ARRAY[0]; for (unsigned int i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) { if (ARRAY[i] < cumulative_min) { cumulative_min = ARRAY[i]; } output[i] = cumulative_min; } return output; }

double *restrict cummax(const double *restrict ARRAY, const unsigned int NO_OF_ARRAY_ELEMENTS) { //this takes the same name of the R function which it copies //this requires a free() afterward where it is used if (NO_OF_ARRAY_ELEMENTS < 1) { puts("function requires at least one element.\n"); printf("Failed at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } double *restrict output = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (output == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } double cumulative_max = ARRAY[0]; for (size_t i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) { if (ARRAY[i] > cumulative_max) { cumulative_max = ARRAY[i]; } output[i] = cumulative_max; } return output; }

double *restrict pminx(const double *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS, const double X) { //named after the R function pmin if (NO_OF_ARRAY_ELEMENTS < 1) { puts("pmin requires at least one element.\n"); printf("Failed at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } double *restrict pmin_array = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (pmin_array == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { if (ARRAY[index] < X) { pmin_array[index] = ARRAY[index]; } else { pmin_array[index] = X; } } return pmin_array; }

void double_say (const double *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) { printf("[1] %e", ARRAY[0]); for (size_t i = 1; i < NO_OF_ARRAY_ELEMENTS; i++) { printf(" %.10f", ARRAY[i]); if (((i+1) % 5) == 0) { printf("\n[%zu]", i+1); } } puts("\n"); }

/*void uint_say (const unsigned int *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) { //for debugging printf("%u", ARRAY[0]); for (size_t i = 1; i < NO_OF_ARRAY_ELEMENTS; i++) { printf(",%u", ARRAY[i]); } puts("\n"); }*/

double *restrict uint2double (const unsigned int *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) { double *restrict doubleArray = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (doubleArray == NULL) { printf("Failure to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { doubleArray[index] = (double)ARRAY[index]; } return doubleArray; }

double min2 (const double N1, const double N2) { if (N1 < N2) { return N1; } else { return N2; } }

double *restrict p_adjust (const double *restrict PVALUES, const size_t NO_OF_ARRAY_ELEMENTS, const char *restrict STRING) { //this function is a translation of R's p.adjust "BH" method // i is always i[index] = NO_OF_ARRAY_ELEMENTS - index - 1 if (NO_OF_ARRAY_ELEMENTS < 1) { puts("p_adjust requires at least one element.\n"); printf("Failed at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } short int TYPE = -1; if (strcasecmp(STRING, "BH") == 0) { TYPE = 0; } else if (strcasecmp(STRING, "fdr") == 0) { TYPE = 0; } else if (strcasecmp(STRING, "by") == 0) { TYPE = 1; } else if (strcasecmp(STRING, "Bonferroni") == 0) { TYPE = 2; } else if (strcasecmp(STRING, "hochberg") == 0) { TYPE = 3; } else if (strcasecmp(STRING, "holm") == 0) { TYPE = 4; } else if (strcasecmp(STRING, "hommel") == 0) { TYPE = 5; } else { printf("%s doesn't match any accepted FDR methods.\n", STRING); printf("Failed at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } //--------------------------------------------------------------------------- //--------------------------------------------------------------------------- if (TYPE == 2) {//Bonferroni method double *restrict bonferroni = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (bonferroni == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { const double BONFERRONI = PVALUES[index] * NO_OF_ARRAY_ELEMENTS; if (BONFERRONI >= 1.0) { bonferroni[index] = 1.0; } else if ((0.0 <= BONFERRONI) && (BONFERRONI < 1.0)) { bonferroni[index] = BONFERRONI; } else { printf("%g is outside of the interval I planned.\n", BONFERRONI); printf("Failure at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } } return bonferroni; //--------------------------------------------------------------------------- //--------------------------------------------------------------------------- } else if (TYPE == 4) {//Holm method /*these values are computed separately from BH, BY, and Hochberg because they are computed differently*/ unsigned int *restrict o = order(PVALUES, NO_OF_ARRAY_ELEMENTS, false); //sorted in reverse of methods 0-3 double *restrict o2double = uint2double(o, NO_OF_ARRAY_ELEMENTS); double *restrict cummax_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { cummax_input[index] = (NO_OF_ARRAY_ELEMENTS - index ) * PVALUES[o[index]]; // printf("cummax_input[%zu] = %e\n", index, cummax_input[index]); } free(o); o = NULL; unsigned int *restrict ro = order(o2double, NO_OF_ARRAY_ELEMENTS, false); free(o2double); o2double = NULL;

double *restrict cummax_output = cummax(cummax_input, NO_OF_ARRAY_ELEMENTS); free(cummax_input); cummax_input = NULL;

double *restrict pmin = pminx(cummax_output, NO_OF_ARRAY_ELEMENTS, 1); free(cummax_output); cummax_output = NULL; double *restrict qvalues = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { qvalues[index] = pmin[ro[index]]; } free(pmin); pmin = NULL; free(ro); ro = NULL; return qvalues; //--------------------------------------------------------------------------- //--------------------------------------------------------------------------- } else if (TYPE == 5) {//Hommel method //i <- seq_len(n) //o <- order(p) unsigned int *restrict o = order(PVALUES, NO_OF_ARRAY_ELEMENTS, false);//false is R's default //p <- p[o] double *restrict p = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (p == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { p[index] = PVALUES[o[index]]; } //ro <- order(o) double *restrict o2double = uint2double(o, NO_OF_ARRAY_ELEMENTS); free(o); o = NULL; unsigned int *restrict ro = order(o2double, NO_OF_ARRAY_ELEMENTS, false); free(o2double); o2double = NULL; // puts("ro"); //q <- pa <- rep.int(min(n * p/i), n) double *restrict q = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (q == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } double *restrict pa = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (pa == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } double min = (double)NO_OF_ARRAY_ELEMENTS * p[0]; for (size_t index = 1; index < NO_OF_ARRAY_ELEMENTS; index++) { const double TEMP = (double)NO_OF_ARRAY_ELEMENTS * p[index] / (1+index); if (TEMP < min) { min = TEMP; } } for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { pa[index] = min; q[index] = min; } // puts("q & pa"); // double_say(q, NO_OF_ARRAY_ELEMENTS); /*for (j in (n - 1):2) {

           ij <- seq_len(n - j + 1)
           i2 <- (n - j + 2):n
           q1 <- min(j * p[i2]/(2:j))
           q[ij] <- pmin(j * p[ij], q1)
           q[i2] <- q[n - j + 1]
           pa <- pmax(pa, q)
       }

/

for (size_t j = (NO_OF_ARRAY_ELEMENTS-1); j >= 2; j--) { // printf("j = %zu\n", j); unsigned int *restrict ij = seq_len(1,NO_OF_ARRAY_ELEMENTS - j + 1); for (size_t i = 0; i < NO_OF_ARRAY_ELEMENTS - j + 1; i++) { ij[i]--;//R's indices are 1-based, C's are 0-based } const size_t I2_LENGTH = j - 1; unsigned int *restrict i2 = malloc(I2_LENGTH * sizeof(unsigned int)); for (size_t i = 0; i < I2_LENGTH; i++) { i2[i] = NO_OF_ARRAY_ELEMENTS-j+2+i-1; //R's indices are 1-based, C's are 0-based, I added the -1 }

double q1 = j * p[i2[0]] / 2.0; for (size_t i = 1; i < I2_LENGTH; i++) {//loop through 2:j const double TEMP_Q1 = (double)j * p[i2[i]] / (2 + i); if (TEMP_Q1 < q1) { q1 = TEMP_Q1; } }

for (size_t i = 0; i < (NO_OF_ARRAY_ELEMENTS - j + 1); i++) {//q[ij] <- pmin(j * p[ij], q1) q[ij[i]] = min2( j*p[ij[i]], q1); } free(ij); ij = NULL;

for (size_t i = 0; i < I2_LENGTH; i++) {//q[i2] <- q[n - j + 1] q[i2[i]] = q[NO_OF_ARRAY_ELEMENTS - j];//subtract 1 because of starting index difference } free(i2); i2 = NULL;

for (size_t i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) {//pa <- pmax(pa, q) if (pa[i] < q[i]) { pa[i] = q[i]; } } // printf("j = %zu, pa = \n", j); // double_say(pa, N); }//end j loop free(p); p = NULL; for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { q[index] = pa[ro[index]];//Hommel q-values } //now free memory free(ro); ro = NULL; free(pa); pa = NULL; return q; } //The methods are similarly computed and thus can be combined for clarity unsigned int *restrict o = order(PVALUES, NO_OF_ARRAY_ELEMENTS, true); if (o == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } double *restrict o_double = uint2double(o, NO_OF_ARRAY_ELEMENTS); for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { if ((PVALUES[index] < 0) || (PVALUES[index] > 1)) { printf("array[%u] = %lf, which is outside the interval [0,1]\n", index, PVALUES[index]); printf("died at %s line %u\n", __FILE__, __LINE__); exit(EXIT_FAILURE); } }

unsigned int *restrict ro = order(o_double, NO_OF_ARRAY_ELEMENTS, false); if (ro == NULL) { printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__); perror(""); exit(EXIT_FAILURE); } free(o_double); o_double = NULL; double *restrict cummin_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS); if (TYPE == 0) {//BH method for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { const double NI = (double)NO_OF_ARRAY_ELEMENTS / (NO_OF_ARRAY_ELEMENTS - index);// n/i simplified cummin_input[index] = NI * PVALUES[o[index]];//PVALUES[o[index]] is p[o] } } else if (TYPE == 1) {//BY method double q = 1.0; for (size_t index = 2; index < (1+NO_OF_ARRAY_ELEMENTS); index++) { q += (double) 1.0/index; } for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { const double NI = (double)NO_OF_ARRAY_ELEMENTS / (NO_OF_ARRAY_ELEMENTS - index);// n/i simplified cummin_input[index] = q * NI * PVALUES[o[index]];//PVALUES[o[index]] is p[o] } } else if (TYPE == 3) {//Hochberg method for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { // pmin(1, cummin((n - i + 1L) * p[o]))[ro] cummin_input[index] = (index + 1) * PVALUES[o[index]]; } } free(o); o = NULL; double *restrict cummin_array = NULL; cummin_array = cummin(cummin_input, NO_OF_ARRAY_ELEMENTS); free(cummin_input); cummin_input = NULL;//I don't need this anymore double *restrict pmin = pminx(cummin_array, NO_OF_ARRAY_ELEMENTS, 1); free(cummin_array); cummin_array = NULL; double *restrict q_array = malloc(NO_OF_ARRAY_ELEMENTS*sizeof(double)); for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) { q_array[index] = pmin[ro[index]]; }

free(ro); ro = NULL; free(pmin); pmin = NULL; return q_array; }

int main(void) { const double PVALUES[] = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01, 8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01, 4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01, 8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02, 3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01, 1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02, 4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04, 3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04, 1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04, 2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03};//just the pvalues const double CORRECT_ANSWERS[6][50] = {//each first index is type {6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01, 9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01, 6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01, 9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01, 4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01, 2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01, 1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03, 2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03, 4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03, 2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02},//Benjamini-Hochberg {1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01, 7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02, 1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02, 2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02, 1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02},//Benjamini & Yekutieli {1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00, 2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02, 1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02, 9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02, 1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01},//Bonferroni {9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01, 1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01},//Hochberg {1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00, 1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01},//Holm { 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01, 1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02, 1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02, 8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02, 9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01}//Hommel }; //the following loop checks each type with R's answers const char *restrict TYPES[] = {"bh", "by", "bonferroni", "hochberg", "holm", "hommel"}; for (unsigned short int type = 0; type <= 5; type++) { double *restrict q = p_adjust(PVALUES, sizeof(PVALUES) / sizeof(*PVALUES), TYPES[type]); double error = fabs(q[0] - CORRECT_ANSWERS[type][0]); // printf("%e - %e = %g\n", q[0], CORRECT_ANSWERS[type][0], error); // puts("p q"); // printf("%g\t%g\n", pvalues[0], q[0]); for (unsigned int i = 1; i < sizeof(PVALUES) / sizeof(*PVALUES); i++) { const double this_error = fabs(q[i] - CORRECT_ANSWERS[type][i]); // printf("%e - %e = %g\n", q[i], CORRECT_ANSWERS[type][i], error); error += this_error; } double_say(q, sizeof(PVALUES) / sizeof(*PVALUES)); free(q); q = NULL; printf("\ntype %u = '%s' has cumulative error of %g\n", type, TYPES[type], error); }

return 0; } </lang>

Output:

[1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]


type 0 = 'bh' has cumulative error of 8.03053e-07
[1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]


type 1 = 'by' has cumulative error of 3.64072e-07
[1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]


type 2 = 'bonferroni' has cumulative error of 6.5e-08
[1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]


type 3 = 'hochberg' has cumulative error of 2.7375e-07
[1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]


type 4 = 'holm' has cumulative error of 2.8095e-07
[1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]


type 5 = 'hommel' has cumulative error of 4.35302e-07

Version 2

Works with: C89

Translation of: Kotlin

To avoid licensing issues, this version is a translation of the Kotlin entry (Version 2) which is itself a partial translation of the Perl 6 entry. If using gcc, you need to link to the math library (-lm). <lang C>#include <stdio.h>

include <stdlib.h>
include <math.h>

define SIZE 50
define each_i(start, end) for (i = start; i < end; ++i)

typedef enum { UP, DOWN } direction;

typedef struct { int index; double value; } iv1;

typedef struct { int index; int value; } iv2;

/* test also for 'Unknown' correction type */ const char *types[8] = {

   "Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
   "Holm", "Hommel", "Šidák", "Unknown"

};

int compare_iv1(const void *a, const void *b) {

   double aa = ((iv1 *)a) -> value;
   double bb = ((iv1 *)b) -> value;
   if (aa > bb) return 1;
   if (aa < bb) return -1;
   return 0;

}

int compare_iv1_desc(const void *a, const void *b) {

   return -compare_iv1(a, b);

}

int compare_iv2(const void *a, const void *b) {

   return ((iv2 *)a) -> value - ((iv2 *)b) -> value;

}

void ratchet(double *pa, direction dir) {

   int i;
   double m = pa[0];
   if (dir == UP) {
       each_i(1, SIZE) {
           if (pa[i] > m) pa[i] = m;
           m = pa[i];
       }
   }
   else {
       each_i(1, SIZE) {
           if (pa[i] < m) pa[i] = m;
           m = pa[i];
       }
   }
   each_i(0, SIZE) if (pa[i] > 1.0) pa[i] = 1.0;

}

void schwartzian(const double *p, double *pa, direction dir) {

   int i;
   int order[SIZE];
   int order2[SIZE];
   iv1 iv1s[SIZE];
   iv2 iv2s[SIZE];
   double pa2[SIZE];
   each_i(0, SIZE) { iv1s[i].index = i; iv1s[i].value = p[i]; }    
   if (dir == UP) 
       qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1_desc);
   else 
       qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1);
   each_i(0, SIZE) order[i] = iv1s[i].index;   
   each_i(0, SIZE) pa[i] *= p[order[i]];
   ratchet(pa, dir);
   each_i(0, SIZE) { iv2s[i].index = i; iv2s[i].value = order[i]; }
   qsort(iv2s, SIZE, sizeof(iv2s[0]), compare_iv2);
   each_i(0, SIZE) order2[i] = iv2s[i].index;
   each_i(0, SIZE) pa2[i] = pa[order2[i]];
   each_i(0, SIZE) pa[i] = pa2[i];

}

void adjust(const double *p, double *pa, const char *type) {

   int i;
   if (!strcmp(type, "Benjamini-Hochberg")) {
       each_i(0, SIZE) pa[i] = (double)SIZE / (SIZE - i);
       schwartzian(p, pa, UP);
   }
   else if (!strcmp(type, "Benjamini-Yekutieli")) {
       double q = 0.0;
       each_i(1, SIZE + 1) q += 1.0 / i;
       each_i(0, SIZE) pa[i] = q * SIZE / (SIZE - i);
       schwartzian(p, pa, UP);
   }
   else if (!strcmp(type, "Bonferroni")) {
       each_i(0, SIZE) pa[i] = (p[i] * SIZE > 1.0) ? 1.0 : p[i] * SIZE;
   }
   else if (!strcmp(type, "Hochberg")) {
       each_i(0, SIZE) pa[i]  = i + 1.0;
       schwartzian(p, pa, UP);
   }
   else if (!strcmp(type, "Holm")) {
       each_i(0, SIZE) pa[i] = SIZE - i;
       schwartzian(p, pa, DOWN);
   }
   else if (!strcmp(type, "Hommel")) {
       int i, j;
       int order[SIZE];
       int order2[SIZE];
       iv1 iv1s[SIZE];
       iv2 iv2s[SIZE];
       double s[SIZE];
       double q[SIZE];
       double pa2[SIZE];
       int indices[SIZE];
       each_i(0, SIZE) { iv1s[i].index = i; iv1s[i].value = p[i]; }
       qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1);
       each_i(0, SIZE) order[i] = iv1s[i].index;
       each_i(0, SIZE) s[i] = p[order[i]];
       double min = s[0] * SIZE;
       each_i(1, SIZE) {
           double temp = s[i] / (i + 1.0);
           if (temp < min) min = temp;
       }
       each_i(0, SIZE) q[i] = min;
       each_i(0, SIZE) pa2[i] = min;
       for (j = SIZE - 1; j >= 2; --j) {
           each_i(0, SIZE) indices[i] = i;
           int upper_start = SIZE - j + 1;      /* upper indices start index */
           int upper_size = j - 1;              /* size of upper indices */ 
           int lower_size = SIZE - upper_size;  /* size of lower indices */
           double qmin = j * s[indices[upper_start]] / 2.0;
           each_i(1, upper_size) {
               double temp = s[indices[upper_start + i]] * j / (2.0 + i);
               if (temp < qmin) qmin = temp;
           }
           each_i(0, lower_size) {
               double temp = s[indices[i]] * j;
               q[indices[i]] = (temp < qmin) ? temp : qmin;
           }
           each_i(0, upper_size) q[indices[upper_start + i]] = q[SIZE - j];
           each_i(0, SIZE) if (pa2[i] < q[i]) pa2[i] = q[i];
       }
       each_i(0, SIZE) { iv2s[i].index = i; iv2s[i].value = order[i]; }
       qsort(iv2s, SIZE, sizeof(iv2s[0]), compare_iv2);
       each_i(0, SIZE) order2[i] = iv2s[i].index;
       each_i(0, SIZE) pa[i] = pa2[order2[i]];
   }
   else if (!strcmp(type, "Šidák")) {
       each_i(0, SIZE) pa[i] = 1.0 - pow(1.0 - p[i], SIZE);
   }
   else {
       printf("\nSorry, do not know how to do '%s' correction.\n", type);
       printf("Perhaps you want one of these?:\n");
       each_i(0, 7) printf("  %s\n", types[i]);
       exit(1);
   }

}

void adjusted(const double *p, const char *type) {

   int i;
   double pa[SIZE] = { 0.0 };
   if (check(p)) {
       adjust(p, pa, type);
       printf("\n%s", type);
       each_i(0, SIZE) {
           if (!(i % 5)) printf("\n[%2d]  ", i);
           printf("%1.10f ", pa[i]);
       }
       printf("\n");
   }
   else {
       printf("p-values must be in range 0.0 to 1.0\n");
       exit(1);
   }

}

int check(const double* p) {

   int i;
   each_i(0, SIZE) {
       if (p[i] < 0.0 || p[i] > 1.0) return 0;
   }
   return 1;

}

int main() {

   int i;
   double p_values[SIZE] = {
       4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
       8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
       4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
       8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
       3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
       1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
       4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
       3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
       1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
       2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
   };
   each_i(0, 8) adjusted(p_values, types[i]);
   return 0;

}</lang>

Output:

Same as Kotlin (Version 2) output.

C++

Translation of: Java

<lang cpp>#include <algorithm>

include <functional>
include <iostream>
include <numeric>
include <vector>

std::vector<int> seqLen(int start, int end) {

   std::vector<int> result;

   if (start == end) {
       result.resize(end + 1);
       std::iota(result.begin(), result.end(), 1);
   } else if (start < end) {
       result.resize(end - start + 1);
       std::iota(result.begin(), result.end(), start);
   } else {
       result.resize(start - end + 1);
       std::iota(result.rbegin(), result.rend(), end);
   }

   return result;

}

std::vector<int> order(const std::vector<double>& arr, bool decreasing) {

   std::vector<int> idx(arr.size());
   std::iota(idx.begin(), idx.end(), 0);

   std::function<bool(int, int)> cmp;
   if (decreasing) {
       cmp = [&arr](int a, int b) { return arr[b] < arr[a]; };
   } else {
       cmp = [&arr](int a, int b) { return arr[a] < arr[b]; };
   }

   std::sort(idx.begin(), idx.end(), cmp);
   return idx;

}

std::vector<double> cummin(const std::vector<double>& arr) {

   if (arr.empty()) throw std::runtime_error("cummin requries at least one element");
   std::vector<double> output(arr.size());
   double cumulativeMin = arr[0];
   std::transform(arr.cbegin(), arr.cend(), output.begin(), [&cumulativeMin](double a) {
       if (a < cumulativeMin) cumulativeMin = a;
       return cumulativeMin;
   });
   return output;

}

std::vector<double> cummax(const std::vector<double>& arr) {

   if (arr.empty()) throw std::runtime_error("cummax requries at least one element");
   std::vector<double> output(arr.size());
   double cumulativeMax = arr[0];
   std::transform(arr.cbegin(), arr.cend(), output.begin(), [&cumulativeMax](double a) {
       if (cumulativeMax < a) cumulativeMax = a;
       return cumulativeMax;
   });
   return output;

}

std::vector<double> pminx(const std::vector<double>& arr, double x) {

   if (arr.empty()) throw std::runtime_error("pmin requries at least one element");
   std::vector<double> result(arr.size());
   std::transform(arr.cbegin(), arr.cend(), result.begin(), [&x](double a) {
       if (a < x) return a;
       return x;
   });
   return result;

}

void doubleSay(const std::vector<double>& arr) {

   printf("[ 1] %.10f", arr[0]);
   for (size_t i = 1; i < arr.size(); ++i) {
       printf(" %.10f", arr[i]);
       if ((i + 1) % 5 == 0) printf("\n[%2d]", i + 1);
   }

}

std::vector<double> pAdjust(const std::vector<double>& pvalues, const std::string& str) {

   if (pvalues.empty()) throw std::runtime_error("pAdjust requires at least one element");
   size_t size = pvalues.size();

   int type;
   if ("bh" == str || "fdr" == str) {
       type = 0;
   } else if ("by" == str) {
       type = 1;
   } else if ("bonferroni" == str) {
       type = 2;
   } else if ("hochberg" == str) {
       type = 3;
   } else if ("holm" == str) {
       type = 4;
   } else if ("hommel" == str) {
       type = 5;
   } else {
       throw std::runtime_error(str + " doesn't match any accepted FDR types");
   }

   // Bonferroni method
   if (2 == type) {
       std::vector<double> result(size);
       for (size_t i = 0; i < size; ++i) {
           double b = pvalues[i] * size;
           if (b >= 1) {
               result[i] = 1;
           } else if (0 <= b && b < 1) {
               result[i] = b;
           } else {
               throw std::runtime_error("a value is outside [0, 1)");
           }
       }
       return result;
   }
   // Holm method
   else if (4 == type) {
       auto o = order(pvalues, false);
       std::vector<double> o2Double(o.begin(), o.end());
       std::vector<double> cummaxInput(size);
       for (size_t i = 0; i < size; ++i) {
           cummaxInput[i] = (size - i) * pvalues[o[i]];
       }
       auto ro = order(o2Double, false);
       auto cummaxOutput = cummax(cummaxInput);
       auto pmin = pminx(cummaxOutput, 1.0);
       std::vector<double> result(size);
       std::transform(ro.cbegin(), ro.cend(), result.begin(), [&pmin](int a) { return pmin[a]; });
       return result;
   }
   // Hommel
   else if (5 == type) {
       auto indices = seqLen(size, size);
       auto o = order(pvalues, false);
       std::vector<double> p(size);
       std::transform(o.cbegin(), o.cend(), p.begin(), [&pvalues](int a) { return pvalues[a]; });
       std::vector<double> o2Double(o.begin(), o.end());
       auto ro = order(o2Double, false);
       std::vector<double> q(size);
       std::vector<double> pa(size);
       std::vector<double> npi(size);
       for (size_t i = 0; i < size; ++i) {
           npi[i] = p[i] * size / indices[i];
       }
       double min = *std::min_element(npi.begin(), npi.end());
       std::fill(q.begin(), q.end(), min);
       std::fill(pa.begin(), pa.end(), min);
       for (int j = size; j >= 2; --j) {
           auto ij = seqLen(1, size - j + 1);
           std::transform(ij.cbegin(), ij.cend(), ij.begin(), [](int a) { return a - 1; });
           int i2Length = j - 1;
           std::vector<int> i2(i2Length);
           for (int i = 0; i < i2Length; ++i) {
               i2[i] = size - j + 2 + i - 1;
           }
           double q1 = j * p[i2[0]] / 2.0;
           for (int i = 1; i < i2Length; ++i) {
               double temp_q1 = p[i2[i]] * j / (2.0 + i);
               if (temp_q1 < q1) q1 = temp_q1;
           }
           for (size_t i = 0; i < size - j + 1; ++i) {
               q[ij[i]] = std::min(p[ij[i]] * j, q1);
           }
           for (int i = 0; i < i2Length; ++i) {
               q[i2[i]] = q[size - j];
           }
           for (size_t i = 0; i < size; ++i) {
               if (pa[i] < q[i]) {
                   pa[i] = q[i];
               }
           }
       }
       std::transform(ro.cbegin(), ro.cend(), q.begin(), [&pa](int a) { return pa[a]; });
       return q;
   }

   std::vector<double> ni(size);
   std::vector<int> o = order(pvalues, true);
   std::vector<double> od(o.begin(), o.end());
   for (size_t i = 0; i < size; ++i) {
       if (pvalues[i] < 0 || pvalues[i]>1) {
           throw std::runtime_error("a value is outside [0, 1]");
       }
       ni[i] = (double)size / (size - i);
   }
   auto ro = order(od, false);
   std::vector<double> cumminInput(size);
   if (0 == type) {        // BH method
       for (size_t i = 0; i < size; ++i) {
           cumminInput[i] = ni[i] * pvalues[o[i]];
       }
   } else if (1 == type) { // BY method
       double q = 0;
       for (size_t i = 1; i < size + 1; ++i) {
           q += 1.0 / i;
       }
       for (size_t i = 0; i < size; ++i) {
           cumminInput[i] = q * ni[i] * pvalues[o[i]];
       }
   } else if (3 == type) { // Hochberg method
       for (size_t i = 0; i < size; ++i) {
           cumminInput[i] = (i + 1) * pvalues[o[i]];
       }
   }
   auto cumminArray = cummin(cumminInput);
   auto pmin = pminx(cumminArray, 1.0);
   std::vector<double> result(size);
   for (size_t i = 0; i < size; ++i) {
       result[i] = pmin[ro[i]];
   }
   return result;

}

int main() {

   using namespace std;

   vector<double> pvalues{
       4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
       8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
       4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
       8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
       3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
       1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
       4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
       3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
       1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
       2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
   };

   vector<vector<double>> correctAnswers{
       // Benjamini-Hochberg
       {
           6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
           9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
           6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
           9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
           4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
           2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
           1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
           2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
           4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
           2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
       },
       // Benjamini & Yekutieli
       {
           1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
           7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
           1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
           2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
           1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
       },
       // Bonferroni
       {
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
           2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
           1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
           9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
           1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
       },
       // Hochberg
       {
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
           1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
           1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
           8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
           1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
       },
       // Holm
       {
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
           1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
           1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
           8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
           1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
       },
       // Hommel
       {
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
           1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
           1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
           8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
           9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
       }
   };

   vector<string> types{ "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
   for (size_t type = 0; type < types.size(); ++type) {
       auto q = pAdjust(pvalues, types[type]);
       double error = 0.0;
       for (size_t i = 0; i < pvalues.size(); ++i) {
           error += abs(q[i] - correctAnswers[type][i]);
       }
       doubleSay(q);
       printf("\ntype = %d = '%s' has a cumulative error of %g\n\n\n", type, types[type].c_str(), error);
   }

   return 0;

}</lang>

Output:

[ 1] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type = 0 = 'bh' has a cumulative error of 8.03053e-07


[ 1] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]
type = 1 = 'by' has a cumulative error of 3.64072e-07


[ 1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type = 2 = 'bonferroni' has a cumulative error of 6.5e-08


[ 1] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type = 3 = 'hochberg' has a cumulative error of 2.7375e-07


[ 1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type = 4 = 'holm' has a cumulative error of 2.8095e-07


[ 1] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type = 5 = 'hommel' has a cumulative error of 4.35302e-07

C#

Translation of: Java

<lang csharp>using System; using System.Collections.Generic; using System.Linq;

namespace PValueCorrection {

   class Program {
       static List<int> SeqLen(int start, int end) {
           var result = new List<int>();
           if (start == end) {
               for (int i = 0; i < end + 1; ++i) {
                   result.Add(i + 1);
               }
           } else if (start < end) {
               for (int i = 0; i < end - start + 1; ++i) {
                   result.Add(start + i);
               }
           } else {
               for (int i = 0; i < start - end + 1; ++i) {
                   result.Add(start - i);
               }
           }
           return result;
       }

       static List<int> Order(List<double> array, bool decreasing) {
           List<int> idx = new List<int>();
           for (int i = 0; i < array.Count; ++i) {
               idx.Add(i);
           }

           IComparer<int> cmp;
           if (decreasing) {
               cmp = Comparer<int>.Create((a, b) => array[a] < array[b] ? 1 : array[b] < array[a] ? -1 : 0);
           } else {
               cmp = Comparer<int>.Create((a, b) => array[b] < array[a] ? 1 : array[a] < array[b] ? -1 : 0);
           }

           idx.Sort(cmp);
           return idx;
       }

       static List<double> Cummin(List<double> array) {
           if (array.Count < 1) throw new ArgumentOutOfRangeException("cummin requires at least one element");
           var output = new List<double>();
           double cumulativeMin = array[0];
           for (int i = 0; i < array.Count; ++i) {
               if (array[i] < cumulativeMin) cumulativeMin = array[i];
               output.Add(cumulativeMin);
           }
           return output;
       }

       static List<double> Cummax(List<double> array) {
           if (array.Count < 1) throw new ArgumentOutOfRangeException("cummax requires at least one element");
           var output = new List<double>();
           double cumulativeMax = array[0];
           for (int i = 0; i < array.Count; ++i) {
               if (array[i] > cumulativeMax) cumulativeMax = array[i];
               output.Add(cumulativeMax);
           }
           return output;
       }

       static List<double> Pminx(List<double> array, double x) {
           if (array.Count < 1) throw new ArgumentOutOfRangeException("pmin requires at least one element");
           var result = new List<double>();
           for (int i = 0; i < array.Count; ++i) {
               if (array[i] < x) {
                   result.Add(array[i]);
               } else {
                   result.Add(x);
               }
           }
           return result;
       }

       static void Say(List<double> array) {
           Console.Write("[ 1] {0:E}", array[0]);
           for (int i = 1; i < array.Count; ++i) {
               Console.Write(" {0:E}", array[i]);
               if ((i + 1) % 5 == 0) Console.Write("\n[{0,2}]", i + 1);
           }
           Console.WriteLine();
       }

       static List<double> PAdjust(List<double> pvalues, string str) {
           var size = pvalues.Count;
           if (size < 1) throw new ArgumentOutOfRangeException("pAdjust requires at least one element");

           int type;
           switch (str.ToLower()) {
               case "bh":
               case "fdr":
                   type = 0;
                   break;
               case "by":
                   type = 1;
                   break;
               case "bonferroni":
                   type = 2;
                   break;
               case "hochberg":
                   type = 3;
                   break;
               case "holm":
                   type = 4;
                   break;
               case "hommel":
                   type = 5;
                   break;
               default:
                   throw new ArgumentException(str + " doesn't match any accepted FDR types");
           }

           if (2 == type) { // Bonferroni method
               var result2 = new List<double>();
               for (int i = 0; i < size; ++i) {
                   double b = pvalues[i] * size;
                   if (b >= 1) {
                       result2.Add(1);
                   } else if (0 <= b && b < 1) {
                       result2.Add(b);
                   } else {
                       throw new Exception(b + " is outside [0, 1)");
                   }
               }
               return result2;
           } else if (4 == type) { // Holm method
               var o4 = Order(pvalues, false);
               var o4d = o4.ConvertAll(x => (double)x);
               var cummaxInput = new List<double>();
               for (int i = 0; i < size; ++i) {
                   cummaxInput.Add((size - i) * pvalues[o4[i]]);
               }
               var ro4 = Order(o4d, false);
               var cummaxOutput = Cummax(cummaxInput);
               var pmin4 = Pminx(cummaxOutput, 1.0);
               var hr = new List<double>();
               for (int i = 0; i < size; ++i) {
                   hr.Add(pmin4[ro4[i]]);
               }
               return hr;
           } else if (5 == type) { // Hommel method
               var indices = SeqLen(size, size);
               var o5 = Order(pvalues, false);
               var p = new List<double>();
               for (int i = 0; i < size; ++i) {
                   p.Add(pvalues[o5[i]]);
               }
               var o5d = o5.ConvertAll(x => (double)x);
               var ro5 = Order(o5d, false);
               var q = new List<double>();
               var pa = new List<double>();
               var npi = new List<double>();
               for (int i = 0; i < size; ++i) {
                   npi.Add(p[i] * size / indices[i]);
               }
               double min = npi.Min();
               q.AddRange(Enumerable.Repeat(min, size));
               pa.AddRange(Enumerable.Repeat(min, size));
               for (int j = size; j >= 2; --j) {
                   var ij = SeqLen(1, size - j + 1);
                   for (int i = 0; i < size - j + 1; ++i) {
                       ij[i]--;
                   }
                   int i2Length = j - 1;
                   var i2 = new List<int>();
                   for (int i = 0; i < i2Length; ++i) {
                       i2.Add(size - j + 2 + i - 1);
                   }
                   double q1 = j * p[i2[0]] / 2.0;
                   for (int i = 1; i < i2Length; ++i) {
                       double temp_q1 = p[i2[i]] * j / (2.0 + i);
                       if (temp_q1 < q1) q1 = temp_q1;
                   }
                   for (int i = 0; i < size - j + 1; ++i) {
                       q[ij[i]] = Math.Min(p[ij[i]] * j, q1);
                   }
                   for (int i = 0; i < i2Length; ++i) {
                       q[i2[i]] = q[size - j];
                   }
                   for (int i = 0; i < size; ++i) {
                       if (pa[i] < q[i]) {
                           pa[i] = q[i];
                       }
                   }
               }
               for (int i = 0; i < size; ++i) {
                   q[i] = pa[ro5[i]];
               }
               return q;
           }

           var ni = new List<double>();
           var o = Order(pvalues, true);
           var od = o.ConvertAll(x => (double)x);
           for (int i = 0; i < size; ++i) {
               if (pvalues[i] < 0 || pvalues[i] > 1) {
                   throw new Exception("array[" + i + "] = " + pvalues[i] + " is outside [0, 1]");
               }
               ni.Add((double)size / (size - i));
           }
           var ro = Order(od, false);
           var cumminInput = new List<double>();
           if (0 == type) {       // BH method
               for (int i = 0; i < size; ++i) {
                   cumminInput.Add(ni[i] * pvalues[o[i]]);
               }
           } else if (1 == type) { // BY method
               double q = 0;
               for (int i = 1; i < size + 1; ++i) {
                   q += 1.0 / i;
               }
               for (int i = 0; i < size; ++i) {
                   cumminInput.Add(q * ni[i] * pvalues[o[i]]);
               }
           } else if (3 == type) { // Hochberg method
               for (int i = 0; i < size; ++i) {
                   cumminInput.Add((i + 1) * pvalues[o[i]]);
               }
           }
           var cumminArray = Cummin(cumminInput);
           var pmin = Pminx(cumminArray, 1.0);
           var result = new List<double>();
           for (int i = 0; i < size; ++i) {
               result.Add(pmin[ro[i]]);
           }
           return result;
       }

       static void Main(string[] args) {
           var pvalues = new List<double> {
               4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
               8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
               4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
               8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
               3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
               1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
               4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
               3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
               1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
               2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
           };
           var correctAnswers = new List<List<double>> {
               new List<double> { // Benjamini-Hochberg
                   6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
                   9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
                   6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
                   9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
                   4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
                   2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
                   1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
                   2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
                   4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
                   2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
               },
               new List<double> { // Benjamini & Yekutieli
                   1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
                   7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
                   1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
                   2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
                   1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
               },
               new List<double> { // Bonferroni
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
                   2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
                   1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
                   9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
                   1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
               },
               new List<double> { // Hochberg
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
                   1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
                   1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
                   8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
                   1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
               },
               new List<double> { // Holm
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
                   1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
                   1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
                   1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
                   8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
                   1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
               },
               new List<double> { // Hommel
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
                   9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
                   9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
                   1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
                   1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
                   8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
                   9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
               }
           };

           string[] types = { "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
           for (int type = 0; type < types.Length; ++type) {
               var q = PAdjust(pvalues, types[type]);
               double error = 0.0;
               for (int i = 0; i < pvalues.Count; ++i) {
                   error += Math.Abs(q[i] - correctAnswers[type][i]);
               }
               Say(q);
               Console.WriteLine("type {0} = '{1}' has a cumulative error of {2:E}", type, types[type], error);
               Console.WriteLine();
           }
       }
   }

}</lang>

Output:

[ 1] 6.126681E-001 8.521710E-001 1.987205E-001 1.891595E-001 3.217789E-001
[ 5] 9.301450E-001 4.870370E-001 9.301450E-001 6.049731E-001 6.826753E-001
[10] 6.482629E-001 7.253723E-001 5.280973E-001 8.769926E-001 4.705703E-001
[15] 9.241867E-001 6.049731E-001 7.856107E-001 4.887526E-001 1.136717E-001
[20] 4.991891E-001 8.769926E-001 9.991834E-001 3.217789E-001 9.301450E-001
[25] 2.304958E-001 5.832475E-001 3.899547E-002 8.521710E-001 1.476843E-001
[30] 1.683638E-002 2.562902E-003 3.516084E-002 6.250189E-002 3.636589E-003
[35] 2.562902E-003 2.946883E-002 6.166064E-003 3.899547E-002 2.688991E-003
[40] 4.502863E-004 1.252228E-005 7.881555E-002 3.142613E-002 4.846527E-003
[45] 2.562902E-003 4.846527E-003 1.101708E-003 7.252033E-002 2.205958E-002
[50]
type 0 = 'bh' has a cumulative error of 8.030529E-007

[ 1] 1.000000E+000 1.000000E+000 8.940844E-001 8.510676E-001 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 5.114323E-001
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 1.754486E-001 1.000000E+000 6.644618E-001
[30] 7.575031E-002 1.153102E-002 1.581959E-001 2.812089E-001 1.636176E-002
[35] 1.153102E-002 1.325863E-001 2.774239E-002 1.754486E-001 1.209832E-002
[40] 2.025930E-003 5.634031E-005 3.546073E-001 1.413926E-001 2.180552E-002
[45] 1.153102E-002 2.180552E-002 4.956812E-003 3.262838E-001 9.925057E-002
[50]
type 1 = 'by' has a cumulative error of 3.640716E-007

[ 1] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 7.019185E-001 1.000000E+000 1.000000E+000
[30] 2.020365E-001 1.516675E-002 5.625735E-001 1.000000E+000 2.909271E-002
[35] 1.537741E-002 4.125636E-001 6.782670E-002 6.803480E-001 1.882294E-002
[40] 9.005725E-004 1.252228E-005 1.000000E+000 4.713920E-001 4.395577E-002
[45] 1.088916E-002 4.846527E-002 3.305125E-003 1.000000E+000 2.867745E-001
[50]
type 2 = 'bonferroni' has a cumulative error of 6.500000E-008

[ 1] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[ 5] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[10] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[15] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[20] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[25] 9.991834E-001 9.991834E-001 4.632662E-001 9.991834E-001 9.991834E-001
[30] 1.575885E-001 1.383967E-002 3.938015E-001 7.600230E-001 2.501973E-002
[35] 1.383967E-002 3.052971E-001 5.426136E-002 4.626366E-001 1.656419E-002
[40] 8.825611E-004 1.252228E-005 9.930759E-001 3.394022E-001 3.692284E-002
[45] 1.023581E-002 3.974152E-002 3.172920E-003 8.992520E-001 2.179486E-001
[50]
type 3 = 'hochberg' has a cumulative error of 2.737500E-007

[ 1] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 4.632662E-001 1.000000E+000 1.000000E+000
[30] 1.575885E-001 1.395341E-002 3.938015E-001 7.600230E-001 2.501973E-002
[35] 1.395341E-002 3.052971E-001 5.426136E-002 4.626366E-001 1.656419E-002
[40] 8.825611E-004 1.252228E-005 9.930759E-001 3.394022E-001 3.692284E-002
[45] 1.023581E-002 3.974152E-002 3.172920E-003 8.992520E-001 2.179486E-001
[50]
type 4 = 'holm' has a cumulative error of 2.809500E-007

[ 1] 9.991834E-001 9.991834E-001 9.991834E-001 9.987624E-001 9.991834E-001
[ 5] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[10] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[15] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.595180E-001
[20] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[25] 9.991834E-001 9.991834E-001 4.351895E-001 9.991834E-001 9.766523E-001
[30] 1.414256E-001 1.304340E-002 3.530937E-001 6.887709E-001 2.385602E-002
[35] 1.322457E-002 2.722920E-001 5.426136E-002 4.218158E-001 1.581127E-002
[40] 8.825611E-004 1.252228E-005 8.743649E-001 3.016908E-001 3.516461E-002
[45] 9.582456E-003 3.877222E-002 3.172920E-003 8.122276E-001 1.950067E-001
[50]
type 5 = 'hommel' has a cumulative error of 4.353024E-007

D

Translation of: Kotlin

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses. <lang D>import std.algorithm; import std.conv; import std.math; import std.stdio; import std.string;

int[] seqLen(int start, int end) {

   int[] result;
   if (start == end) {
       result.length = end+1;
       for (int i; i<result.length; i++) {
           result[i] = i+1;
       }
   } else if (start < end) {
       result.length = end - start + 1;
       for (int i; i<result.length; i++) {
           result[i] = start+i;
       }
   } else {
       result.length = start - end + 1;
       for (int i; i<result.length; i++) {
           result[i] = start-i;
       }
   }
   return result;

}

int[] order(double[] array, bool decreasing) {

   int size = array.length;
   int[] idx;
   idx.length = size;
   double[] baseArr;
   baseArr.length = size;
   for (int i; i<size; i++) {
       baseArr[i] = array[i];
       idx[i] = i;
   }
   if (!decreasing) {
       alias comp = (a,b) => baseArr[a] < baseArr[b];
       idx.sort!comp;
   } else {
       alias comp = (a,b) => baseArr[b] < baseArr[a];
       idx.sort!comp;
   }
   return idx;

}

double[] cummin(double[] array) {

   int size = array.length;
   if (size < 1) throw new Exception("cummin requires at least one element");
   double[] output;
   output.length = size;
   auto cumulativeMin = array[0];
   foreach (i; 0..size) {
       if (array[i] < cumulativeMin) cumulativeMin = array[i];
       output[i] = cumulativeMin;
   }
   return output;

}

double[] cummax(double[] array) {

   auto size = array.length;
   if (size < 1) throw new Exception("cummax requires at least one element");
   double[] output;
   output.length = size;
   auto cumulativeMax = array[0];
   foreach (i; 0..size) {
       if (array[i] > cumulativeMax) cumulativeMax = array[i];
       output[i] = cumulativeMax;
   }
   return output;

}

double[] pminx(double[] array, double x) {

   auto size = array.length;
   if (size < 1) throw new Exception("pmin requires at least one element");
   double[] result;
   result.length = size;
   foreach (i; 0..size) {
       if (array[i] < x) {
           result[i] = array[i];
       } else {
           result[i] = x;
       }
   }
   return result;

}

void doubleSay(double[] array) {

   writef("[ 1] %e", array[0]);
   foreach (i; 1..array.length) {
       writef(" %.10f", array[i]);
       if ((i+1) % 5 == 0) writef("\n[%2d]", i+1);
   }
   writeln;

}

auto toArray(T,U)(U[] array) {

   T[] result;
   result.length = array.length;
   foreach(i; 0..array.length) {
       result[i] = to!T(array[i]);
   }
   return result;

}

double[] pAdjust(double[] pvalues, string str) {

   auto size = pvalues.length;
   if (size < 1) throw new Exception("pAdjust requires at least one element");
   int type = str.toLower.predSwitch!"a==b"(
       "bh",         0,
       "fdr",        0,
       "by",         1,
       "bonferroni", 2,
       "hochberg",   3,
       "holm",       4,
       "hommel",     5,
       { throw new Exception(text("'",str,"' doesn't match any accepted FDR types")); }()
   );
   if (type == 2) {  // Bonferroni method
       double[] result;
       result.length = size;
       foreach (i; 0..size) {
           auto b = pvalues[i] * size;
           if (b >= 1) {
               result[i] = 1;
           } else if (0 <= b && b < 1) {
               result[i] = b;
           } else {
               throw new Exception(text(b," is outside [0, 1)"));
           }
       }
       return result;
   } else if (type == 4) {  // Holm method
       auto o = order(pvalues, false);
       auto o2Double = toArray!(double,int)(o);
       double[] cummaxInput;
       cummaxInput.length = size;
       foreach (i; 0..size) {
           cummaxInput[i] = (size-i) * pvalues[o[i]];
       }
       auto ro = order(o2Double, false);
       auto cummaxOutput = cummax(cummaxInput);
       auto pmin = pminx(cummaxOutput, 1.0);
       double[] result;
       result.length = size;
       foreach (i; 0..size) {
           result[i] = pmin[ro[i]];
       }
       return result;
   } else if (type == 5) {
       auto indices = seqLen(size, size);
       auto o = order(pvalues, false);
       double[] p;
       p.length = size;
       foreach (i; 0..size) {
           p[i] = pvalues[o[i]];
       }
       auto o2Double = toArray!double(o);
       auto ro = order(o2Double, false);
       double[] q;
       q.length = size;
       double[] pa;
       pa.length = size;
       double[] npi;
       npi.length = size;
       foreach (i; 0..size) {
           npi[i] = p[i] * size / indices[i];
       }
       auto min_ = reduce!min(npi);
       q[] = min_;
       pa[] = min_;
       foreach_reverse (j; 2..size) {
           auto ij = seqLen(1, size - j + 1);
           foreach (i; 0..size-j+1) {
               ij[i]--;
           }
           auto i2Length = j-1;
           int[] i2;
           i2.length = i2Length;
           foreach(i; 0..i2Length) {
               i2[i] = size-j+2+i-1;
           }
           auto pi2Length = i2Length;
           double q1 = j*p[i2[0]] / 2.0;
           foreach (i; 1..pi2Length) {
               auto temp_q1 = p[i2[i]] * j / (2.0 + i);
               if (temp_q1 < q1) q1 = temp_q1;
           }
           foreach (i; 0..size-j+1) {
               q[ij[i]] = min(p[ij[i]] * j, q1);
           }
           foreach(i; 0..i2Length) {
               q[i2[i]] = q[size-j];
           }
           foreach(i; 0..size) if (pa[i] < q[i]) pa[i] = q[i];
       }
       foreach (index; 0..size) {
           q[index] = pa[ro[index]];
       }
       return q;
   }

   double[] ni;
   ni.length = size;
   auto o = order(pvalues, true);
   auto oDouble = toArray!double(o);
   foreach (index; 0..size) {
       if (pvalues[index] < 0 || pvalues[index] > 1) {
           throw new Exception(text("array[", index, "] = ", pvalues[index], " is outside [0, 1]"));
       }
       ni[index] = cast(double) size / (size - index);
   }
   auto ro = order(oDouble, false);
   double[] cumminInput;
   cumminInput.length = size;
   if (type == 0) {  // BH method
       foreach (index; 0..size) {
           cumminInput[index] = ni[index] * pvalues[o[index]];
       }
   } else if (type == 1) {  // BY method
       double q = 0;
       foreach (index; 1..size+1) q += 1.0 / index;
       foreach (index; 0..size) {
           cumminInput[index] = q * ni[index] * pvalues[o[index]];
       }
   } else if (type == 3) {  // Hochberg method
       foreach (index; 0..size) {
           cumminInput[index] = (index + 1) * pvalues[o[index]];
       }
   }
   auto cumminArray  =cummin(cumminInput);
   auto pmin = pminx(cumminArray, 1.0);
   double[] result;
   result.length = size;
   foreach (i; 0..size) {
       result[i] = pmin[ro[i]];
   }
   return result;

}

void main() {

   double[] pvalues = [
       4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
       8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
       4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
       8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
       3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
       1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
       4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
       3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
       1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
       2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
   ];

   double[][] correctAnswers = [
       [  // Benjamini-Hochberg
           6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
           9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
           6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
           9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
           4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
           2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
           1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
           2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
           4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
           2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
       ],
       [  // Benjamini & Yekutieli
           1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
           7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
           1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
           2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
           1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
       ],
       [  // Bonferroni
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
           2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
           1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
           9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
           1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
       ],
       [  // Hochberg
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
           1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
           1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
           8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
           1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
       ],
       [  // Holm
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
           1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
           1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
           8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
           1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
       ],
       [   // Hommel
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
           1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
           1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
           8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
           9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
       ]
   ];
   auto types = ["bh", "by", "bonferroni", "hochberg", "holm", "hommel"];
   foreach (type; 0..types.length) {
       auto q = pAdjust(pvalues, types[type]);
       double error = 0.0;
       foreach (i; 0..pvalues.length) {
           error += abs(q[i] - correctAnswers[type][i]);
       }
       doubleSay(q);
       writefln("\ntype %d = '%s' has a cumulative error of %g", type, types[type], error);
   }

}</lang>

Output:

[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629016 0.0351608437 0.0625018947 0.0036365887
[35] 0.0025629016 0.0294688285 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125222 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629016 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]

type 0 = 'bh' has a cumulative error of 8.03053e-07
[ 1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503082 0.0115310208 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310208 0.1325863108 0.0277423864 0.1754486368 0.0120983245
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055201
[45] 0.0115310208 0.0218055201 0.0049568120 0.3262838334 0.0992505662
[50]

type 1 = 'by' has a cumulative error of 3.64072e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125222 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]

type 2 = 'bonferroni' has a cumulative error of 6.5e-08
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125222 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]

type 3 = 'hochberg' has a cumulative error of 2.7375e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125222 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]

type 4 = 'holm' has a cumulative error of 2.8095e-07
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125222 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]

type 5 = 'hommel' has a cumulative error of 4.35302e-07

Go

Translation of: Kotlin (Version 2)

<lang go>package main

import (

   "fmt"
   "log"
   "math"
   "os"
   "sort"
   "strconv"
   "strings"

)

type pvalues = []float64

type iv1 struct {

   index int
   value float64

} type iv2 struct{ index, value int }

type direction int

const (

   up direction = iota
   down

)

// Test also for 'Unknown' correction type. var ctypes = []string{

   "Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
   "Holm", "Hommel", "Šidák", "Unknown",

}

func minimum(p pvalues) float64 {

   m := p[0]
   for i := 1; i < len(p); i++ {
       if p[i] < m {
           m = p[i]
       }
   }
   return m

}

func maximum(p pvalues) float64 {

   m := p[0]
   for i := 1; i < len(p); i++ {
       if p[i] > m {
           m = p[i]
       }
   }
   return m

}

func adjusted(p pvalues, ctype string) (string, error) {

   err := check(p)
   if err != nil {
       return "", err
   }
   temp := pformat(adjust(p, ctype), 5)
   return fmt.Sprintf("\n%s\n%s", ctype, temp), nil

}

func pformat(p pvalues, cols int) string {

   var lines []string
   for i := 0; i < len(p); i += cols {
       fchunk := p[i : i+cols]
       schunk := make([]string, cols)
       for j := 0; j < cols; j++ {
           schunk[j] = strconv.FormatFloat(fchunk[j], 'f', 10, 64)
       }
       lines = append(lines, fmt.Sprintf("[%2d]  %s", i, strings.Join(schunk, " ")))
   }
   return strings.Join(lines, "\n")

}

func check(p []float64) error {

   cond := len(p) > 0 && minimum(p) >= 0 && maximum(p) <= 1
   if !cond {
       return fmt.Errorf("p-values must be in range 0.0 to 1.0")
   }
   return nil

}

func ratchet(p pvalues, dir direction) {

   size := len(p)
   m := p[0]
   if dir == up {
       for i := 1; i < size; i++ {
           if p[i] > m {
               p[i] = m
           }
           m = p[i]
       }
   } else {
       for i := 1; i < size; i++ {
           if p[i] < m {
               p[i] = m
           }
           m = p[i]
       }
   }
   for i := 0; i < size; i++ {
       if p[i] > 1.0 {
           p[i] = 1.0
       }
   }

}

func schwartzian(p pvalues, mult pvalues, dir direction) pvalues {

   size := len(p)
   order := make([]int, size)
   iv1s := make([]iv1, size)
   for i := 0; i < size; i++ {
       iv1s[i] = iv1{i, p[i]}
   }
   if dir == up {
       sort.Slice(iv1s, func(i, j int) bool {
           return iv1s[i].value > iv1s[j].value
       })
   } else {
       sort.Slice(iv1s, func(i, j int) bool {
           return iv1s[i].value < iv1s[j].value
       })
   }
   for i := 0; i < size; i++ {
       order[i] = iv1s[i].index
   }
   pa := make(pvalues, size)
   for i := 0; i < size; i++ {
       pa[i] = mult[i] * p[order[i]]
   }
   ratchet(pa, dir)
   order2 := make([]int, size)
   iv2s := make([]iv2, size)
   for i := 0; i < size; i++ {
       iv2s[i] = iv2{i, order[i]}
   }
   sort.Slice(iv2s, func(i, j int) bool {
       return iv2s[i].value < iv2s[j].value
   })
   for i := 0; i < size; i++ {
       order2[i] = iv2s[i].index
   }
   pa2 := make(pvalues, size)
   for i := 0; i < size; i++ {
       pa2[i] = pa[order2[i]]
   }
   return pa2

}

func adjust(p pvalues, ctype string) pvalues {

   size := len(p)
   if size == 0 {
       return p
   }
   fsize := float64(size)
   switch ctype {
   case "Benjamini-Hochberg":
       mult := make(pvalues, size)
       for i := 0; i < size; i++ {
           mult[i] = fsize / float64(size-i)
       }
       return schwartzian(p, mult, up)
   case "Benjamini-Yekutieli":
       q := 0.0
       for i := 1; i <= size; i++ {
           q += 1.0 / float64(i)
       }
       mult := make(pvalues, size)
       for i := 0; i < size; i++ {
           mult[i] = q * fsize / (fsize - float64(i))
       }
       return schwartzian(p, mult, up)
   case "Bonferroni":
       p2 := make(pvalues, size)
       for i := 0; i < size; i++ {
           p2[i] = math.Min(p[i]*fsize, 1.0)
       }
       return p2
   case "Hochberg":
       mult := make(pvalues, size)
       for i := 0; i < size; i++ {
           mult[i] = float64(i) + 1
       }
       return schwartzian(p, mult, up)
   case "Holm":
       mult := make(pvalues, size)
       for i := 0; i < size; i++ {
           mult[i] = fsize - float64(i)
       }
       return schwartzian(p, mult, down)
   case "Hommel":
       order := make([]int, size)
       iv1s := make([]iv1, size)
       for i := 0; i < size; i++ {
           iv1s[i] = iv1{i, p[i]}
       }
       sort.Slice(iv1s, func(i, j int) bool {
           return iv1s[i].value < iv1s[j].value
       })
       for i := 0; i < size; i++ {
           order[i] = iv1s[i].index
       }
       s := make(pvalues, size)
       for i := 0; i < size; i++ {
           s[i] = p[order[i]]
       }
       m := make(pvalues, size)
       for i := 0; i < size; i++ {
           m[i] = s[i] * fsize / (float64(i) + 1)
       }
       min := minimum(m)
       q := make(pvalues, size)
       for i := 0; i < size; i++ {
           q[i] = min
       }
       pa := make(pvalues, size)
       for i := 0; i < size; i++ {
           pa[i] = min
       }
       for j := size - 1; j >= 2; j-- {
           lower := make([]int, size-j+1) // lower indices
           for i := 0; i < len(lower); i++ {
               lower[i] = i
           }
           upper := make([]int, j-1) // upper indices
           for i := 0; i < len(upper); i++ {
               upper[i] = size - j + 1 + i
           }
           qmin := float64(j) * s[upper[0]] / 2.0
           for i := 1; i < len(upper); i++ {
               temp := s[upper[i]] * float64(j) / (2.0 + float64(i))
               if temp < qmin {
                   qmin = temp
               }
           }
           for i := 0; i < len(lower); i++ {
               q[lower[i]] = math.Min(s[lower[i]]*float64(j), qmin)
           }
           for i := 0; i < len(upper); i++ {
               q[upper[i]] = q[size-j]
           }
           for i := 0; i < size; i++ {
               if pa[i] < q[i] {
                   pa[i] = q[i]
               }
           }
       }
       order2 := make([]int, size)
       iv2s := make([]iv2, size)
       for i := 0; i < size; i++ {
           iv2s[i] = iv2{i, order[i]}
       }
       sort.Slice(iv2s, func(i, j int) bool {
           return iv2s[i].value < iv2s[j].value
       })
       for i := 0; i < size; i++ {
           order2[i] = iv2s[i].index
       }
       pa2 := make(pvalues, size)
       for i := 0; i < size; i++ {
           pa2[i] = pa[order2[i]]
       }
       return pa2
   case "Šidák":
       p2 := make(pvalues, size)
       for i := 0; i < size; i++ {
           p2[i] = 1.0 - math.Pow(1.0-float64(p[i]), fsize)
       }
       return p2
   default:
       fmt.Printf("\nSorry, do not know how to do '%s' correction.\n", ctype)
       fmt.Println("Perhaps you want one of these?:")
       temp := make([]string, len(ctypes)-1)
       for i := 0; i < len(temp); i++ {
           temp[i] = fmt.Sprintf("  %s", ctypes[i])
       }
       fmt.Println(strings.Join(temp, "\n"))
       os.Exit(1)
   }
   return p

}

func main() {

   p := pvalues{
       4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
       8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
       4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
       8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
       3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
       1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
       4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
       3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
       1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
       2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03,
   }
   for _, ctype := range ctypes {
       s, err := adjusted(p, ctype)
       if err != nil {
           log.Fatal(err)
       }
       fmt.Println(s)
   }

}</lang>

Output:

Benjamini-Hochberg
[ 0]  0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5]  0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10]  0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15]  0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20]  0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25]  0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30]  0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35]  0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40]  0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45]  0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769

Benjamini-Yekutieli
[ 0]  1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25]  1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30]  0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35]  0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40]  0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45]  0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663

Bonferroni
[ 0]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25]  1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30]  0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35]  0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40]  0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45]  0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000

Hochberg
[ 0]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25]  0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30]  0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35]  0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40]  0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45]  0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200

Holm
[ 0]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25]  1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30]  0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35]  0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40]  0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45]  0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200

Hommel
[ 0]  0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25]  0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30]  0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35]  0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40]  0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45]  0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600

Šidák
[ 0]  1.0000000000 1.0000000000 0.9946598274 0.9914285749 0.9999515274
[ 5]  1.0000000000 0.9999999688 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 0.9999999995 1.0000000000 0.9999998801
[15]  1.0000000000 1.0000000000 1.0000000000 0.9999999855 0.9231179729
[20]  0.9999999956 1.0000000000 1.0000000000 0.9999317605 1.0000000000
[25]  0.9983109511 1.0000000000 0.5068253940 1.0000000000 0.9703301333
[30]  0.1832692440 0.0150545753 0.4320729669 0.6993672225 0.0286818157
[35]  0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
[40]  0.0009001752 0.0000125222 0.8142104886 0.3772612062 0.0430222116
[45]  0.0108312558 0.0473319661 0.0032997780 0.7705015898 0.2499384839

Sorry, do not know how to do 'Unknown' correction.
Perhaps you want one of these?:
  Benjamini-Hochberg
  Benjamini-Yekutieli
  Bonferroni
  Hochberg
  Holm
  Hommel
  Šidák

Java

Translation of: D

Works with: Java version 8

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses. <lang Java>import java.util.Arrays; import java.util.Comparator;

public class PValueCorrection {

   private static int[] seqLen(int start, int end) {
       int[] result;
       if (start == end) {
           result = new int[end + 1];
           for (int i = 0; i < result.length; ++i) {
               result[i] = i + 1;
           }
       } else if (start < end) {
           result = new int[end - start + 1];
           for (int i = 0; i < result.length; ++i) {
               result[i] = start + i;
           }
       } else {
           result = new int[start - end + 1];
           for (int i = 0; i < result.length; ++i) {
               result[i] = start - i;
           }
       }
       return result;
   }

   private static int[] order(double[] array, boolean decreasing) {
       int size = array.length;
       int[] idx = new int[size];
       double[] baseArr = new double[size];
       for (int i = 0; i < size; ++i) {
           baseArr[i] = array[i];
           idx[i] = i;
       }

       Comparator<Integer> cmp;
       if (!decreasing) {
           cmp = Comparator.comparingDouble(a -> baseArr[a]);
       } else {
           cmp = (a, b) -> Double.compare(baseArr[b], baseArr[a]);
       }

       return Arrays.stream(idx)
           .boxed()
           .sorted(cmp)
           .mapToInt(a -> a)
           .toArray();
   }

   private static double[] cummin(double[] array) {
       if (array.length < 1) throw new IllegalArgumentException("cummin requires at least one element");
       double[] output = new double[array.length];
       double cumulativeMin = array[0];
       for (int i = 0; i < array.length; ++i) {
           if (array[i] < cumulativeMin) cumulativeMin = array[i];
           output[i] = cumulativeMin;
       }
       return output;
   }

   private static double[] cummax(double[] array) {
       if (array.length < 1) throw new IllegalArgumentException("cummax requires at least one element");
       double[] output = new double[array.length];
       double cumulativeMax = array[0];
       for (int i = 0; i < array.length; ++i) {
           if (array[i] > cumulativeMax) cumulativeMax = array[i];
           output[i] = cumulativeMax;
       }
       return output;
   }

   private static double[] pminx(double[] array, double x) {
       if (array.length < 1) throw new IllegalArgumentException("pmin requires at least one element");
       double[] result = new double[array.length];
       for (int i = 0; i < array.length; ++i) {
           if (array[i] < x) {
               result[i] = array[i];
           } else {
               result[i] = x;
           }
       }
       return result;
   }

   private static void doubleSay(double[] array) {
       System.out.printf("[ 1] %e", array[0]);
       for (int i = 1; i < array.length; ++i) {
           System.out.printf(" %.10f", array[i]);
           if ((i + 1) % 5 == 0) System.out.printf("\n[%2d]", i + 1);
       }
       System.out.println();
   }

   private static double[] intToDouble(int[] array) {
       double[] result = new double[array.length];
       for (int i = 0; i < array.length; i++) {
           result[i] = array[i];
       }
       return result;
   }

   private static double doubleArrayMin(double[] array) {
       if (array.length < 1) throw new IllegalArgumentException("pAdjust requires at least one element");
       return Arrays.stream(array).min().orElse(Double.NaN);
   }

   private static double[] pAdjust(double[] pvalues, String str) {
       int size = pvalues.length;
       if (size < 1) throw new IllegalArgumentException("pAdjust requires at least one element");
       int type;
       switch (str.toLowerCase()) {
           case "bh":
           case "fdr":
               type = 0;
               break;
           case "by":
               type = 1;
               break;
           case "bonferroni":
               type = 2;
               break;
           case "hochberg":
               type = 3;
               break;
           case "holm":
               type = 4;
               break;
           case "hommel":
               type = 5;
               break;
           default:
               throw new IllegalArgumentException(str + " doesn't match any accepted FDR types");
       }

       if (type == 2) {  // Bonferroni method
           double[] result = new double[size];
           for (int i = 0; i < size; ++i) {
               double b = pvalues[i] * size;
               if (b >= 1) {
                   result[i] = 1;
               } else if (0 <= b && b < 1) {
                   result[i] = b;
               } else {
                   throw new RuntimeException("" + b + " is outside [0, 1)");
               }
           }
           return result;
       } else if (type == 4) {  // Holm method
           int[] o = order(pvalues, false);
           double[] o2Double = intToDouble(o);
           double[] cummaxInput = new double[size];
           for (int i = 0; i < size; ++i) {
               cummaxInput[i] = (size - i) * pvalues[o[i]];
           }
           int[] ro = order(o2Double, false);
           double[] cummaxOutput = cummax(cummaxInput);
           double[] pmin = pminx(cummaxOutput, 1.0);
           double[] result = new double[size];
           for (int i = 0; i < size; ++i) {
               result[i] = pmin[ro[i]];
           }
           return result;
       } else if (type == 5) {
           int[] indices = seqLen(size, size);
           int[] o = order(pvalues, false);
           double[] p = new double[size];
           for (int i = 0; i < size; ++i) {
               p[i] = pvalues[o[i]];
           }
           double[] o2Double = intToDouble(o);
           int[] ro = order(o2Double, false);
           double[] q = new double[size];
           double[] pa = new double[size];
           double[] npi = new double[size];
           for (int i = 0; i < size; ++i) {
               npi[i] = p[i] * size / indices[i];
           }
           double min = doubleArrayMin(npi);
           Arrays.fill(q, min);
           Arrays.fill(pa, min);
           for (int j = size; j >= 2; --j) {
               int[] ij = seqLen(1, size - j + 1);
               for (int i = 0; i < size - j + 1; ++i) {
                   ij[i]--;
               }
               int i2Length = j - 1;
               int[] i2 = new int[i2Length];
               for (int i = 0; i < i2Length; ++i) {
                   i2[i] = size - j + 2 + i - 1;
               }
               double q1 = j * p[i2[0]] / 2.0;
               for (int i = 1; i < i2Length; ++i) {
                   double temp_q1 = p[i2[i]] * j / (2.0 + i);
                   if (temp_q1 < q1) q1 = temp_q1;
               }
               for (int i = 0; i < size - j + 1; ++i) {
                   q[ij[i]] = Math.min(p[ij[i]] * j, q1);
               }
               for (int i = 0; i < i2Length; ++i) {
                   q[i2[i]] = q[size - j];
               }
               for (int i = 0; i < size; ++i) {
                   if (pa[i] < q[i]) {
                       pa[i] = q[i];
                   }
               }
           }
           for (int i = 0; i < size; ++i) {
               q[i] = pa[ro[i]];
           }
           return q;
       }

       double[] ni = new double[size];
       int[] o = order(pvalues, true);
       double[] oDouble = intToDouble(o);
       for (int i = 0; i < size; ++i) {
           if (pvalues[i] < 0 || pvalues[i] > 1) {
               throw new RuntimeException("array[" + i + "] = " + pvalues[i] + " is outside [0, 1]");
           }
           ni[i] = (double) size / (size - i);
       }
       int[] ro = order(oDouble, false);
       double[] cumminInput = new double[size];
       if (type == 0) {  // BH method
           for (int i = 0; i < size; ++i) {
               cumminInput[i] = ni[i] * pvalues[o[i]];
           }
       } else if (type == 1) {  // BY method
           double q = 0;
           for (int i = 1; i < size + 1; ++i) {
               q += 1.0 / i;
           }
           for (int i = 0; i < size; ++i) {
               cumminInput[i] = q * ni[i] * pvalues[o[i]];
           }
       } else if (type == 3) {  // Hochberg method
           for (int i = 0; i < size; ++i) {
               cumminInput[i] = (i + 1) * pvalues[o[i]];
           }
       }
       double[] cumminArray = cummin(cumminInput);
       double[] pmin = pminx(cumminArray, 1.0);
       double[] result = new double[size];
       for (int i = 0; i < size; ++i) {
           result[i] = pmin[ro[i]];
       }
       return result;
   }

   public static void main(String[] args) {
       double[] pvalues = new double[]{
           4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
           8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
           4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
           8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
           3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
           1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
           4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
           3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
           1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
           2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
       };

       double[][] correctAnswers = new double[][]{
           new double[]{  // Benjamini-Hochberg
               6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
               9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
               6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
               9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
               4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
               2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
               1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
               2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
               4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
               2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
           },
           new double[]{  // Benjamini & Yekutieli
               1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
               7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
               1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
               2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
               1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
           },
           new double[]{  // Bonferroni
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
               2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
               1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
               9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
               1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
           },
           new double[]{  // Hochberg
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
               1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
               1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
               8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
               1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
           },
           new double[]{  // Holm
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
               1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
               1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
               1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
               8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
               1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
           },
           new double[]{  // Hommel
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
               9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
               9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
               1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
               1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
               8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
               9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
           }
       };

       String[] types = new String[]{"bh", "by", "bonferroni", "hochberg", "holm", "hommel"};
       for (int type = 0; type < types.length; ++type) {
           double[] q = pAdjust(pvalues, types[type]);
           double error = 0.0;
           for (int i = 0; i < pvalues.length; ++i) {
               error += Math.abs(q[i] - correctAnswers[type][i]);
           }
           doubleSay(q);
           System.out.printf("\ntype %d = '%s' has a cumulative error of %g\n", type, types[type], error);
       }
   }

}</lang>

Output:

[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]

type 0 = 'bh' has a cumulative error of 8.03053e-07
[ 1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]

type 1 = 'by' has a cumulative error of 3.64072e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]

type 2 = 'bonferroni' has a cumulative error of 6.50000e-08
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]

type 3 = 'hochberg' has a cumulative error of 2.73750e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]

type 4 = 'holm' has a cumulative error of 2.80950e-07
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]

type 5 = 'hommel' has a cumulative error of 4.35302e-07

Julia

Works with: Julia version 0.6

<lang julia>using MultipleTesting using IterTools

p = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,

    8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
    4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
    8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
    3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
    1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
    4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
    3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
    1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
    2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03]

function printpvalues(v)

   for chunk in partition(v, 10)
       println(join((@sprintf("%4.7f", p) for p in chunk), ", "))
   end

end

println("Original p-values:") printpvalues(p) for corr in (Bonferroni(), BenjaminiHochberg(), BenjaminiYekutieli(), Holm(), Hochberg(), Hommel())

   println("\n", corr)
   printpvalues(adjust(p, corr))

end</lang>

Output:

Original p-values:
0.4533744, 0.7296024, 0.0993603, 0.0907966, 0.1801962, 0.8752257, 0.2922222, 0.9115421, 0.4355806, 0.5324867
0.4926798, 0.5802978, 0.3485442, 0.7883130, 0.2729308, 0.8502518, 0.4268138, 0.6442008, 0.3030266, 0.0500155
0.3194810, 0.7892933, 0.9991834, 0.1745691, 0.9037516, 0.1198578, 0.3966083, 0.0140384, 0.7328671, 0.0679348
0.0040407, 0.0003033, 0.0112515, 0.0237507, 0.0005819, 0.0003075, 0.0082513, 0.0013565, 0.0136070, 0.0003765
0.0000180, 0.0000003, 0.0331025, 0.0094278, 0.0008791, 0.0002178, 0.0009693, 0.0000661, 0.0290081, 0.0057355

MultipleTesting.Bonferroni()
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.7019185, 1.0000000, 1.0000000
0.2020365, 0.0151667, 0.5625735, 1.0000000, 0.0290927, 0.0153774, 0.4125636, 0.0678267, 0.6803480, 0.0188229
0.0009006, 0.0000125, 1.0000000, 0.4713920, 0.0439558, 0.0108892, 0.0484653, 0.0033051, 1.0000000, 0.2867745

MultipleTesting.BenjaminiHochberg()
0.6126681, 0.8521710, 0.1987205, 0.1891595, 0.3217789, 0.9301450, 0.4870370, 0.9301450, 0.6049731, 0.6826753
0.6482629, 0.7253722, 0.5280973, 0.8769926, 0.4705703, 0.9241867, 0.6049731, 0.7856107, 0.4887526, 0.1136717
0.4991891, 0.8769926, 0.9991834, 0.3217789, 0.9301450, 0.2304958, 0.5832475, 0.0389955, 0.8521710, 0.1476843
0.0168364, 0.0025629, 0.0351608, 0.0625019, 0.0036366, 0.0025629, 0.0294688, 0.0061661, 0.0389955, 0.0026890
0.0004503, 0.0000125, 0.0788155, 0.0314261, 0.0048465, 0.0025629, 0.0048465, 0.0011017, 0.0725203, 0.0220596

MultipleTesting.BenjaminiYekutieli()
1.0000000, 1.0000000, 0.8940844, 0.8510676, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.5114323
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.1754486, 1.0000000, 0.6644618
0.0757503, 0.0115310, 0.1581959, 0.2812089, 0.0163618, 0.0115310, 0.1325863, 0.0277424, 0.1754486, 0.0120983
0.0020259, 0.0000563, 0.3546073, 0.1413926, 0.0218055, 0.0115310, 0.0218055, 0.0049568, 0.3262838, 0.0992506

MultipleTesting.Holm()
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.4632662, 1.0000000, 1.0000000
0.1575885, 0.0139534, 0.3938014, 0.7600230, 0.0250197, 0.0139534, 0.3052971, 0.0542614, 0.4626366, 0.0165642
0.0008826, 0.0000125, 0.9930759, 0.3394022, 0.0369228, 0.0102358, 0.0397415, 0.0031729, 0.8992520, 0.2179486

MultipleTesting.Hochberg()
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.4632662, 0.9991834, 0.9991834
0.1575885, 0.0138397, 0.3938014, 0.7600230, 0.0250197, 0.0138397, 0.3052971, 0.0542614, 0.4626366, 0.0165642
0.0008826, 0.0000125, 0.9930759, 0.3394022, 0.0369228, 0.0102358, 0.0397415, 0.0031729, 0.8992520, 0.2179486

MultipleTesting.Hommel()
0.9991834, 0.9991834, 0.9991834, 0.9987624, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9595180
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.4351895, 0.9991834, 0.9766522
0.1414256, 0.0130434, 0.3530937, 0.6887709, 0.0238560, 0.0132246, 0.2722920, 0.0542614, 0.4218158, 0.0158113
0.0008826, 0.0000123, 0.8743649, 0.3016908, 0.0351646, 0.0095825, 0.0387722, 0.0031729, 0.8122276, 0.1950067

Kotlin

Version 1

Translation of: C

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses.

<lang scala>// version 1.1.51

import java.util.Arrays

typealias IAE = IllegalArgumentException

fun seqLen(start: Int, end: Int) =

   when {
       start == end -> IntArray(end + 1) { it + 1 }
       start < end  -> IntArray(end - start + 1) { start + it }
       else         -> IntArray(start - end + 1) { start - it }
   }

var baseArr: DoubleArray? = null

fun compareIncrease(a: Int, b: Int): Int = baseArr!![b].compareTo(baseArr!![a])

fun compareDecrease(a: Int, b: Int): Int = baseArr!![a].compareTo(baseArr!![b])

fun order(array: DoubleArray, decreasing: Boolean): IntArray {

   val size = array.size
   var idx = IntArray(size) { it }
   baseArr = array.copyOf()
   if (!decreasing) {
       idx = Arrays.stream(idx)
                   .boxed()
                   .sorted { a, b -> compareDecrease(a, b) }
                   .mapToInt { it }
                   .toArray()
   }
   else {
       idx = Arrays.stream(idx)
                   .boxed()
                   .sorted { a, b -> compareIncrease(a, b) }
                   .mapToInt { it }
                   .toArray()
   }
   baseArr = null
   return idx

}

fun cummin(array: DoubleArray): DoubleArray {

   val size = array.size
   if (size < 1) throw IAE("cummin requires at least one element")
   val output = DoubleArray(size)
   var cumulativeMin = array[0]
   for (i in 0 until size) {
       if (array[i] < cumulativeMin) cumulativeMin = array[i]
       output[i] = cumulativeMin
   }
   return output

}

fun cummax(array: DoubleArray): DoubleArray {

   val size = array.size
   if (size < 1) throw IAE("cummax requires at least one element")
   val output = DoubleArray(size)
   var cumulativeMax = array[0]
   for (i in 0 until size) {
       if (array[i] > cumulativeMax) cumulativeMax = array[i]
       output[i] = cumulativeMax
   }
   return output

}

fun pminx(array: DoubleArray, x: Double): DoubleArray {

   val size = array.size
   if (size < 1) throw IAE("pmin requires at least one element")
   return DoubleArray(size) { if (array[it] < x) array[it] else x }

}

fun doubleSay(array: DoubleArray) {

   print("[ 1] %e".format(array[0]))
   for (i in 1 until array.size) {
       print(" %.10f".format(array[i]))
       if ((i + 1) % 5 == 0) print("\n[%2d]".format(i + 1))
   }
   println()

}

fun intToDouble(array: IntArray) = DoubleArray(array.size) { array[it].toDouble() }

fun doubleArrayMin(array: DoubleArray) =

   if (array.size < 1) throw IAE("pAdjust requires at least one element")
   else array.min()!!

fun pAdjust(pvalues: DoubleArray, str: String): DoubleArray {

   val size = pvalues.size
   if (size < 1) throw IAE("pAdjust requires at least one element")
   val type = when(str.toLowerCase()) {
       "bh", "fdr"  -> 0
       "by"         -> 1
       "bonferroni" -> 2
       "hochberg"   -> 3
       "holm"       -> 4
       "hommel"     -> 5
       else         -> throw IAE("'$str' doesn't match any accepted FDR types")
   }
   if (type == 2) {  // Bonferroni method
       return DoubleArray(size) {
           val b = pvalues[it] * size
           when {
               b >= 1           -> 1.0
               0 <= b && b < 1  -> b
               else -> throw RuntimeException("$b is outside [0, 1)")
           }
       }
   }
   else if (type == 4) {  // Holm method
       val o = order(pvalues, false)
       val o2Double = intToDouble(o)
       val cummaxInput = DoubleArray(size) { (size - it) * pvalues[o[it]] }
       val ro = order(o2Double, false)
       val cummaxOutput = cummax(cummaxInput)
       val pmin = pminx(cummaxOutput, 1.0)
       return DoubleArray(size) { pmin[ro[it]] }
   }
   else if (type == 5) { // Hommel method
       val indices = seqLen(size, size)
       val o = order(pvalues, false)
       val p = DoubleArray(size) { pvalues[o[it]] }
       val o2Double = intToDouble(o)
       val ro = order(o2Double, false)
       val q = DoubleArray(size)
       val pa = DoubleArray(size)
       val npi = DoubleArray(size) { p[it] * size / indices[it] }
       val min = doubleArrayMin(npi)
       q.fill(min)
       pa.fill(min)
       for (j in size - 1 downTo 2) {
           val ij = seqLen(1, size - j + 1)
           for (i in 0 until size - j + 1) ij[i]--
           val i2Length = j - 1
           val i2 = IntArray(i2Length) { size - j + 2 + it - 1 }
           val pi2Length = i2Length
           var q1 = j * p[i2[0]] / 2.0
           for (i in 1 until pi2Length) {
               val temp_q1 = p[i2[i]] * j / (2.0 + i)
               if(temp_q1 < q1) q1 = temp_q1
           }
           for (i in 0 until size - j + 1) {
               q[ij[i]] = minOf(p[ij[i]] * j, q1)
           }
           for (i in 0 until i2Length) q[i2[i]] = q[size - j]
           for (i in 0 until size) if (pa[i] < q[i]) pa[i] = q[i]
       }
       for (index in 0 until size) q[index] = pa[ro[index]]
       return q
   }
   val ni = DoubleArray(size)
   val o = order(pvalues, true)
   val oDouble = intToDouble(o)
   for (index in 0 until size) {
       if (pvalues[index] !in 0.0 .. 1.0) {
           throw RuntimeException("array[$index] = ${pvalues[index]} is outside [0, 1]")
       }
       ni[index] = size.toDouble() / (size - index)
   }
   val ro = order(oDouble, false)
   val cumminInput = DoubleArray(size)
   if (type == 0) {  // BH method
       for (index in 0 until size) {
           cumminInput[index] = ni[index] * pvalues[o[index]]
       }
   }
   else if (type == 1) {  // BY method
       var q = 0.0
       for (index in 1 until size + 1) q += 1.0 / index
       for (index in 0 until size) {
           cumminInput[index] = q * ni[index] * pvalues[o[index]]
       }
   }
   else if (type == 3) {  // Hochberg method
       for (index in 0 until size) {
           cumminInput[index] = (index + 1) * pvalues[o[index]]
       }
   }
   val cumminArray = cummin(cumminInput)
   val pmin = pminx(cumminArray, 1.0)
   return DoubleArray(size) { pmin[ro[it]] }

}

fun main(args: Array<String>) {

   val pvalues = doubleArrayOf(
       4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
       8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
       4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
       8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
       3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
       1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
       4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
       3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
       1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
       2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
   )

   val correctAnswers = listOf(
       doubleArrayOf(  // Benjamini-Hochberg
           6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
           9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
           6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
           9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
           4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
           2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
           1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
           2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
           4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
           2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
       ),
       doubleArrayOf(  // Benjamini & Yekutieli
           1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
           7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
           1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
           2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
           1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
       ),
       doubleArrayOf(  // Bonferroni
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
           2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
           1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
           9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
           1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
       ),
       doubleArrayOf(  // Hochberg
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
           1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
           1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
           8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
           1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
       ),
       doubleArrayOf(  // Holm
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
           1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
           1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
           1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
           8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
           1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
       ),
       doubleArrayOf(  // Hommel
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
           9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
           9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
           1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
           1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
           8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
           9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
       )
   )
   val types = listOf("bh", "by", "bonferroni", "hochberg", "holm", "hommel")
   val f = "\ntype %d = '%s' has cumulative error of %g"
   for (type in 0 until types.size) {
       val q = pAdjust(pvalues, types[type])
       var error = 0.0
       for (i in 0 until pvalues.size) {
           error += Math.abs(q[i] - correctAnswers[type][i])
       }
       doubleSay(q)
       println(f.format(type, types[type], error))
   }

}</lang>

Output:

[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]

type 0 = 'bh' has cumulative error of 8.03053e-07
[ 1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]

type 1 = 'by' has cumulative error of 3.64072e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]

type 2 = 'bonferroni' has cumulative error of 6.50000e-08
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]

type 3 = 'hochberg' has cumulative error of 2.73750e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]

type 4 = 'holm' has cumulative error of 2.80950e-07
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]

type 5 = 'hommel' has cumulative error of 4.35302e-07

Version 2

Translation of: Perl 6

To avoid licensing issues, this version follows the approach of the Perl 6 entry of which it is a partial translation. However, the correction routines themselves have been coded independently, common code factored out into separate functions (analogous to Perl 6) and (apart from the Šidák method) agree with the Perl 6 results. <lang scala>// version 1.2.21

typealias DList = List<Double>

enum class Direction { UP, DOWN }

// test also for 'Unknown' correction type val types = listOf(

   "Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
   "Holm", "Hommel", "Šidák", "Unknown"

)

fun adjusted(p: DList, type: String) = "\n$type\n${pFormat(adjust(check(p), type))}"

fun pFormat(p: DList, cols: Int = 5): String {

   var i = -cols
   val fmt = "%1.10f"
   return p.chunked(cols).map { chunk ->
       i += cols
       "[%2d]  %s".format(i, chunk.map { fmt.format(it) }.joinToString(" "))
   }.joinToString("\n")

}

fun check(p: DList): DList {

   require(p.size > 0 && p.min()!! >= 0.0 && p.max()!! <= 1.0) {
       "p-values must be in range 0.0 to 1.0"
   }
   return p

}

fun ratchet(p: DList, dir: Direction): DList {

   val pp = p.toMutableList()
   var m = pp[0]
   if (dir == Direction.UP) {
       for (i in 1 until pp.size) {
           if (pp[i] > m) pp[i] = m
           m = pp[i]
       }
   }
   else {
       for (i in 1 until pp.size) {
           if (pp[i] < m) pp[i] = m
           m = pp[i]
       }
   }
   return pp.map { if (it < 1.0) it else 1.0 }

}

fun schwartzian(p: DList, mult: DList, dir: Direction): DList {

   val size = p.size
   val order = if (dir == Direction.UP)
       p.withIndex().sortedByDescending { it.value }.map { it.index }
   else
       p.withIndex().sortedBy { it.value }.map { it.index }
   var pa = List(size) { mult[it] * p[order[it]] }
   pa = ratchet(pa, dir)
   val order2 = order.withIndex().sortedBy{ it.value }.map { it.index }
   return List(size) { pa[order2[it]] }

}

fun adjust(p: DList, type: String): DList {

   val size = p.size
   require(size > 0)
   when (type) {
       "Benjamini-Hochberg" -> {
           val mult = List(size) { size.toDouble() / (size - it) }
           return schwartzian(p, mult, Direction.UP)
       }

       "Benjamini-Yekutieli" -> {
           val q = (1..size).sumByDouble { 1.0 / it }
           val mult = List(size) { q * size / (size - it) }
           return schwartzian(p, mult, Direction.UP)
       }

       "Bonferroni" -> {
           return p.map { minOf(it * size, 1.0) }
       }

       "Hochberg" -> {
           val mult = List(size) { (it + 1).toDouble() }
           return schwartzian(p, mult, Direction.UP)
       }

       "Holm" -> {
           val mult = List(size) { (size - it).toDouble() }
           return schwartzian(p, mult, Direction.DOWN)
       }

       "Hommel" -> {
           val order = p.withIndex().sortedBy { it.value }.map { it.index }
           val s = List(size) { p[order[it]] }
           val min = List(size){ s[it] * size / ( it + 1) }.min()!!
           val q = MutableList(size) { min }
           val pa = MutableList(size) { min }
           for (j in size - 1 downTo 2) {
               val lower = IntArray(size - j + 1) { it }          // lower indices
               val upper = IntArray(j - 1) { size - j + 1 + it }  // upper indices
               var qmin = j * s[upper[0]] / 2.0
               for (i in 1 until upper.size) {
                   val temp = s[upper[i]] * j / (2.0 + i)
                   if (temp < qmin) qmin = temp
               }
               for (i in 0 until lower.size) {
                   q[lower[i]] = minOf(s[lower[i]] * j, qmin)
               }
               for (i in 0 until upper.size) q[upper[i]] = q[size - j]
               for (i in 0 until size) if (pa[i] < q[i]) pa[i] = q[i]
           }
           val order2 = order.withIndex().sortedBy{ it.value }.map { it.index }
           return List(size) { pa[order2[it]] }
       }

       "Šidák" -> {
           val m = size.toDouble()
           return p.map { 1.0 - Math.pow(1.0 - it, m) }
       }

       else -> {
           println(
               "\nSorry, do not know how to do '$type' correction.\n" +
               "Perhaps you want one of these?:\n" +
               types.dropLast(1).map { "  $it" }.joinToString("\n")
           )
           System.exit(1)
       }
   }
   return p

}

fun main(args: Array<String>) {

   val pValues = listOf(
       4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
       8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
       4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
       8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
       3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
       1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
       4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
       3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
       1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
       2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
   )

   types.forEach { println(adjusted(pValues, it)) }

}</lang>

Output:

Same as Perl 6 entry except:

....

Šidák
[ 0]  1.0000000000 1.0000000000 0.9946598274 0.9914285749 0.9999515274
[ 5]  1.0000000000 0.9999999688 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 0.9999999995 1.0000000000 0.9999998801
[15]  1.0000000000 1.0000000000 1.0000000000 0.9999999855 0.9231179729
[20]  0.9999999956 1.0000000000 1.0000000000 0.9999317605 1.0000000000
[25]  0.9983109511 1.0000000000 0.5068253940 1.0000000000 0.9703301333
[30]  0.1832692440 0.0150545753 0.4320729669 0.6993672225 0.0286818157
[35]  0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
[40]  0.0009001752 0.0000125222 0.8142104886 0.3772612062 0.0430222116
[45]  0.0108312558 0.0473319661 0.0032997780 0.7705015898 0.2499384839

Sorry, do not know how to do 'Unknown' correction.
Perhaps you want one of these?:
  Benjamini-Hochberg
  Benjamini-Yekutieli
  Bonferroni
  Hochberg
  Holm
  Hommel
  Šidák

Perl

Translation of: C

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses. <lang perl>#!/usr/bin/env perl

use strict; use warnings;

sub pmin { my $array_ref = shift; my $x = 1; unless ((ref $array_ref) =~ m/ARRAY/) { print "cummin requires an array.\n"; die; } my @pmin_array; my $n = scalar @$array_ref; for (my $index = 0; $index < $n; $index++) { if (@$array_ref[$index] < $x) { $pmin_array[$index] = @$array_ref[$index]; } else { $pmin_array[$index] = $x; } } return @pmin_array; }

sub cummin { my $array_ref = shift; unless ((ref $array_ref) =~ m/ARRAY/) { print "cummin requires an array.\n"; die; } my @cummin; my $cumulative_min = @$array_ref[0]; foreach my $p (@$array_ref) { if ($p < $cumulative_min) { $cumulative_min = $p; } push @cummin, $cumulative_min; } return @cummin; }

sub cummax { my $array_ref = shift; unless ((ref $array_ref) =~ m/ARRAY/) { print "cummin requires an array.\n"; die; } my @cummax; my $cumulative_max = @$array_ref[0]; foreach my $p (@$array_ref) { if ($p > $cumulative_max) { $cumulative_max = $p; } push @cummax, $cumulative_max; } return @cummax; }

sub order {#made to match R's "order" my $array_ref = shift; my $decreasing = 'false'; if (defined $_[0]) { my $option = shift; if ($option =~ m/true/i) { $decreasing = 'true'; } elsif ($option =~ m/false/i) { #do nothing, it's already set to false } else { print "2nd option should only be case-insensitive 'true' or 'false'"; die; } } unless ((ref $array_ref) =~ m/ARRAY/) { print "You should have entered an array.\n"; die; } my @array; my $max_index = scalar @$array_ref-1; if ($decreasing eq 'false') { @array = sort { @$array_ref[$a] <=> @$array_ref[$b] } 0..$max_index; } elsif ($decreasing eq 'true') { @array = sort { @$array_ref[$b] <=> @$array_ref[$a] } 0..$max_index; } }

use List::Util 'min';

sub p_adjust { my $pvalues_ref = shift; unless ((ref $pvalues_ref) =~ m/ARRAY/) { print "p_adjust requires an array.\n"; die; } my $method; if (defined $_[0]) { $method = shift; } else { $method = 'Holm'; } my %methods = ( 'bh' => 1, 'fdr' => 1, 'by' => 1, 'holm' => 1, 'hommel' => 1, 'bonferroni' => 1, 'hochberg' => 1 ); my $method_found = 'no'; foreach my $key (keys %methods) { if ((uc $method) eq (uc $key)) { $method = $key; $method_found = 'yes'; last; } } if ($method_found eq 'no') { if ($method =~ m/benjamini-?\s*hochberg/i) { $method = 'bh'; $method_found = 'yes'; } elsif ($method =~ m/benjamini-?\s*yekutieli/i) { $method = 'by'; $method_found = 'yes'; } } if ($method_found eq 'no') { print "No method could be determined from $method.\n"; die; } my $lp = scalar @$pvalues_ref; my $n = $lp; my @qvalues; if ($method eq 'hochberg') { my @o = order($pvalues_ref, 'TRUE'); my @cummin_input; for (my $index = 0; $index < $n; $index++) { $cummin_input[$index] = ($index+1)* @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o] } my @cummin = cummin(\@cummin_input); undef @cummin_input; my @pmin = pmin(\@cummin); undef @cummin; my @ro = order(\@o); undef @o; @qvalues = @pmin[@ro]; } elsif ($method eq 'bh') { my @o = order($pvalues_ref, 'TRUE'); my @cummin_input; for (my $index = 0; $index < $n; $index++) { $cummin_input[$index] = ($n/($n-$index))* @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o] } my @ro = order(\@o); undef @o; my @cummin = cummin(\@cummin_input); undef @cummin_input; my @pmin = pmin(\@cummin); undef @cummin; @qvalues = @pmin[@ro]; } elsif ($method eq 'by') { my $q = 0.0; my @o = order($pvalues_ref, 'TRUE'); my @ro = order(\@o); for (my $index = 1; $index < ($n+1); $index++) { $q += 1.0 / $index; } my @cummin_input; for (my $index = 0; $index < $n; $index++) { $cummin_input[$index] = $q * ($n/($n-$index)) * @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o] } my @cummin = cummin(\@cummin_input); undef @cummin_input; my @pmin = pmin(\@cummin); undef @cummin; @qvalues = @pmin[@ro]; } elsif ($method eq 'bonferroni') { for (my $index = 0; $index < $n; $index++) { my $q = @$pvalues_ref[$index]*$n; if ((0 <= $q) && ($q < 1)) { $qvalues[$index] = $q; } elsif ($q >= 1) { $qvalues[$index] = 1.0; } else { print "Failed to get Bonferroni adjusted p."; die; } } } elsif ($method eq 'holm') { my @o = order($pvalues_ref); my @cummax_input; for (my $index = 0; $index < $n; $index++) { $cummax_input[$index] = ($n - $index) * @$pvalues_ref[$o[$index]]; } my @ro = order(\@o); undef @o; my @cummax = cummax(\@cummax_input); undef @cummax_input; my @pmin = pmin(\@cummax); undef @cummax; @qvalues = @pmin[@ro]; } elsif ($method eq 'hommel') { my @i = 1..$n; my @o = order($pvalues_ref); my @p = @$pvalues_ref[@o]; my @ro = order(\@o); undef @o; my @pa; my @q; my $min = $n*$p[0]; for (my $index = 0; $index < $n; $index++) { my $temp = $n*$p[$index] / ($index + 1); if ($temp < $min) { $min = $temp; } } for (my $index = 0; $index < $n; $index++) { $pa[$index] = $min;#q <- pa <- rep.int(min(n * p/i), n) $q[$index] = $min;#q <- pa <- rep.int(min(n * p/i), n) } for (my $j = ($n-1); $j >= 2; $j--) {

printf("j = %zu\n", j);

my @ij = 1..($n - $j + 1);#ij <- seq_len(n - j + 1) for (my $i = 0; $i < $n - $j + 1; $i++) { $ij[$i]--;#R's indices are 1-based, C's are 0-based } my $I2_LENGTH = $j - 1; my @i2; for (my $i = 0; $i < $I2_LENGTH; $i++) { $i2[$i] = $n-$j+2+$i-1;

R's indices are 1-based, C's are 0-based, I added the -1

}

my $q1 = $j * $p[$i2[0]] / 2.0; for (my $i = 1; $i < $I2_LENGTH; $i++) {#loop through 2:j my $TEMP_Q1 = $j * $p[$i2[$i]] / (2 + $i); if ($TEMP_Q1 < $q1) { $q1 = $TEMP_Q1; } }

for (my $i = 0; $i < ($n - $j + 1); $i++) {#q[ij] <- pmin(j * p[ij], q1) $q[$ij[$i]] = min( $j*$p[$ij[$i]], $q1); }

for (my $i = 0; $i < $I2_LENGTH; $i++) {#q[i2] <- q[n - j + 1] $q[$i2[$i]] = $q[$n - $j];#subtract 1 because of starting index difference }

for (my $i = 0; $i < $n; $i++) {#pa <- pmax(pa, q) if ($pa[$i] < $q[$i]) { $pa[$i] = $q[$i]; } }

printf("j = %zu, pa = \n", j);
double_say(pa, N);

}#end j loop @qvalues = @pa[@ro]; } else { print "$method doesn't fit my types.\n"; die; } return @qvalues; } my @pvalues = (4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01, 8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01, 4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01, 8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02, 3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01, 1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02, 4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04, 3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04, 1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04, 2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03);

my %correct_answers = ( 'Benjamini-Hochberg' => [6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01, 9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01, 6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01, 9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01, 4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01, 2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01, 1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03, 2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03, 4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03, 2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02], 'Benjamini-Yekutieli' => [1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01, 7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02, 1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02, 2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02, 1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02], 'Bonferroni' => [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00, 2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02, 1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02, 9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02, 1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01],

'Hochberg' => [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01, 1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01], 'Holm' => [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00, 1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01],

'Hommel' => [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01, 1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02, 1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02, 8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02, 9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01]);

foreach my $method ('Hochberg','Benjamini-Hochberg','Benjamini-Yekutieli', 'Bonferroni', 'Holm', 'Hommel') { print "$method\n"; my @qvalues = p_adjust(\@pvalues, $method); my $error = 0.0; foreach my $q (0..$#qvalues) { $error += abs($qvalues[$q] - $correct_answers{$method}[$q]); } printf("type $method has cumulative error of %g.\n", $error); } </lang>

Output:

Hochberg
type Hochberg has cumulative error of 2.7375e-07.
Benjamini-Hochberg
type Benjamini-Hochberg has cumulative error of 8.03053e-07.
Benjamini-Yekutieli
type Benjamini-Yekutieli has cumulative error of 3.64072e-07.
Bonferroni
type Bonferroni has cumulative error of 6.5e-08.
Holm
type Holm has cumulative error of 2.8095e-07.
Hommel
type Hommel has cumulative error of 4.35302e-07.

Perl 6

Works with: Rakudo version 2017.10

<lang perl6>########################### Helper subs ###########################

sub adjusted (@p, $type) { "\n$type\n" ~ format adjust( check(@p), $type ) }

sub format ( @p, $cols = 5 ) {

   my $i = -$cols;
   my $fmt = "%1.10f";
   join "\n", @p.rotor($cols, :partial).map:
     { sprintf "[%2d]  { join ' ', $fmt xx $_ }", $i+=$cols, $_ };

}

sub check ( @p ) { die 'p-values must be in range 0.0 to 1.0' if @p.min < 0 or 1 < @p.max; @p }

multi ratchet ( 'up', @p ) { my $m; @p[$_] min= $m, $m = @p[$_] for ^@p; @p }

multi ratchet ( 'dn', @p ) { my $m; @p[$_] max= $m, $m = @p[$_] for ^@p .reverse; @p }

sub schwartzian ( @p, &transform, :$ratchet ) {

   my @pa = @p.map( {[$_, $++]} ).sort( -*.[0] ).map: { [transform(.[0]), .[1]] };
   @pa[*;0] = ratchet($ratchet, @pa»[0]);
   @pa.sort( *.[1] )»[0]

}

1. 1. 1. 1. The various p-value correction routines #############

multi adjust( @p, 'Benjamini-Hochberg' ) {

   @p.&schwartzian: * * @p / (@p - $++) min 1, :ratchet('up')

}

multi adjust( @p, 'Benjamini-Yekutieli' ) {

   my \r = ^@p .map( { 1 / ++$ } ).sum;
   @p.&schwartzian: * * r * @p / (@p - $++) min 1, :ratchet('up')

}

multi adjust( @p, 'Hochberg' ) {

   my \m = @p.max;
   @p.&schwartzian: * * ++$ min m, :ratchet('up')

}

multi adjust( @p, 'Holm' ) {

   @p.&schwartzian: * * ++$ min 1, :ratchet('dn')

}

multi adjust( @p, 'Šidák' ) {

   @p.&schwartzian: 1 - (1 - *) ** ++$, :ratchet('dn')

}

multi adjust( @p, 'Bonferroni' ) {

   @p.map: * * @p min 1

}

Hommel correction can't be easily reduced to a one pass transform

multi adjust( @p, 'Hommel' ) {

   my @s  = @p.map( {[$_, $++]} ).sort: *.[0] ; # sorted
   my \z  = +@p; # array si(z)e
   my @pa = @s»[0].map( * * z / ++$ ).min xx z; # p adjusted
   my @q;        # scratch array
   for (1 ..^ z).reverse -> $i {
       my @L  = 0 .. z - $i; # lower indices
       my @U  = z - $i ^..^ z; # upper indices
       my $q  = @s[@U]»[0].map( { $_ * $i / (2 + $++) } ).min;
       @q[@L] = @s[@L]»[0].map: { [min] $_ * $i, $q, @s[*-1][0] };
       @pa    = ^z .map: { [max] @pa[$_], @q[$_] }
   }
   @pa[@s[*;1].map( {[$_, $++]} ).sort( *.[0] )»[1]]

}

multi adjust ( @p, $unknown ) {

   note "\nSorry, do not know how to do $unknown correction.\n" ~
   "Perhaps you want one of these?:\n" ~
   <Benjamini-Hochberg Benjamini-Yekutieli Bonferroni Hochberg
   Holm Hommel Šidák>.join("\n");
   exit

}

1. 1. 1. 1. The task ###########################

my @p-values =

   4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
   8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
   4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
   8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
   3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
   1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
   4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
   3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
   1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
   2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03

for < Benjamini-Hochberg Benjamini-Yekutieli Bonferroni Hochberg Holm Hommel Šidák > {

   say adjusted @p-values, $_

}</lang>

Output:

Benjamini-Hochberg
[ 0]  0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5]  0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10]  0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15]  0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20]  0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25]  0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30]  0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35]  0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40]  0.0004502863 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45]  0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769

Benjamini-Yekutieli
[ 0]  1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25]  1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30]  0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35]  0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40]  0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45]  0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663

Bonferroni
[ 0]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25]  1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30]  0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35]  0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40]  0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45]  0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000

Hochberg
[ 0]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25]  0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30]  0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35]  0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40]  0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45]  0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200

Holm
[ 0]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20]  1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25]  1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30]  0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35]  0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40]  0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45]  0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200

Hommel
[ 0]  0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20]  0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25]  0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30]  0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35]  0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40]  0.0008825611 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45]  0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600

Šidák
[ 0]  0.9998642526 0.9999922727 0.9341844137 0.9234670175 0.9899922294
[ 5]  0.9999922727 0.9992955735 0.9999922727 0.9998642526 0.9998909746
[10]  0.9998642526 0.9999288207 0.9995533892 0.9999922727 0.9990991210
[15]  0.9999922727 0.9998642526 0.9999674876 0.9992955735 0.7741716825
[20]  0.9993332472 0.9999922727 0.9999922727 0.9899922294 0.9999922727
[25]  0.9589019598 0.9998137104 0.3728369461 0.9999922727 0.8605248833
[30]  0.1460714182 0.0138585952 0.3270159382 0.5366136349 0.0247164330
[35]  0.0138585952 0.2640282766 0.0528503728 0.3723753774 0.0164308228
[40]  0.0008821796 0.0000125222 0.6357389664 0.2889497995 0.0362651575
[45]  0.0101847015 0.0389807074 0.0031679962 0.5985019850 0.1963376344

Phix

Translation of Kotlin (version 2), except for the Hommel part, which is translated from Go.
Note that sq_min(), extract(), and custom_sort() as used below require 0.8.0+ <lang Phix>enum UP, DOWN

function ratchet(sequence p, integer direction)

   atom m = p[1]
   for i=1 to length(p) do
       if iff(direction=UP?p[i]>m:p[i]<m) then p[i] = m end if
       m = p[i]
   end for
   return sq_min(p,1)

end function

function schwartzian(sequence p, mult, integer direction)

   sequence order = custom_sort(p,tagset(length(p)))
   if direction=UP then order = reverse(order) end if
   sequence pa = ratchet(sq_mul(mult,extract(p,order)), direction)
   return extract(pa,order,invert:=true)

end function

function adjust(sequence p, string method)

   integer size = length(p)
   sequence mult = tagset(size)
   switch method

       case "Benjamini-Hochberg":
           mult = sq_div(size,sq_sub(size+1,mult))
           return schwartzian(p, mult, UP)

       case "Benjamini-Yekutieli":
           atom q = sum(sq_div(1,mult))
           mult = sq_div(q*size,sq_sub(size+1,mult))
           return schwartzian(p, mult, UP)

       case "Bonferroni":
           return sq_min(sq_mul(p,size),1)

       case "Hochberg":
           return schwartzian(p, mult, UP)

       case "Holm":
           mult = sq_sub(size+1,mult)
           return schwartzian(p, mult, DOWN)

       case "Hommel":
           sequence ivdx = repeat(0,size)
           for i=1 to size do ivdx[i] = {p[i],i} end for
           ivdx = sort(ivdx)
           sequence s = vslice(ivdx,1),
                    m = sq_div(sq_mul(s,size),mult),
                    {q,pa} @= repeat(min(m),size),
                    order = vslice(ivdx,2)
           for j=size-1 to 2 by -1 do
               sequence lwr = tagset(size-j+1),
                        upr = sq_add(size-j+1,tagset(j-1))
               atom qmin = j*s[upr[1]]/2
               for i=2 to length(upr) do
                   qmin = min(s[upr[i]]*j/(i+1),qmin)
               end for
               for i=1 to length(lwr) do
                   q[lwr[i]] = min(s[lwr[i]]*j, qmin)
               end for
               for i=1 to length(upr) do
                   q[upr[i]] = q[size-j+1]
               end for
               pa = sq_max(pa,q)
           end for
           return extract(pa,order,invert:=true)

       case "Sidak":
           for i=1 to length(p) do
               p[i] = 1 - power(1-p[i],size)
           end for
           return p

       else
           return {}   -- (unknown method)

   end switch
   return p

end function

constant {types,correct_answers} = columnize({

   {"Benjamini-Hochberg",
    {6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
     9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
     6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
     9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
     4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
     2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
     1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
     2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
     4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
     2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02}},
   {"Benjamini-Yekutieli",
    {1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
     7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
     1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
     2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
     1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02}},
   {"Bonferroni",
    {1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
     2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
     1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
     9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
     1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01}},
   {"Hochberg",
    {9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
     1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
     1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
     8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
     1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01}},
   {"Holm",
    {1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
     1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
     1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
     1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
     8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
     1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01}},
   {"Hommel",
    {9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
     9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
     9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
     1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
     1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
     8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
     9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01}},
   {"Sidak",
    {1.0000000000, 1.0000000000, 0.9946598274, 0.9914285749, 0.9999515274,
     1.0000000000, 0.9999999688, 1.0000000000, 1.0000000000, 1.0000000000,
     1.0000000000, 1.0000000000, 0.9999999995, 1.0000000000, 0.9999998801,
     1.0000000000, 1.0000000000, 1.0000000000, 0.9999999855, 0.9231179729,
     0.9999999956, 1.0000000000, 1.0000000000, 0.9999317605, 1.0000000000,
     0.9983109511, 1.0000000000, 0.5068253940, 1.0000000000, 0.9703301333,
     0.1832692440, 0.0150545753, 0.4320729669, 0.6993672225, 0.0286818157,
     0.0152621104, 0.3391808707, 0.0656206307, 0.4959194266, 0.0186503726,
     0.0009001752, 0.0000125222, 0.8142104886, 0.3772612062, 0.0430222116,
     0.0108312558, 0.0473319661, 0.0032997780, 0.7705015898, 0.2499384839}}})

-- {"Unknown",{1}}})

constant pValues = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,

                   8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
                   4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
                   8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
                   3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
                   1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
                   4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
                   3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
                   1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
                   2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03}

if length(pValues)=0 or min(pValues)<0 or max(pValues)>1 then

   crash("p-values must be in range 0.0 to 1.0")

end if

for i=1 to length(types) do

   string ti = types[i]
   sequence res = adjust(pValues,ti)
   if res={} then
       printf(1,"\nSorry, do not know how to do %s correction.\n"&
                "Perhaps you want one of these?:\n  %s\n",
                {ti,join(types[1..$-1],"\n  ")})
       exit
   end if

-- printf(1,"%s\n",{ti}) -- res = correct_answers[i] -- (for easier comparison only) -- pp(res,{pp_FltFmt,"%13.10f",pp_IntFmt,"%13.10f",pp_Maxlen,75,pp_Pause,0})

   atom error = sum(sq_abs(sq_sub(res,correct_answers[i])))
   printf(1,"%s has cumulative error of %g\n", {ti,error})

end for</lang>

Output:

Matches Kotlin (etc) when some of those lines just above are uncommented.

Benjamini-Hochberg has cumulative error of 8.03052e-7
Benjamini-Yekutieli has cumulative error of 3.64071e-7
Bonferroni has cumulative error of 6.5e-8
Hochberg has cumulative error of 2.7375e-7
Holm has cumulative error of 2.8095e-7
Hommel has cumulative error of 4.35302e-7
Sidak has cumulative error of 7.26897e-10

Python

Translation of: Perl

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses. <lang python>from __future__ import division import sys

def pminf(array):

   x = 1
   pmin_list = []
   N = len(array)
   for index in range(N):
       if array[index] < x:
           pmin_list.insert(index, array[index])
       else:
           pmin_list.insert(index, x)
   return pmin_list

end function

def cumminf(array):

   cummin = []
   cumulative_min = array[0]
   for p in array:
       if p < cumulative_min:
           cumulative_min = p
       cummin.append(cumulative_min)
   return cummin

end

def cummaxf(array):

   cummax = []
   cumulative_max = array[0]
   for e in array:
       if e > cumulative_max:
           cumulative_max = e
       cummax.append(cumulative_max)
   return cummax

end

def order(*args):

   if len(args) > 1:
       if args[1].lower() == 'false':# if ($string1 eq $string2) {
           return sorted(range(len(args[0])), key = lambda k: args[0][k])
       elif list(args[1].lower()) == list('true'):
           return sorted(range(len(args[0])), key = lambda k: args[0][k], reverse = True)
       else:
           print "%s isn't a recognized parameter" % args[1]
           sys.exit()
   elif len(args) == 1:
       return sorted(range(len(args[0])), key = lambda k: args[0][k])

end

def p_adjust(*args):

   method = "bh"
   pvalues = args[0]
   if len(args) > 1:
       methods = {"bh", "fdr", "by", "holm", "hommel", "bonferroni", "hochberg"}
       metharg = arg[1].lower()
       if metharg in methods:
           method = metharg
   lp = len(pvalues)
   n = lp
   qvalues = []

   if method == 'hochberg':#already all lower case
       o = order(pvalues, 'TRUE')
       cummin_input = []
       for index in range(n):
           cummin_input.insert(index, (index+1)*pvalues[o[index]])
       cummin = cumminf(cummin_input)
       pmin = pminf(cummin)
       ro = order(o)
       qvalues = [pmin[i] for i in ro]
   elif method == 'bh':
       o = order(pvalues, 'TRUE')
       cummin_input = []
       for index in range(n):
           cummin_input.insert(index, (n/(n-index))* pvalues[o[index]])
       ro = order(o)
       cummin = cumminf(cummin_input)
       pmin = pminf(cummin)
       qvalues = [pmin[i] for i in ro]
   elif method == 'by':
       q = 0.0
       o = order(pvalues, 'TRUE')
       ro = order(o)
       for index in range(1, n+1):
           q += 1.0 / index;
       cummin_input = []
       for index in range(n):
           cummin_input.insert(index, q * (n/(n-index)) * pvalues[o[index]])
       cummin = cumminf(cummin_input)
       pmin = pminf(cummin)
       qvalues = [pmin[i] for i in ro]
   elif method == 'bonferroni':
       for index in range(n):
           q = pvalues[index] * n
           if (0 <= q) and (q < 1):
               qvalues.insert(index, q)
           elif q >= 1:
               qvalues.insert(index, 1)
           else:
               print '%g won\'t give a Bonferroni adjusted p' % q
               sys.exit()
   elif method == 'holm':
       o = order(pvalues)
       cummax_input = []
       for index in range(n):
           cummax_input.insert(index, (n - index) * pvalues[o[index]])
       ro = order(o)
       cummax = cummaxf(cummax_input)
       pmin = pminf(cummax)
       qvalues = [pmin[i] for i in ro]
   elif method == 'hommel':
       i = range(1,n+1)
       o = order(pvalues)
       p = [pvalues[index] for index in o]
       ro = order(o)
       pa = []
       q = []
       smin = n*p[0]
       for index in range(n):
           temp = n*p[index] / (index + 1)
           if temp < smin:
               smin = temp
       for index in range(n):
           pa.insert(index, smin)
           q.insert(index, smin)
       for j in range(n-1,1,-1):
           ij = range(1,n-j+2)
           for x in range(len(ij)):
               ij[x] -= 1
           I2_LENGTH = j - 1
           i2 = []
           for index in range(I2_LENGTH+1):
               i2.insert(index, n - j + 2 + index - 1)
           q1 = j * p[i2[0]] / 2.0
           for index in range(1,I2_LENGTH):
               TEMP_Q1 = j * p[i2[index]] / (2.0 + index)
               if TEMP_Q1 < q1:
                   q1 = TEMP_Q1
           for index in range(n - j + 1):
               q[ij[index]] = min(j * p[ij[index]], q1)
           for index in range(I2_LENGTH):
               q[i2[index]] = q[n-j]
           for index in range(n):
               if pa[index] < q[index]:
                   pa[index] = q[index]
           qvalues = [pa[index] for index in ro]
   else:
       print "method %s isn't defined." % method
       sys.exit()
   return qvalues

pvalues = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01, 8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01, 4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01, 8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02, 3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01, 1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02, 4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04, 3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04, 1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04, 2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03]

correct_answers = {}

correct_answers['bh'] = [6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01, 9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01, 6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01, 9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01, 4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01, 2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01, 1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03, 2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03, 4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03, 2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02]

correct_answers['by'] = [1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01, 7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02, 1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02, 2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02, 1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02]

correct_answers['bonferroni'] = [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00, 2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02, 1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02, 9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02, 1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01]

correct_answers['hochberg'] = [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01, 1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01]

correct_answers['holm'] = [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00, 1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01]

correct_answers['hommel'] = [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01, 1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02, 1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02, 8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02, 9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01]

for key in correct_answers.keys():

   error = 0.0
   q = p_adjust(pvalues, key)
   for i in range(len(q)):
       error += abs(q[i] - correct_answers[key][i])
   print '%s error = %g' % (key.upper(), error)

</lang>

Output:

BONFERRONI error = 6.5e-08
BH error = 8.03053e-07
HOLM error = 2.8095e-07
HOMMEL error = 4.35302e-07
HOCHBERG error = 2.7375e-07
BY error = 3.64072e-07

R

The p.adjust function is built-in, see R manual.

<lang R>p <- c(4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,

      8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
      4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
      8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
      3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
      1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
      4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
      3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
      1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
      2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03)

p.adjust(p, method = 'BH') print("Benjamini-Hochberg") writeLines("\n")

p.adjust(p, method = 'BY') print("Benjamini & Yekutieli") writeLines("\n")

p.adjust(p, method = 'bonferroni') print("Bonferroni") writeLines("\n")

p.adjust(p, method = 'hochberg') print("Hochberg") writeLines("\n");

p.adjust(p, method = 'hommel') writeLines("Hommel\n")</lang>

Output:

 [1] 6.126681e-01 8.521710e-01 1.987205e-01 1.891595e-01 3.217789e-01
 [6] 9.301450e-01 4.870370e-01 9.301450e-01 6.049731e-01 6.826753e-01
[11] 6.482629e-01 7.253722e-01 5.280973e-01 8.769926e-01 4.705703e-01
[16] 9.241867e-01 6.049731e-01 7.856107e-01 4.887526e-01 1.136717e-01
[21] 4.991891e-01 8.769926e-01 9.991834e-01 3.217789e-01 9.301450e-01
[26] 2.304958e-01 5.832475e-01 3.899547e-02 8.521710e-01 1.476843e-01
[31] 1.683638e-02 2.562902e-03 3.516084e-02 6.250189e-02 3.636589e-03
[36] 2.562902e-03 2.946883e-02 6.166064e-03 3.899547e-02 2.688991e-03
[41] 4.502862e-04 1.252228e-05 7.881555e-02 3.142613e-02 4.846527e-03
[46] 2.562902e-03 4.846527e-03 1.101708e-03 7.252032e-02 2.205958e-02
[1] "Benjamini-Hochberg"


 [1] 1.000000e+00 1.000000e+00 8.940844e-01 8.510676e-01 1.000000e+00
 [6] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 5.114323e-01
[21] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26] 1.000000e+00 1.000000e+00 1.754486e-01 1.000000e+00 6.644618e-01
[31] 7.575031e-02 1.153102e-02 1.581959e-01 2.812089e-01 1.636176e-02
[36] 1.153102e-02 1.325863e-01 2.774239e-02 1.754486e-01 1.209832e-02
[41] 2.025930e-03 5.634031e-05 3.546073e-01 1.413926e-01 2.180552e-02
[46] 1.153102e-02 2.180552e-02 4.956812e-03 3.262838e-01 9.925057e-02
[1] "Benjamini & Yekutieli"


 [1] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
 [6] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[21] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26] 1.000000e+00 1.000000e+00 7.019185e-01 1.000000e+00 1.000000e+00
[31] 2.020365e-01 1.516674e-02 5.625735e-01 1.000000e+00 2.909271e-02
[36] 1.537741e-02 4.125636e-01 6.782670e-02 6.803480e-01 1.882294e-02
[41] 9.005725e-04 1.252228e-05 1.000000e+00 4.713920e-01 4.395577e-02
[46] 1.088915e-02 4.846527e-02 3.305125e-03 1.000000e+00 2.867745e-01
[1] "Bonferroni"


 [1] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
 [6] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[21] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26] 9.991834e-01 9.991834e-01 4.632662e-01 9.991834e-01 9.991834e-01
[31] 1.575885e-01 1.383967e-02 3.938014e-01 7.600230e-01 2.501973e-02
[36] 1.383967e-02 3.052971e-01 5.426136e-02 4.626366e-01 1.656419e-02
[41] 8.825610e-04 1.252228e-05 9.930759e-01 3.394022e-01 3.692284e-02
[46] 1.023581e-02 3.974152e-02 3.172920e-03 8.992520e-01 2.179486e-01
[1] "Hochberg"


 [1] 9.991834e-01 9.991834e-01 9.991834e-01 9.987624e-01 9.991834e-01
 [6] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.595180e-01
[21] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26] 9.991834e-01 9.991834e-01 4.351895e-01 9.991834e-01 9.766522e-01
[31] 1.414256e-01 1.304340e-02 3.530937e-01 6.887709e-01 2.385602e-02
[36] 1.322457e-02 2.722920e-01 5.426136e-02 4.218158e-01 1.581127e-02
[41] 8.825610e-04 1.252228e-05 8.743649e-01 3.016908e-01 3.516461e-02
[46] 9.582456e-03 3.877222e-02 3.172920e-03 8.122276e-01 1.950067e-01
Hommel

SAS

<lang sas>data pvalues; input raw_p @@; cards; 4.533744e-01 7.296024e-01 9.936026e-02 9.079658e-02 1.801962e-01 8.752257e-01 2.922222e-01 9.115421e-01 4.355806e-01 5.324867e-01 4.926798e-01 5.802978e-01 3.485442e-01 7.883130e-01 2.729308e-01 8.502518e-01 4.268138e-01 6.442008e-01 3.030266e-01 5.001555e-02 3.194810e-01 7.892933e-01 9.991834e-01 1.745691e-01 9.037516e-01 1.198578e-01 3.966083e-01 1.403837e-02 7.328671e-01 6.793476e-02 4.040730e-03 3.033349e-04 1.125147e-02 2.375072e-02 5.818542e-04 3.075482e-04 8.251272e-03 1.356534e-03 1.360696e-02 3.764588e-04 1.801145e-05 2.504456e-07 3.310253e-02 9.427839e-03 8.791153e-04 2.177831e-04 9.693054e-04 6.610250e-05 2.900813e-02 5.735490e-03

run;

proc multtest pdata=pvalues bon sid hom hoc holm; run;</lang>

Stata

The qqvalue package on SSC provides the equivalent of the R function p.adjust.

First, install the package with:

<lang stata>ssc install qqvalue</lang>

Given a dataset containing the p-values in a variable, the qqvalue command generates another variable with the adjusted p-values. For instance, for the Holm correction:

<lang stata>qqvalue p, method(holm) qvalue(q)</lang>

zkl

Translation of: C

This work is based on R source code covered by the GPL license. It is thus a modified version, also covered by the GPL. See the FAQ about GNU licenses.

<lang zkl>fcn bh(pvalues){ // Benjamini-Hochberg

  psz,pszf := pvalues.len(), psz.toFloat();
  n_i      := psz.pump(List,'wrap(n){ pszf/(psz - n) }); # N/(N-0),N/(N-1),..
  o,ro     := order(pvalues,True),order(o,False); # sort pvalues, sort indices
  in	    := psz.pump(List,'wrap(n){ n_i[n]*pvalues[o[n]] });
  pmin     := cummin(in).apply((1.0).min); # (min(1,c[0]),min(1,c[1]),...)
  ro.apply(pmin.get);		# (pmin[ro[0]],pmin[ro[1]],...)

}

fcn by(pvalues){ // Benjamini & Yekutieli

  psz,pszf := pvalues.len(), psz.toFloat();
  o,ro     := order(pvalues,True),order(o,False); # sort pvalues, sort indices
  n_i      := psz.pump(List,'wrap(n){ pszf/(psz - n) }); # N/(N-0),N/(N-1),..
  q	    := [1..psz].reduce(fcn(q,n){ q+=1.0/n },0.0);
  in	    := psz.pump(List,'wrap(n){ q * n_i[n] * pvalues[o[n]] });
  cummin(in).apply((1.0).min) : ro.apply(_.get);

}

fcn hochberg(pvalues){

  psz,pszf := pvalues.len(), psz.toFloat();
  o,ro     := order(pvalues,True),order(o,False); # sort pvalues, sort indices
  n_i      := psz.pump(List,'wrap(n){ pszf/(psz - n) }); # N/(N-0),N/(N-1),..
  in	    := psz.pump(List,'wrap(n){ pvalues[o[n]]*(n + 1) });
  cummin(in).apply((1.0).min) : ro.apply(_.get);

}

fcn cummin(pvalues){ // R's cumulative minima --> list of mins

  out,m := List.createLong(pvalues.len()), pvalues[0];
  foreach pv in (pvalues){ out.append(m=m.min(pv)) }
  out

} fcn order(list,downUp){ // True==increasing, --> List(int) sorted indices

  f:=(downUp) and fcn(a,b){ a[1]>b[1] } or fcn(a,b){ a[1]<b[1] };
  [0..].zip(list).pump(List()).sort(f).pump(List,T("get",0))

}

fcn bonferroni(pvalues){ // -->List

  sz,r := pvalues.len(),List();
  foreach pv in (pvalues){
     b:=pv*sz;
     if(b>=1.0) r.append(1.0);
     else if(0.0<=b<1.0) r.append(b);
     else throw(Exception.ValueError(

"%g is outside of the interval I planned.".fmt(b)));

  }
  r

}

fcn hommel(pvalues){

  psz,indices := pvalues.len(), [1..psz].walk();	// 1,2,3,4...
  o,ro        := order(pvalues,False),order(o,False); # sort pvalues, sort indices
  p           := o.apply('wrap(n){ pvalues[n] }).copy(); // pvalues[*o]
  npi         := [1..].zip(p).apply('wrap([(n,p)]){ p*psz/n });
  min	       := (0.0).min(npi);	 // min value in npi
  pa,q	       := List.createLong(psz,min), pa.copy(); #(min,min,,,)
  foreach j in ([psz - 1..2,-1]){
     ij:=[0..psz - j].walk();
     i2:=(j - 1).pump(List,'+(psz - j + 1));
     q1:=(0.0).min((j-1).pump(List,'wrap(n){ p[i2[n]]*j/(2 + n) }));
     foreach i in (psz - j + 1){ q[ij[i]] = q1.min(p[ij[i]]*j) }
     foreach i in (j - 1){ q[i2[i]] = q[psz - j] }
     foreach i in (psz){ pa[i] = pa[i].max(q[i]) }
  }
  psz.pump(List,'wrap(n){ pa[ro[n]] }); // Hommel q-values

}</lang> <lang zkl>pvalues:=T(

  4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
  8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
  4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
  8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
  3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
  1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
  4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
  3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
  1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
  2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03);

bh(pvalues) : format(_,"\nBenjamini-Hochberg"); by(pvalues) : format(_,"\nBenjamini & Yekutieli"); bonferroni(pvalues) : format(_,"\nBonferroni"); hochberg(pvalues) : format(_,"\nHochberg"); hommel(pvalues) : format(_,"\nHommel");

fcn format(list,title){

  print(title,":");
  foreach n in ([1..list.len(),5]){
     print("\n[%2d]:".fmt(n));
     foreach x in (list[n-1,5]){ print(" %.6e".fmt(x)) }
  }
  println();

}</lang>

Output:

Benjamini-Hochberg:
[ 1]: 6.126681e-01 8.521710e-01 1.987205e-01 1.891595e-01 3.217789e-01
[ 6]: 9.301450e-01 4.870370e-01 9.301450e-01 6.049731e-01 6.826753e-01
[11]: 6.482629e-01 7.253722e-01 5.280973e-01 8.769926e-01 4.705703e-01
[16]: 9.241867e-01 6.049731e-01 7.856107e-01 4.887526e-01 1.136717e-01
[21]: 4.991891e-01 8.769926e-01 9.991834e-01 3.217789e-01 9.301450e-01
[26]: 2.304958e-01 5.832475e-01 3.899547e-02 8.521710e-01 1.476843e-01
[31]: 1.683638e-02 2.562902e-03 3.516084e-02 6.250189e-02 3.636589e-03
[36]: 2.562902e-03 2.946883e-02 6.166064e-03 3.899547e-02 2.688991e-03
[41]: 4.502862e-04 1.252228e-05 7.881555e-02 3.142613e-02 4.846527e-03
[46]: 2.562902e-03 4.846527e-03 1.101708e-03 7.252032e-02 2.205958e-02

Benjamini & Yekutieli:
[ 1]: 1.000000e+00 1.000000e+00 8.940844e-01 8.510676e-01 1.000000e+00
[ 6]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 5.114323e-01
[21]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26]: 1.000000e+00 1.000000e+00 1.754486e-01 1.000000e+00 6.644618e-01
[31]: 7.575031e-02 1.153102e-02 1.581959e-01 2.812089e-01 1.636176e-02
[36]: 1.153102e-02 1.325863e-01 2.774239e-02 1.754486e-01 1.209832e-02
[41]: 2.025930e-03 5.634031e-05 3.546073e-01 1.413926e-01 2.180552e-02
[46]: 1.153102e-02 2.180552e-02 4.956812e-03 3.262838e-01 9.925057e-02

Bonferroni:
[ 1]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[ 6]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[21]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26]: 1.000000e+00 1.000000e+00 7.019185e-01 1.000000e+00 1.000000e+00
[31]: 2.020365e-01 1.516674e-02 5.625735e-01 1.000000e+00 2.909271e-02
[36]: 1.537741e-02 4.125636e-01 6.782670e-02 6.803480e-01 1.882294e-02
[41]: 9.005725e-04 1.252228e-05 1.000000e+00 4.713920e-01 4.395577e-02
[46]: 1.088915e-02 4.846527e-02 3.305125e-03 1.000000e+00 2.867745e-01

Hochberg:
[ 1]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[ 6]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[21]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26]: 9.991834e-01 9.991834e-01 4.632662e-01 9.991834e-01 9.991834e-01
[31]: 1.575885e-01 1.383967e-02 3.938014e-01 7.600230e-01 2.501973e-02
[36]: 1.383967e-02 3.052971e-01 5.426136e-02 4.626366e-01 1.656419e-02
[41]: 8.825610e-04 1.252228e-05 9.930759e-01 3.394022e-01 3.692284e-02
[46]: 1.023581e-02 3.974152e-02 3.172920e-03 8.992520e-01 2.179486e-01

Hommel:
[ 1]: 9.991834e-01 9.991834e-01 9.991834e-01 9.987624e-01 9.991834e-01
[ 6]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.595180e-01
[21]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26]: 9.991834e-01 9.991834e-01 4.351895e-01 9.991834e-01 9.766522e-01
[31]: 1.414256e-01 1.304340e-02 3.530937e-01 6.887709e-01 2.385602e-02
[36]: 1.322457e-02 2.722920e-01 5.426136e-02 4.218158e-01 1.581127e-02
[41]: 8.825610e-04 1.252228e-05 8.743649e-01 3.016908e-01 3.516461e-02
[46]: 9.582456e-03 3.877222e-02 3.172920e-03 8.122276e-01 1.950067e-01