P-value correction
You are encouraged to solve this task according to the task description, using any language you may know.
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
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
#include <stdio.h>//printf
#include <stdlib.h>//qsort
#include <math.h>//fabs
#include <stdbool.h>//bool data type
#include <strings.h>//strcasecmp
#include <assert.h>//assert, necessary for random integer selection
unsigned int * seq_len(const unsigned int START, const unsigned int END) {
//named after R function of same name, but simpler function
unsigned start = (unsigned)START;
unsigned end = (unsigned)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 (unsigned i = 0; i < end; i++) {
sequence[i] = i+1;
}
return sequence;
}
if (START > END) {
end = (unsigned)START;
start = (unsigned)END;
}
const unsigned 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 (unsigned index = 0; index <= LENGTH; index++) {
sequence[index] = start + index;
}
} else {
for (unsigned 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 * 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 * 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 * 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 (unsigned int i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) {
if (ARRAY[i] > cumulative_max) {
cumulative_max = ARRAY[i];
}
output[i] = cumulative_max;
}
return output;
}
double * pminx(const double *restrict ARRAY, const unsigned int 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 (unsigned int i = 1; i < NO_OF_ARRAY_ELEMENTS; i++) {
printf(" %.10f", ARRAY[i]);
if (((i+1) % 5) == 0) {
printf("\n[%u]", 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 * uint2double (const unsigned int *restrict ARRAY, const unsigned int 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 (unsigned int 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 * p_adjust (const double *restrict PVALUES, const unsigned int 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 (STRING == NULL) {
TYPE = 0;
} else 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 (unsigned int 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 (unsigned index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
cummax_input[index] = (NO_OF_ARRAY_ELEMENTS - index ) * (double)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 (unsigned int 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 (unsigned int 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 (unsigned index = 1; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double TEMP = (double)NO_OF_ARRAY_ELEMENTS * p[index] / (double)(1+index);
if (TEMP < min) {
min = TEMP;
}
}
for (unsigned int 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 (unsigned j = (NO_OF_ARRAY_ELEMENTS-1); j >= 2; j--) {
// printf("j = %zu\n", j);
unsigned int *restrict ij = seq_len(0,NO_OF_ARRAY_ELEMENTS - j);
const size_t I2_LENGTH = j - 1;
unsigned int *restrict i2 = malloc(I2_LENGTH * sizeof(unsigned int));
for (unsigned 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 = (double)j * p[i2[0]] / 2.0;
for (unsigned int i = 1; i < I2_LENGTH; i++) {//loop through 2:j
const double TEMP_Q1 = (double)j * p[i2[i]] / (double)(2 + i);
if (TEMP_Q1 < q1) {
q1 = TEMP_Q1;
}
}
for (unsigned int i = 0; i < (NO_OF_ARRAY_ELEMENTS - j + 1); i++) {//q[ij] <- pmin(j * p[ij], q1)
q[ij[i]] = min2( (double)j*p[ij[i]], q1);
}
free(ij); ij = NULL;
for (unsigned int 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 (unsigned int 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 (unsigned int 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 (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double NI = (double)NO_OF_ARRAY_ELEMENTS / (double)(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 (unsigned int index = 2; index < (1+NO_OF_ARRAY_ELEMENTS); index++) {
q += 1.0/(double)index;
}
for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double NI = (double)NO_OF_ARRAY_ELEMENTS / (double)(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 (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
// pmin(1, cummin((n - i + 1L) * p[o]))[ro]
cummin_input[index] = (double)(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;
}
- 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
To avoid licensing issues, this version is a translation of the Kotlin entry (Version 2) which is itself a partial translation of the Raku entry. If using gcc, you need to link to the math library (-lm).
#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;
}
- Output:
Same as Kotlin (Version 2) output.
C#
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();
}
}
}
}
- 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
C++
#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;
}
- 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
D
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.
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);
}
}
- 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
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)
}
}
- 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
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.
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);
}
}
}
- 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
jq
Adapted from Wren
Works with jq, the C implementation of jq
Works with gojq, the Go implementation of jq
Works with jaq, the Rust implementation of jq
The def of `_nwise` is included for the sake of gojq; it may be omitted if using jq or jaq.
### For gojq
# Require $n > 0
def nwise($n):
def _n: if length <= $n then . else .[:$n] , (.[$n:] | _n) end;
if $n <= 0 then "nwise: argument should be non-negative" else _n end;
### Generic functions
def array($n): . as $in | [range(0;$n)|$in];
def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
def rpad($len): tostring | ($len - length) as $l | . + (" " * $l);
def round($ndec): pow(10;$ndec) as $p | . * $p | round / $p;
# tabular print
def tprint($columns; $width):
reduce _nwise($columns) as $row ("";
. + ($row|map(lpad($width)) | join(" ")) + "\n" );
# Emit the permutation p such that [range(0;length) as $i | .[$p[$i]]] is sorted
def sort_index:
[range(0;length) as $i | [$i, .[$i]]]
| sort_by(.[1])
| map(.[0]);
### p-value Corrections
def types: [
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák"
];
######################################
# The functions in this section expect
# an array of p-values as input.
######################################
def pFormat($cols):
map(round(10) | rpad(12)) | tprint($cols; 12);
def check:
if (length == 0 or min < 0 or max > 1)
then "p-values must be in the range 0 to 1 inclusive" | error
else .
end;
# $dir should be "UP" or "DOWN"
def ratchet($dir):
{ m: .[0], p: .}
| if $dir == "UP"
then reduce range(1; .p|length) as $i (.;
if (.p[$i] > .m) then .p[$i] = .m end
| .m = .p[$i])
else reduce range(1; .p|length) as $i (.;
if (.p[$i] < .m) then .p[$i] = .m end
| .m = .p[$i] )
end
| .p
| map( if . < 1 then . else 1 end);
# If $dir is "UP" then reverse is called
def schwartzian($mult; $dir):
length as $size
| (sort_index | if $dir == "UP" then reverse else . end) as $order
| ([range(0;$size) as $i | $mult[$i] * .[$order[$i]] ]
| ratchet($dir)) as $pa
| ($order | sort_index) as $order2
| [ range(0; $size) as $i | $pa[$order2[$i]]] ;
# $type should be one of `types`
def adjust($type):
length as $size
| if $size == 0 then "The array of p-values cannot be empty." | error end
| if $type == "Benjamini-Hochberg"
then
[range(0;$size) as $i | $size / ($size - $i)] as $mult
| schwartzian($mult; "UP")
elif $type == "Benjamini-Yekutieli"
then (reduce range(1; 1+$size) as $i (0; . + (1/$i))) as $q
| [range(0; $size) as $i | $q * $size / ($size - $i)] as $mult
| schwartzian($mult; "UP")
elif $type == "Bonferroni"
then map( [(. * $size), 1] | min)
elif $type == "Hochberg"
then
[range(0;$size) as $i | $i + 1] as $mult
| schwartzian($mult; "UP")
elif $type == "Holm"
then
[range(0; $size) as $i | $size - $i] as $mult
| schwartzian($mult; "DOWN")
elif $type == "Hommel"
then
sort_index as $order
| [range(0; $size) as $i | .[$order[$i]]] as $s
| [range(0; $size) as $i | $s[$i] * $size / ($i + 1)] as $m
| ($m | min) as $min
| { q: ($min | array($size)),
pa: ($min | array($size)) }
| reduce range($size-1; 1; -1) as $j (.;
.lower = (0 | array($size - $j + 1)) # lower indices
| reduce range(0; .lower|length) as $i (.; .lower[$i] = $i)
| .upper = (0|array($j - 1))
| reduce range(0; .upper|length) as $i (.; .upper[$i] = $size - $j + 1 + $i)
| .qmin = ($j * $s[.upper[0]] / 2)
| reduce range(1; .upper|length) as $i (.;
($s[.upper[$i]] * $j / (2 + $i)) as $temp
| if $temp < .qmin then .qmin = $temp end )
| reduce range(0; .lower|length) as $i (.;
.q[.lower[$i]] = ([.qmin, ($s[.lower[$i]] * $j)] | min) )
| reduce range(0; .upper|length) as $i (.; .q[.upper[$i]] = .q[$size - $j])
| reduce range(0; $size) as $i (.; if (.pa[$i] < .q[$i]) then .pa[$i] = .q[$i] end)
)
| ($order | sort_index) as $order2
| [range(0; $size) as $i | .pa[$order2[$i] ]]
elif $type == "Šidák"
then map(1 - pow(1 - .; $size) )
else
"\nSorry, do not know how to do '\($type)' correction.\n" +
"Perhaps you want one of the following?\n" +
(types | map( " \(.)" ) | join("\n") )
end;
def adjusted($type):
"\n\($type)",
(check | adjust($type) | pFormat(5));
### Example
def 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
];
pValues | adjusted( types[] )- Output:
The output shown here is from a run using jq. The output using gojq is the same except that numbers are presented without using scientific notation.
Benjamini-Hochberg 0.6126681081 0.8521710465 0.19872052 0.1891595417 0.3217789286 0.930145 0.487037 0.930145 0.6049730556 0.6826752564 0.6482628947 0.72537225 0.5280972727 0.8769925556 0.4705703448 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045 0.4991890625 0.8769925556 0.9991834 0.3217789286 0.930145 0.2304957692 0.5832475 0.0389954722 0.8521710465 0.1476842609 0.016836375 0.0025629017 0.0351608437 0.0625018947 0.0036365888 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914 0.0004502863 1.25223e-05 0.0788155476 0.03142613 0.004846527 0.0025629017 0.004846527 0.0011017083 0.072520325 0.0220595769 Benjamini-Yekutieli 1 1 0.8940844244 0.8510676197 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5114323399 1 1 1 1 1 1 1 0.1754486368 1 0.6644618149 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246 0.0020259303 5.63403e-05 0.3546073326 0.1413926119 0.0218055202 0.0115310209 0.0218055202 0.004956812 0.3262838334 0.0992505663 Bonferroni 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.7019185 1 1 0.2020365 0.015166745 0.5625735 1 0.02909271 0.01537741 0.4125636 0.0678267 0.680348 0.01882294 0.0009005725 1.25223e-05 1 0.47139195 0.043955765 0.010889155 0.04846527 0.003305125 1 0.2867745 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 0.46326621 0.9991834 0.9991834 0.15758847 0.013839669 0.39380145 0.76002304 0.0250197306 0.013839669 0.305297064 0.05426136 0.46263664 0.0165641872 0.0008825611 1.25223e-05 0.9930759 0.339402204 0.0369228426 0.0102358057 0.0397415214 0.00317292 0.89925203 0.21794862 Holm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.46326621 1 1 0.15758847 0.0139534054 0.39380145 0.76002304 0.0250197306 0.0139534054 0.305297064 0.05426136 0.46263664 0.0165641872 0.0008825611 1.25223e-05 0.9930759 0.339402204 0.0369228426 0.0102358057 0.0397415214 0.00317292 0.89925203 0.21794862 Hommel 0.9991834 0.9991834 0.9991834 0.99876238 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 0.959518 0.9991834 0.9991834 0.9991834 0.9991834 0.9991834 0.9991834 0.9991834 0.43518947 0.9991834 0.97665225 0.14142555 0.0130434007 0.3530936533 0.68877088 0.0238560222 0.0132245726 0.272291976 0.05426136 0.42181576 0.0158112696 0.0008825611 1.25223e-05 0.8743649143 0.301690848 0.035164612 0.0095824564 0.038772216 0.00317292 0.81222764 0.19500666 Šidák 1 1 0.9946598274 0.9914285749 0.9999515274 1 0.9999999688 1 1 1 1 1 0.9999999995 1 0.9999998801 1 1 1 0.9999999855 0.9231179729 0.9999999956 1 1 0.9999317605 1 0.9983109511 1 0.506825394 1 0.9703301333 0.183269244 0.0150545753 0.4320729669 0.6993672225 0.0286818157 0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726 0.0009001752 1.25222e-05 0.8142104886 0.3772612062 0.0430222116 0.0108312558 0.0473319661 0.003299778 0.7705015898 0.2499384839
Julia
using MultipleTesting, IterTools, Printf
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
- 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
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.
// 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))
}
}
- 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
To avoid licensing issues, this version follows the approach of the Raku 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 Raku) and (apart from the Šidák method) agree with the Raku results.
// 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)) }
}
- Output:
Same as Raku 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
Nim
import algorithm, math, sequtils, strformat, strutils, sugar
type
CorrectionType {.pure.} = enum
BenjaminiHochberg = "Benjamini-Hochberg"
BenjaminiYekutieli = "Benjamini-Yekutieli"
Bonferroni = "Bonferroni"
Hochberg = "Hochberg"
Holm = "Holm"
Hommel = "Hommel"
Šidák = "Šidák"
Direction {.pure.} = enum Up, Down
PValues = seq[float]
template newPValues(length: Natural): PValues =
## Create a PValues object of given length.
newSeq[float](length)
func ratchet(p: var PValues; dir: Direction) =
var m = p[0]
case dir
of Up:
for i in 1..p.high:
if p[i] > m: p[i] = m
m = p[i]
of Down:
for i in 1..p.high:
if p[i] < m: p[i] = m
m = p[i]
for i in 0..p.high:
if p[i] > 1: p[i] = 1
func schwartzian(p, mult: PValues; dir: Direction): PValues =
let length = p.len
let sortOrder = if dir == Up: Descending else: Ascending
let order1 = toSeq(p.pairs).sorted((x, y) => cmp(x.val, y.val), sortOrder).mapIt(it.key)
var pa = newPValues(length)
for i in 0..pa.high:
pa[i] = mult[i] * p[order1[i]]
ratchet(pa, dir)
let order2 = toSeq(order1.pairs).sortedByIt(it.val).mapIt(it.key)
for idx in order2:
result.add pa[idx]
proc adjust(p: PValues; ctype: CorrectionType): PValues =
let length = p.len
assert length > 0
let flength = length.toFloat
case ctype
of BenjaminiHochberg:
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = flength / (flength - i.toFloat)
return schwartzian(p, mult, Up)
of BenjaminiYekutieli:
var q = 0.0
for i in 1..length: q += 1 / i
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = (q * flength) / (flength - i.toFloat)
return schwartzian(p, mult, Up)
of Bonferroni:
result = newPValues(length)
for i in 0..result.high:
result[i] = min(p[i] * flength, 1)
return
of Hochberg:
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = i.toFloat + 1
return schwartzian(p, mult, Up)
of Holm:
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = flength - i.toFloat
return schwartzian(p, mult, Down)
of Hommel:
let order1 = toSeq(p.pairs).sortedByIt(it.val).mapIt(it.key)
let s = order1.mapIt(p[it])
var m = Inf
for i in 0..s.high:
m = min(m, s[i] * flength / (i + 1).toFloat)
var q, pa = repeat(m, length)
for j in countdown(length - 1, 2):
let lower = toSeq(0..length - j)
let upper = toSeq((length - j + 1)..<length)
var qmin = j.toFloat * s[upper[0]] / 2
for i in 1..upper.high:
let val = s[upper[i]] * j.toFloat / (i + 2).toFloat
if val < qmin: qmin = val
for idx in lower: q[idx] = min(s[idx] * j.toFloat, qmin)
for idx in upper: q[idx] = q[^j]
for i, val in q:
if pa[i] < val: pa[i] = val
let order2 = toSeq(order1.pairs).sortedByIt(it.val).mapIt(it.key)
return order2.mapIt(pa[it])
of Šidák:
result = newPValues(length)
for i in 0..result.high:
result[i] = 1 - (1 - p[i])^length
return
func pformat(p: PValues; cols = 5): string =
var lines: seq[string]
for i in countup(0, p.high, cols):
let fchunk = p[i..<(i + cols)]
var schunk = newSeq[string](fchunk.len)
for j in 0..<cols:
schunk[j] = fchunk[j].formatFloat(ffDecimal, 10)
lines.add &"[{i:2}] {schunk.join(\" \")}"
result = lines.join("\n")
func adjusted(p: PValues; ctype: CorrectionType): string =
doAssert p.len > 0 and min(p) >= 0 and max(p) <= 1, "p-values must be in range 0.0 to 1.0."
result = &"\n{ctype}\n{pformat(p.adjust(ctype))}"
when isMainModule:
const PVals = @[
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 in CorrectionType:
echo adjusted(PVals, ctype)
- 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
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.
#!/usr/bin/env perl
use strict;
use warnings FATAL => 'all';
use autodie ':all';
use List::Util 'min';
use feature 'say';
sub pmin {
my $array = shift;
my $x = 1;
my @pmin_array;
my $n = scalar @$array;
for (my $index = 0; $index < $n; $index++) {
$pmin_array[$index] = min(@$array[$index], $x);
}
@pmin_array
}
sub cummin {
my $array_ref = shift;
my @cummin;
my $cumulative_min = @$array_ref[0];
foreach my $p (@$array_ref) {
if ($p < $cumulative_min) {
$cumulative_min = $p;
}
push @cummin, $cumulative_min;
}
@cummin
}
sub cummax {
my $array_ref = shift;
my @cummax;
my $cumulative_max = @$array_ref[0];
foreach my $p (@$array_ref) {
if ($p > $cumulative_max) {
$cumulative_max = $p;
}
push @cummax, $cumulative_max;
}
@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;
}
}
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;
}
@array
}
sub p_adjust {
my $pvalues_ref = shift;
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);
my @pmin = pmin(\@cummin);
my @ro = order(\@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);
my @cummin = cummin(\@cummin_input);
my @pmin = pmin(\@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