P-value correction: Difference between revisions
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{{
Given a list of [[wp:p-value|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 "[[wp:False discovery rate|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:
Line 15 ⟶ 21:
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:
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* Yosef Hochberg, "A sharper Bonferroni procedure for multiple tests of significance", ''Biometrika'', Vol. 75, No. 4 (1988), pp 800–802, DOI:[https://doi.org/10.1093/biomet/75.4.800 10.1093/biomet/75.4.800] JSTOR:[https://www.jstor.org/stable/2336325 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:[https://doi.org/10.1093/biomet/75.2.383 10.1093/biomet/75.2.383] JSTOR:[https://www.jstor.org/stable/2336190 2336190]
Each method has its own advantages and disadvantages.
<br><br>
=={{header|C}}==
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Link with <code>-lm</code>
<
#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 *
//named after R function of same name, but simpler function
if (START == END) {
unsigned int *restrict sequence = malloc( (end+1) * sizeof(unsigned int));
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exit(EXIT_FAILURE);
}
for (
sequence[i] = i+1;
}
Line 67 ⟶ 77:
}
if (START > END) {
end = (unsigned)START;
start = (unsigned)END;
}
const
unsigned int *restrict sequence = malloc( (1+LENGTH) * sizeof(unsigned int));
if (sequence == NULL) {
Line 78 ⟶ 88:
}
if (START < END) {
for (
sequence[index] = start + index;
}
} else {
for (
sequence[index] = end - index;
}
Line 115 ⟶ 125:
}
unsigned int *
//this has the same name as the same R function
unsigned int *restrict idx = malloc(SIZE * sizeof(unsigned int));
Line 142 ⟶ 152:
}
double *
//this takes the same name of the R function which it copies
//this requires a free() afterward where it is used
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}
double *
//this takes the same name of the R function which it copies
//this requires a free() afterward where it is used
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}
double cumulative_max = ARRAY[0];
for (
if (ARRAY[i] > cumulative_max) {
cumulative_max = ARRAY[i];
Line 190 ⟶ 200:
}
double *
//named after the R function pmin
if (NO_OF_ARRAY_ELEMENTS < 1) {
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void double_say (const double *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) {
printf("[1] %e", ARRAY[0]);
for (
printf(" %.10f", ARRAY[i]);
if (((i+1) % 5) == 0) {
printf("\n[%
}
}
Line 233 ⟶ 243:
}*/
double *
double *restrict doubleArray = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (doubleArray == NULL) {
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exit(EXIT_FAILURE);
}
for (
doubleArray[index] = (double)ARRAY[index];
}
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}
double *
//this function is a translation of R's p.adjust "BH" method
// i is always i[index] = NO_OF_ARRAY_ELEMENTS - index - 1
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}
short int TYPE = -1;
if
TYPE = 0;
} else if (strcasecmp(STRING, "BH") == 0) {
TYPE = 0;
} else if (strcasecmp(STRING, "fdr") == 0) {
Line 291 ⟶ 303:
exit(EXIT_FAILURE);
}
for (
const double BONFERRONI = PVALUES[index] * NO_OF_ARRAY_ELEMENTS;
if (BONFERRONI >= 1.0) {
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double *restrict o2double = uint2double(o, NO_OF_ARRAY_ELEMENTS);
double *restrict cummax_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
for (
cummax_input[index] = (NO_OF_ARRAY_ELEMENTS - index ) * (double)PVALUES[o[index]];
// printf("cummax_input[%zu] = %e\n", index, cummax_input[index]);
}
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free(cummax_output); cummax_output = NULL;
double *restrict qvalues = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
for (
qvalues[index] = pmin[ro[index]];
}
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exit(EXIT_FAILURE);
}
for (
p[index] = PVALUES[o[index]];
}
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}
double min = (double)NO_OF_ARRAY_ELEMENTS * p[0];
for (
const double TEMP = (double)NO_OF_ARRAY_ELEMENTS * p[index] / (double)(1+index);
if (TEMP < min) {
min = TEMP;
}
}
for (
pa[index] = min;
q[index] = min;
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}
*/
for (
// printf("j = %zu\n", j);
unsigned int *restrict ij = seq_len(
const size_t I2_LENGTH = j - 1;
unsigned int *restrict i2 = malloc(I2_LENGTH * sizeof(unsigned int));
for (
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 (
const double TEMP_Q1 = (double)j * p[i2[i]] / (double)(2 + i);
if (TEMP_Q1 < q1) {
q1 = TEMP_Q1;
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}
for (
q[ij[i]] = min2( (double)j*p[ij[i]], q1);
}
free(ij); ij = NULL;
for (
q[i2[i]] = q[NO_OF_ARRAY_ELEMENTS - j];//subtract 1 because of starting index difference
}
free(i2); i2 = NULL;
for (
if (pa[i] < q[i]) {
pa[i] = q[i];
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}//end j loop
free(p); p = NULL;
for (
q[index] = pa[ro[index]];//Hommel q-values
}
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double *restrict cummin_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (TYPE == 0) {//BH method
for (
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 (
q +=
}
for (
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 (
// pmin(1, cummin((n - i + 1L) * p[o]))[ro]
cummin_input[index] = (double)(index + 1) * PVALUES[o[index]];
}
}
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return q_array;
}
int main(void) {
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return 0;
}
</syntaxhighlight>
{{out}}
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{{works with|C89}}
{{trans|Kotlin}}
To avoid licensing issues, this version is a translation of the Kotlin entry (Version 2) which is itself a partial translation of the
<
#include <stdlib.h>
#include <math.h>
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each_i(0, 8) adjusted(p_values, types[i]);
return 0;
}</
{{output}}
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</pre>
=={{header|C
{{trans|Java}}
<syntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.Linq;
Line 1,625 ⟶ 1,227:
}
}
}</
{{out}}
<pre>[ 1] 6.126681E-001 8.521710E-001 1.987205E-001 1.891595E-001 3.217789E-001
Line 1,704 ⟶ 1,306:
[50]
type 5 = 'hommel' has a cumulative error of 4.353024E-007</pre>
=={{header|C++}}==
{{trans|Java}}
<syntaxhighlight lang="cpp">#include <algorithm>
#include <functional>
#include <iostream>
#include <numeric>
#include <vector>
std::vector<int> seqLen(int start, int end) {
std::vector<int> result;
if (start == end) {
result.resize(end + 1);
std::iota(result.begin(), result.end(), 1);
} else if (start < end) {
result.resize(end - start + 1);
std::iota(result.begin(), result.end(), start);
} else {
result.resize(start - end + 1);
std::iota(result.rbegin(), result.rend(), end);
}
return result;
}
std::vector<int> order(const std::vector<double>& arr, bool decreasing) {
std::vector<int> idx(arr.size());
std::iota(idx.begin(), idx.end(), 0);
std::function<bool(int, int)> cmp;
if (decreasing) {
cmp = [&arr](int a, int b) { return arr[b] < arr[a]; };
} else {
cmp = [&arr](int a, int b) { return arr[a] < arr[b]; };
}
std::sort(idx.begin(), idx.end(), cmp);
return idx;
}
std::vector<double> cummin(const std::vector<double>& arr) {
if (arr.empty()) throw std::runtime_error("cummin requries at least one element");
std::vector<double> output(arr.size());
double cumulativeMin = arr[0];
std::transform(arr.cbegin(), arr.cend(), output.begin(), [&cumulativeMin](double a) {
if (a < cumulativeMin) cumulativeMin = a;
return cumulativeMin;
});
return output;
}
std::vector<double> cummax(const std::vector<double>& arr) {
if (arr.empty()) throw std::runtime_error("cummax requries at least one element");
std::vector<double> output(arr.size());
double cumulativeMax = arr[0];
std::transform(arr.cbegin(), arr.cend(), output.begin(), [&cumulativeMax](double a) {
if (cumulativeMax < a) cumulativeMax = a;
return cumulativeMax;
});
return output;
}
std::vector<double> pminx(const std::vector<double>& arr, double x) {
if (arr.empty()) throw std::runtime_error("pmin requries at least one element");
std::vector<double> result(arr.size());
std::transform(arr.cbegin(), arr.cend(), result.begin(), [&x](double a) {
if (a < x) return a;
return x;
});
return result;
}
void doubleSay(const std::vector<double>& arr) {
printf("[ 1] %.10f", arr[0]);
for (size_t i = 1; i < arr.size(); ++i) {
printf(" %.10f", arr[i]);
if ((i + 1) % 5 == 0) printf("\n[%2d]", i + 1);
}
}
std::vector<double> pAdjust(const std::vector<double>& pvalues, const std::string& str) {
if (pvalues.empty()) throw std::runtime_error("pAdjust requires at least one element");
size_t size = pvalues.size();
int type;
if ("bh" == str || "fdr" == str) {
type = 0;
} else if ("by" == str) {
type = 1;
} else if ("bonferroni" == str) {
type = 2;
} else if ("hochberg" == str) {
type = 3;
} else if ("holm" == str) {
type = 4;
} else if ("hommel" == str) {
type = 5;
} else {
throw std::runtime_error(str + " doesn't match any accepted FDR types");
}
// Bonferroni method
if (2 == type) {
std::vector<double> result(size);
for (size_t i = 0; i < size; ++i) {
double b = pvalues[i] * size;
if (b >= 1) {
result[i] = 1;
} else if (0 <= b && b < 1) {
result[i] = b;
} else {
throw std::runtime_error("a value is outside [0, 1)");
}
}
return result;
}
// Holm method
else if (4 == type) {
auto o = order(pvalues, false);
std::vector<double> o2Double(o.begin(), o.end());
std::vector<double> cummaxInput(size);
for (size_t i = 0; i < size; ++i) {
cummaxInput[i] = (size - i) * pvalues[o[i]];
}
auto ro = order(o2Double, false);
auto cummaxOutput = cummax(cummaxInput);
auto pmin = pminx(cummaxOutput, 1.0);
std::vector<double> result(size);
std::transform(ro.cbegin(), ro.cend(), result.begin(), [&pmin](int a) { return pmin[a]; });
return result;
}
// Hommel
else if (5 == type) {
auto indices = seqLen(size, size);
auto o = order(pvalues, false);
std::vector<double> p(size);
std::transform(o.cbegin(), o.cend(), p.begin(), [&pvalues](int a) { return pvalues[a]; });
std::vector<double> o2Double(o.begin(), o.end());
auto ro = order(o2Double, false);
std::vector<double> q(size);
std::vector<double> pa(size);
std::vector<double> npi(size);
for (size_t i = 0; i < size; ++i) {
npi[i] = p[i] * size / indices[i];
}
double min = *std::min_element(npi.begin(), npi.end());
std::fill(q.begin(), q.end(), min);
std::fill(pa.begin(), pa.end(), min);
for (int j = size; j >= 2; --j) {
auto ij = seqLen(1, size - j + 1);
std::transform(ij.cbegin(), ij.cend(), ij.begin(), [](int a) { return a - 1; });
int i2Length = j - 1;
std::vector<int> i2(i2Length);
for (int i = 0; i < i2Length; ++i) {
i2[i] = size - j + 2 + i - 1;
}
double q1 = j * p[i2[0]] / 2.0;
for (int i = 1; i < i2Length; ++i) {
double temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
for (size_t i = 0; i < size - j + 1; ++i) {
q[ij[i]] = std::min(p[ij[i]] * j, q1);
}
for (int i = 0; i < i2Length; ++i) {
q[i2[i]] = q[size - j];
}
for (size_t i = 0; i < size; ++i) {
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
}
std::transform(ro.cbegin(), ro.cend(), q.begin(), [&pa](int a) { return pa[a]; });
return q;
}
std::vector<double> ni(size);
std::vector<int> o = order(pvalues, true);
std::vector<double> od(o.begin(), o.end());
for (size_t i = 0; i < size; ++i) {
if (pvalues[i] < 0 || pvalues[i]>1) {
throw std::runtime_error("a value is outside [0, 1]");
}
ni[i] = (double)size / (size - i);
}
auto ro = order(od, false);
std::vector<double> cumminInput(size);
if (0 == type) { // BH method
for (size_t i = 0; i < size; ++i) {
cumminInput[i] = ni[i] * pvalues[o[i]];
}
} else if (1 == type) { // BY method
double q = 0;
for (size_t i = 1; i < size + 1; ++i) {
q += 1.0 / i;
}
for (size_t i = 0; i < size; ++i) {
cumminInput[i] = q * ni[i] * pvalues[o[i]];
}
} else if (3 == type) { // Hochberg method
for (size_t i = 0; i < size; ++i) {
cumminInput[i] = (i + 1) * pvalues[o[i]];
}
}
auto cumminArray = cummin(cumminInput);
auto pmin = pminx(cumminArray, 1.0);
std::vector<double> result(size);
for (size_t i = 0; i < size; ++i) {
result[i] = pmin[ro[i]];
}
return result;
}
int main() {
using namespace std;
vector<double> pvalues{
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
vector<vector<double>> correctAnswers{
// Benjamini-Hochberg
{
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
},
// Benjamini & Yekutieli
{
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
},
// Bonferroni
{
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
},
// Hochberg
{
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
// Holm
{
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
// Hommel
{
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
}
};
vector<string> types{ "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
for (size_t type = 0; type < types.size(); ++type) {
auto q = pAdjust(pvalues, types[type]);
double error = 0.0;
for (size_t i = 0; i < pvalues.size(); ++i) {
error += abs(q[i] - correctAnswers[type][i]);
}
doubleSay(q);
printf("\ntype = %d = '%s' has a cumulative error of %g\n\n\n", type, types[type].c_str(), error);
}
return 0;
}</syntaxhighlight>
{{out}}
<pre>[ 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</pre>
=={{header|D}}==
{{trans|Kotlin}}
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<
import std.conv;
import std.math;
Line 2,047 ⟶ 2,057:
writefln("\ntype %d = '%s' has a cumulative error of %g", type, types[type], error);
}
}</
{{out}}
<pre>[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
Line 2,130 ⟶ 2,140:
=={{header|Go}}==
{{trans|Kotlin (Version 2)}}
<
import (
Line 2,433 ⟶ 2,443:
fmt.Println(s)
}
}</
{{out}}
Line 2,536 ⟶ 2,546:
{{works with|Java|8}}
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<
import java.util.Comparator;
Line 2,885 ⟶ 2,895:
}
}
}</
{{out}}
<pre>[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
Line 2,966 ⟶ 2,976:
type 5 = 'hommel' has a cumulative error of 4.35302e-07</pre>
=={{header|
'''Adapted from [[#Wren|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.
<syntaxhighlight lang="jq">
### 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[] )
</syntaxhighlight>
{{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.
<pre>
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
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using MultipleTesting, IterTools, Printf
p = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
Line 2,994 ⟶ 3,261:
println("\n", corr)
printpvalues(adjust(p, corr))
end</
{{out}}
Line 3,051 ⟶ 3,318:
''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 [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<
import java.util.Arrays
Line 3,332 ⟶ 3,599:
println(f.format(type, types[type], error))
}
}</
{{out}}
Line 3,417 ⟶ 3,684:
===Version 2 ===
{{trans|
To avoid licensing issues, this version follows the approach of the
<
typealias DList = List<Double>
Line 3,565 ⟶ 3,832:
types.forEach { println(adjusted(pValues, it)) }
}</
{{out}}
Same as
<pre>
....
Line 3,594 ⟶ 3,861:
Šidák
</pre>
=={{header|Nim}}==
{{trans|Kotlin (Version 2)}}
<syntaxhighlight lang="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)</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">
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</pre>
=={{header|Perl}}==
{{trans|C}}
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<
use strict;
use warnings FATAL => 'all';
use autodie ':all';
use List::Util 'min';
use feature 'say';
sub pmin {
my $
my $x = 1;
my @pmin_array;
my $n = scalar @$
for (my $index = 0; $index < $n; $index++) {
}
}
sub cummin {
my $array_ref = shift;
my @cummin;
my $cumulative_min = @$array_ref[0];
Line 3,636 ⟶ 4,138:
push @cummin, $cumulative_min;
}
}
sub cummax {
my $array_ref = shift;
my @cummax;
my $cumulative_max = @$array_ref[0];
Line 3,653 ⟶ 4,151:
push @cummax, $cumulative_max;
}
}
Line 3,669 ⟶ 4,167:
die;
}
}
my @array;
Line 3,681 ⟶ 4,175:
@array = sort { @$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 = (
Line 3,711 ⟶ 4,201:
$method = $key;
$method_found = 'yes';
last
}
}
Line 3,725 ⟶ 4,215:
if ($method_found eq 'no') {
print "No method could be determined from $method.\n";
die
}
my $lp = scalar @$pvalues_ref;
Line 3,737 ⟶ 4,227:
}
my @cummin = cummin(\@cummin_input);
my @pmin = pmin(\@cummin);
my @ro = order(\@o);
@qvalues = @pmin[@ro];
} elsif ($method eq 'bh') {
Line 3,750 ⟶ 4,237:
}
my @ro = order(\@o);
my @cummin = cummin(\@cummin_input);
my @pmin = pmin(\@cummin);
@qvalues = @pmin[@ro];
} elsif ($method eq 'by') {
Line 3,767 ⟶ 4,251:
$cummin_input[$index] = $q * ($n/($n-$index)) * @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o]
}
# say join (',', @cummin_input);
# say '@cummin_input # of elements = ' . scalar @cummin_input;
my @cummin = cummin(\@cummin_input);
undef @cummin_input;
my @pmin = pmin(\@cummin);
@qvalues = @pmin[@ro];
} elsif ($method eq 'bonferroni') {
Line 3,780 ⟶ 4,265:
$qvalues[$index] = 1.0;
} else {
die;
}
Line 3,798 ⟶ 4,283:
@qvalues = @pmin[@ro];
} elsif ($method eq 'hommel') {
my @o = order($pvalues_ref);
my @p = @$pvalues_ref[@o];
my @ro = order(\@o);
undef @o;
my (@q, @pa);
my $min = $n*$p[0];
for (my $index = 0; $index < $n; $index++) {
my $temp = $n*$p[$index] / ($index + 1);
}
for (my $index = 0; $index < $n; $index++) {
Line 3,817 ⟶ 4,298:
}
for (my $j = ($n-1); $j >= 2; $j--) {
my @ij = 0..($n - $j);#ij <- seq_len(n - j + 1)
my $I2_LENGTH = $j - 1;
my @i2;
Line 3,832 ⟶ 4,309:
for (my $i = 1; $i < $I2_LENGTH; $i++) {#loop through 2:j
my $TEMP_Q1 = $j * $p[$i2[$i]] / (2 + $i);
}
for (my $i = 0; $i < ($n - $j + 1); $i++) {#q[ij] <- pmin(j * p[ij], q1)
$q[$ij[$i]] = min( $j*$p[$ij[$i]], $q1);
Line 3,842 ⟶ 4,316:
for (my $i = 0; $i < $I2_LENGTH; $i++) {#q[i2] <- q[n - j + 1]
$q[$i2[$i]] = $q[$n - $j];
}
Line 3,856 ⟶ 4,330:
} else {
print "$method doesn't fit my types.\n";
die
}
}
my @pvalues = (4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
Line 3,945 ⟶ 4,419:
printf("type $method has cumulative error of %g.\n", $error);
}
</syntaxhighlight>
{{out}}
Line 3,962 ⟶ 4,436:
type Hommel has cumulative error of 4.35302e-07.
</pre>
=={{header|Phix}}==
Translation of Kotlin (version 2), except for the Hommel part, which is translated from Go.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DOWN</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">ratchet</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">=</span><span style="color: #000000;">UP</span><span style="color: #0000FF;">?</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]></span><span style="color: #000000;">m</span><span style="color: #0000FF;">:</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sq_min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">order</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">custom_sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">=</span><span style="color: #000000;">UP</span> <span style="color: #008080;">then</span> <span style="color: #000000;">order</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">order</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">pa</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ratchet</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">order</span><span style="color: #0000FF;">)),</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">order</span><span style="color: #0000FF;">,</span><span style="color: #000000;">invert</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">adjust</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">method</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">size</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">method</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Benjamini-Hochberg"</span><span style="color: #0000FF;">:</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Benjamini-Yekutieli"</span><span style="color: #0000FF;">:</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">*</span><span style="color: #000000;">size</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Bonferroni"</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sq_min</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Hochberg"</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Holm"</span><span style="color: #0000FF;">:</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DOWN</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Hommel"</span><span style="color: #0000FF;">:</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ivdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">size</span> <span style="color: #008080;">do</span> <span style="color: #000000;">ivdx</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">i</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">ivdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ivdx</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ivdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">qh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">),</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">pa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">),</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">order</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ivdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lwr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">upr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">qmin</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]/</span><span style="color: #000000;">2</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">qmin</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]*</span><span style="color: #000000;">j</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">qmin</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lwr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">qh</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lwr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lwr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]*</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">qmin</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">qh</span><span style="color: #0000FF;">[</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">qh</span><span style="color: #0000FF;">[</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">pa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">qh</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">order</span><span style="color: #0000FF;">,</span><span style="color: #000000;">invert</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Sidak"</span><span style="color: #0000FF;">:</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">-</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
<span style="color: #008080;">else</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- (unknown method)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">types</span><span style="color: #0000FF;">,</span><span style="color: #000000;">correct_answers</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Benjamini-Hochberg"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">6.126681e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.521710e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.987205e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.891595e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.217789e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.301450e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.870370e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.301450e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.049731e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.826753e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">6.482629e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.253722e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.280973e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.769926e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.705703e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.241867e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.049731e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.856107e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.887526e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.136717e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.991891e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.769926e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.217789e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.301450e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.304958e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.832475e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.899547e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.521710e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.476843e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.683638e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.562902e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.516084e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.250189e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.636589e-03</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.562902e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.946883e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.166064e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.899547e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.688991e-03</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.502862e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.881555e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.142613e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.846527e-03</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.562902e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.846527e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.101708e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.252032e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.205958e-02</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Benjamini-Yekutieli"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.940844e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.510676e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.114323e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.754486e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.644618e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">7.575031e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.153102e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.581959e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.812089e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.636176e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.153102e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.325863e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.774239e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.754486e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.209832e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.025930e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.634031e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.546073e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.413926e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.180552e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.153102e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.180552e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.956812e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.262838e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.925057e-02</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Bonferroni"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.019185e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.020365e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.516674e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.625735e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.909271e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.537741e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.125636e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.782670e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.803480e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.882294e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.005725e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.713920e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.395577e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.088915e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.846527e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.305125e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.867745e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Hochberg"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.632662e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.575885e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.383967e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.938014e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.600230e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.501973e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.383967e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.052971e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.426136e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.626366e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.656419e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.825610e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.930759e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.394022e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.692284e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.023581e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.974152e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.172920e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.992520e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.179486e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Holm"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.632662e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.575885e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.395341e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.938014e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.600230e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.501973e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.395341e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.052971e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.426136e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.626366e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.656419e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.825610e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.930759e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.394022e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.692284e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.023581e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.974152e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.172920e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.992520e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.179486e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Hommel"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.987624e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.595180e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.351895e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.766522e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.414256e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.304340e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.530937e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.887709e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.385602e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.322457e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.722920e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.426136e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.218158e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.581127e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.825610e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.743649e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.016908e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.516461e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.582456e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.877222e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.172920e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.122276e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.950067e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Sidak"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9946598274</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9914285749</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999515274</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999999688</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999999995</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999998801</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999999855</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9231179729</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.9999999956</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999317605</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.9983109511</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.5068253940</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9703301333</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.1832692440</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0150545753</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.4320729669</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.6993672225</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0286818157</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.0152621104</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3391808707</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0656206307</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.4959194266</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0186503726</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.0009001752</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0000125222</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.8142104886</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3772612062</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0430222116</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.0108312558</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0473319661</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0032997780</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.7705015898</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.2499384839</span><span style="color: #0000FF;">}}})</span>
<span style="color: #000080;font-style:italic;">-- {"Unknown",{1<nowiki>}}</nowiki>})</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">pValues</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">4.533744e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.296024e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.936026e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.079658e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.801962e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.752257e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.922222e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.115421e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.355806e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.324867e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.926798e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.802978e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.485442e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.883130e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.729308e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.502518e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.268138e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.442008e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.030266e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.001555e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">3.194810e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.892933e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.745691e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.037516e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.198578e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.966083e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.403837e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.328671e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.793476e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.040730e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.033349e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.125147e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.375072e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.818542e-04</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">3.075482e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.251272e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.356534e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.360696e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.764588e-04</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.801145e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.504456e-07</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.310253e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.427839e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.791153e-04</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.177831e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.693054e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.610250e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.900813e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.735490e-03</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">)></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"p-values must be in range 0.0 to 1.0"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">types</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ti</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">types</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">adjust</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nSorry, do not know how to do %s correction.\n"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"Perhaps you want one of these?:\n %s\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">types</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #008000;">"\n "</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- printf(1,"%s\n",{ti})
-- res = correct_answers[i] -- (for easier comparison only)
-- pp(res,{pp_FltFmt,"%13.10f",pp_IntFmt,"%13.10f",pp_Maxlen,75,pp_Pause,0})</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">error</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_abs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">correct_answers</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s has cumulative error of %g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">error</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
Matches Kotlin (etc) when some of those lines just above are uncommented.
Line 4,354 ⟶ 4,649:
{{trans|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 [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<
import sys
Line 4,589 ⟶ 4,884:
error += abs(q[i] - correct_answers[key][i])
print '%s error = %g' % (key.upper(), error)
</syntaxhighlight>
{{out}}
Line 4,604 ⟶ 4,899:
The '''p.adjust''' function is built-in, see [https://stat.ethz.ch/R-manual/R-devel/library/stats/html/p.adjust.html R manual].
<
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,
Line 4,632 ⟶ 4,927:
p.adjust(p, method = 'hommel')
writeLines("Hommel\n")</
{{out}}
Line 4,699 ⟶ 4,994:
[46] 9.582456e-03 3.877222e-02 3.172920e-03 8.122276e-01 1.950067e-01
Hommel</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2019.03.1}}
<syntaxhighlight lang="raku" line>########################### Helper subs ###########################
sub adjusted (@p, $type) { "\n$type\n" ~ format adjust( check(@p), $type ) }
sub format ( @p, $cols = 5 ) {
my $i = -$cols;
my $fmt = "%1.10f";
join "\n", @p.rotor($cols, :partial).map:
{ sprintf "[%2d] { join ' ', $fmt xx $_ }", $i+=$cols, $_ };
}
sub check ( @p ) { die 'p-values must be in range 0.0 to 1.0' if @p.min < 0 or 1 < @p.max; @p }
multi ratchet ( 'up', @p ) { my $m; @p[$_] min= $m, $m = @p[$_] for ^@p; @p }
multi ratchet ( 'dn', @p ) { my $m; @p[$_] max= $m, $m = @p[$_] for ^@p .reverse; @p }
sub schwartzian ( @p, &transform, :$ratchet ) {
my @pa = @p.map( {[$_, $++]} ).sort( -*.[0] ).map: { [transform(.[0]), .[1]] };
@pa[*;0] = ratchet($ratchet, @pa»[0]);
@pa.sort( *.[1] )»[0]
}
############# The various p-value correction routines #############
multi adjust( @p, 'Benjamini-Hochberg' ) {
@p.&schwartzian: * * @p / (@p - $++) min 1, :ratchet('up')
}
multi adjust( @p, 'Benjamini-Yekutieli' ) {
my \r = ^@p .map( { 1 / ++$ } ).sum;
@p.&schwartzian: * * r * @p / (@p - $++) min 1, :ratchet('up')
}
multi adjust( @p, 'Hochberg' ) {
my \m = @p.max;
@p.&schwartzian: * * ++$ min m, :ratchet('up')
}
multi adjust( @p, 'Holm' ) {
@p.&schwartzian: * * ++$ min 1, :ratchet('dn')
}
multi adjust( @p, 'Šidák' ) {
@p.&schwartzian: 1 - (1 - *) ** ++$, :ratchet('dn')
}
multi adjust( @p, 'Bonferroni' ) {
@p.map: * * @p min 1
}
# Hommel correction can't be easily reduced to a one pass transform
multi adjust( @p, 'Hommel' ) {
my @s = @p.map( {[$_, $++]} ).sort: *.[0] ; # sorted
my \z = +@p; # array si(z)e
my @pa = @s»[0].map( * * z / ++$ ).min xx z; # p adjusted
my @q; # scratch array
for (1 ..^ z).reverse -> $i {
my @L = 0 .. z - $i; # lower indices
my @U = z - $i ^..^ z; # upper indices
my $q = @s[@U]»[0].map( { $_ * $i / (2 + $++) } ).min;
@q[@L] = @s[@L]»[0].map: { min $_ * $i, $q, @s[*-1][0] };
@pa = ^z .map: { max @pa[$_], @q[$_] }
}
@pa[@s[*;1].map( {[$_, $++]} ).sort( *.[0] )»[1]]
}
multi adjust ( @p, $unknown ) {
note "\nSorry, do not know how to do $unknown correction.\n" ~
"Perhaps you want one of these?:\n" ~
<Benjamini-Hochberg Benjamini-Yekutieli Bonferroni Hochberg
Holm Hommel Šidák>.join("\n");
exit
}
########################### The task ###########################
my @p-values =
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
;
for < Benjamini-Hochberg Benjamini-Yekutieli Bonferroni Hochberg Holm Hommel Šidák >
{
say adjusted @p-values, $_
}</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">Benjamini-Hochberg
[ 0] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502863 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
Benjamini-Yekutieli
[ 0] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
Bonferroni
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
Hochberg
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Holm
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Hommel
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825611 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
Šidák
[ 0] 0.9998642526 0.9999922727 0.9341844137 0.9234670175 0.9899922294
[ 5] 0.9999922727 0.9992955735 0.9999922727 0.9998642526 0.9998909746
[10] 0.9998642526 0.9999288207 0.9995533892 0.9999922727 0.9990991210
[15] 0.9999922727 0.9998642526 0.9999674876 0.9992955735 0.7741716825
[20] 0.9993332472 0.9999922727 0.9999922727 0.9899922294 0.9999922727
[25] 0.9589019598 0.9998137104 0.3728369461 0.9999922727 0.8605248833
[30] 0.1460714182 0.0138585952 0.3270159382 0.5366136349 0.0247164330
[35] 0.0138585952 0.2640282766 0.0528503728 0.3723753774 0.0164308228
[40] 0.0008821796 0.0000125222 0.6357389664 0.2889497995 0.0362651575
[45] 0.0101847015 0.0389807074 0.0031679962 0.5985019850 0.1963376344</pre>
=={{header|Ruby}}==
{{trans|Perl}}
<syntaxhighlight lang="ruby">def pmin(array)
x = 1
pmin_array = []
array.each_index do |i|
pmin_array[i] = [array[i], x].min
abort if pmin_array[i] > 1
end
pmin_array
end
def cummin(array)
cumulative_min = array[0]
arr_cummin = []
array.each do |p|
cumulative_min = [p, cumulative_min].min
arr_cummin.push(cumulative_min)
end
arr_cummin
end
def cummax(array)
cumulative_max = array[0]
arr_cummax = []
array.each do |p|
cumulative_max = [p, cumulative_max].max
arr_cummax.push(cumulative_max)
end
arr_cummax
end
# decreasing variable is optional
def order(array, decreasing = false)
if decreasing == false
array.sort.map { |n| array.index(n) }
else
array.sort.map { |n| array.index(n) }.reverse
end
end
def p_adjust(arr_pvalues, method = 'Holm')
lp = arr_pvalues.size
n = lp
if method.casecmp('hochberg').zero?
arr_o = order(arr_pvalues, true)
arr_cummin_input = []
(0..n).each do |index|
arr_cummin_input[index] = (index + 1) * arr_pvalues[arr_o[index].to_i]
end
arr_cummin = cummin(arr_cummin_input)
arr_pmin = pmin(arr_cummin)
arr_ro = order(arr_o)
return arr_pmin.values_at(*arr_ro)
elsif method.casecmp('bh').zero? || method.casecmp('benjamini-hochberg').zero?
arr_o = order(arr_pvalues, true)
arr_cummin_input = []
(0..(n - 1)).each do |i|
arr_cummin_input[i] = (n / (n - i).to_f) * arr_pvalues[arr_o[i]]
end
arr_ro = order(arr_o)
arr_cummin = cummin(arr_cummin_input)
arr_pmin = pmin(arr_cummin)
return arr_pmin.values_at(*arr_ro)
elsif method.casecmp('by').zero? || method.casecmp('benjamini-yekutieli').zero?
q = 0.0
arr_o = order(arr_pvalues, true)
arr_ro = order(arr_o)
(1..n).each do |index|
q += 1.0 / index
end
arr_cummin_input = []
(0..(n - 1)).each do |i|
arr_cummin_input[i] = q * (n / (n - i).to_f) * arr_pvalues[arr_o[i]]
end
arr_cummin = cummin(arr_cummin_input)
arr_pmin = pmin(arr_cummin)
return arr_pmin.values_at(*arr_ro)
elsif method.casecmp('bonferroni').zero?
arr_qvalues = []
(0..(n - 1)).each do |i|
q = arr_pvalues[i] * n
if (q >= 0) && (q < 1)
arr_qvalues[i] = q
elsif q >= 1
arr_qvalues[i] = 1.0
else
puts "Falied to get Bonferroni adjusted p for #{arr_pvalues[i]}"
end
end
return arr_qvalues
elsif method.casecmp('holm').zero?
o = order(arr_pvalues)
cummax_input = []
(0..(n - 1)).each do |index|
cummax_input[index] = (n - index) * arr_pvalues[o[index]]
end
ro = order(o)
arr_cummax = cummax(cummax_input)
arr_pmin = pmin(arr_cummax)
return arr_pmin.values_at(*ro)
elsif method.casecmp('hommel').zero?
o = order(arr_pvalues)
arr_p = arr_pvalues.values_at(*o)
ro = order(o)
q = []
pa = []
min = n * arr_p[0]
(0..(n - 1)).each do |index|
temp = n * arr_p[index] / (index + 1)
min = [min, temp].min
end
(0..(n - 1)).each do |index|
pa[index] = min
q[index] = min
end
j = n - 1
while j >= 2
ij = Array 0..(n - j)
i2_length = j - 1
i2 = []
(0..(i2_length - 1)).each do |i|
i2[i] = n - j + 2 + i - 1 # R's indices are 1-based, C's are 0-based
end
q1 = j * arr_p[i2[0]] / 2.0
(1..(i2_length - 1)).each do |i|
temp_q1 = j * arr_p[i2[i]] / (2 + i)
q1 = [temp_q1, q1].min
end
(0..(n - j)).each do |i|
tmp = j * arr_p[ij[i]]
q[ij[i]] = [tmp, q1].min
end
(0..(i2_length - 1)).each do |i|
q[i2[i]] = q[n - j]
end
(0..(n - 1)).each do |i|
pa[i] = q[i] if pa[i] < q[i]
end
j -= 1
end
return pa.values_at(*ro)
else
puts "#{method} isn't accepted."
abort
end
end
pvalues =
[4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02,
1.801962e-01, 8.752257e-01, 2.922222e-01, 9.115421e-01,
4.355806e-01, 5.324867e-01, 4.926798e-01, 5.802978e-01,
3.485442e-01, 7.883130e-01, 2.729308e-01, 8.502518e-01,
4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01,
9.037516e-01, 1.198578e-01, 3.966083e-01, 1.403837e-02,
7.328671e-01, 6.793476e-02, 4.040730e-03, 3.033349e-04,
1.125147e-02, 2.375072e-02, 5.818542e-04, 3.075482e-04,
8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03,
8.791153e-04, 2.177831e-04, 9.693054e-04, 6.610250e-05,
2.900813e-02, 5.735490e-03]
correct_answers = {
'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]
}
# correct_answers.each do |method, answers|
methods = ['Benjamini-Yekutieli', 'Benjamini-Hochberg', 'Hochberg',
'Bonferroni', 'Holm', 'Hommel']
methods.each do |method|
puts method
error = 0.0
arr_q = p_adjust(pvalues, method)
arr_q.each_index do |p|
error += (correct_answers[method][p] - arr_q[p])
end
puts "total error for #{method} = #{error}"
end
</syntaxhighlight>
{{out}}
<pre>Benjamini-Yekutieli
total error for Benjamini-Yekutieli = -1.7373780825929845e-07
Benjamini-Hochberg
total error for Benjamini-Hochberg = -1.4736877299143964e-08
Hochberg
total error for Hochberg = -1.2354999978398105e-07
Bonferroni
total error for Bonferroni = 4.49999999152751e-08
Holm
total error for Holm = -1.163499997815258e-07
Hommel
total error for Hommel = 1.1483094955369324e-07
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">
use std::iter;
#[rustfmt::skip]
const PVALUES:[f64;50] = [
4.533_744e-01, 7.296_024e-01, 9.936_026e-02, 9.079_658e-02, 1.801_962e-01,
8.752_257e-01, 2.922_222e-01, 9.115_421e-01, 4.355_806e-01, 5.324_867e-01,
4.926_798e-01, 5.802_978e-01, 3.485_442e-01, 7.883_130e-01, 2.729_308e-01,
8.502_518e-01, 4.268_138e-01, 6.442_008e-01, 3.030_266e-01, 5.001_555e-02,
3.194_810e-01, 7.892_933e-01, 9.991_834e-01, 1.745_691e-01, 9.037_516e-01,
1.198_578e-01, 3.966_083e-01, 1.403_837e-02, 7.328_671e-01, 6.793_476e-02,
4.040_730e-03, 3.033_349e-04, 1.125_147e-02, 2.375_072e-02, 5.818_542e-04,
3.075_482e-04, 8.251_272e-03, 1.356_534e-03, 1.360_696e-02, 3.764_588e-04,
1.801_145e-05, 2.504_456e-07, 3.310_253e-02, 9.427_839e-03, 8.791_153e-04,
2.177_831e-04, 9.693_054e-04, 6.610_250e-05, 2.900_813e-02, 5.735_490e-03
];
#[derive(Debug)]
enum CorrectionType {
BenjaminiHochberg,
BenjaminiYekutieli,
Bonferroni,
Hochberg,
Holm,
Hommel,
Sidak,
}
enum SortDirection {
Increasing,
Decreasing,
}
/// orders **input** vector by value and multiplies with **multiplier** vector
/// Finally returns the multiplied values in the original order of **input**
fn ordered_multiply(input: &[f64], multiplier: &[f64], direction: &SortDirection) -> Vec<f64> {
let order_by_value = match direction {
SortDirection::Increasing => {
|a: &(f64, usize), b: &(f64, usize)| b.0.partial_cmp(&a.0).unwrap()
}
SortDirection::Decreasing => {
|a: &(f64, usize), b: &(f64, usize)| a.0.partial_cmp(&b.0).unwrap()
}
};
let cmp_minmax = match direction {
SortDirection::Increasing => |a: f64, b: f64| a.gt(&b),
SortDirection::Decreasing => |a: f64, b: f64| a.lt(&b),
};
// add original order index
let mut input_indexed = input
.iter()
.enumerate()
.map(|(idx, &p_value)| (p_value, idx))
.collect::<Vec<_>>();
// order by value desc/asc
input_indexed.sort_unstable_by(order_by_value);
// do the multiplication in place, clamp it at 1.0,
// keep the original index in place
for i in 0..input_indexed.len() {
input_indexed[i] = (
f64::min(1.0, input_indexed[i].0 * multiplier[i]),
input_indexed[i].1,
);
}
// make vector strictly monotonous increasing/decreasing in place
for i in 1..input_indexed.len() {
if cmp_minmax(input_indexed[i].0, input_indexed[i - 1].0) {
input_indexed[i] = (input_indexed[i - 1].0, input_indexed[i].1);
}
}
// re-sort back to original order
input_indexed.sort_unstable_by(|a: &(f64, usize), b: &(f64, usize)| a.1.cmp(&b.1));
// remove ordering index
let (resorted, _): (Vec<_>, Vec<_>) = input_indexed.iter().cloned().unzip();
resorted
}
#[allow(clippy::cast_precision_loss)]
fn hommel(input: &[f64]) -> Vec<f64> {
// using algorith described:
// http://stat.wharton.upenn.edu/~steele/Courses/956/ResourceDetails/MultipleComparision/Writght92.pdf
// add original order index
let mut input_indexed = input
.iter()
.enumerate()
.map(|(idx, &p_value)| (p_value, idx))
.collect::<Vec<_>>();
// order by value asc
input_indexed
.sort_unstable_by(|a: &(f64, usize), b: &(f64, usize)| a.0.partial_cmp(&b.0).unwrap());
let (p_values, order): (Vec<_>, Vec<_>) = input_indexed.iter().cloned().unzip();
let n = input.len();
// initial minimal n*p/i values
// get the smalles of these values
let min_result = (0..n)
.map(|i| ((p_values[i] * n as f64) / (i + 1) as f64))
.fold(1. / 0. /* -inf */, f64::min);
// // initialize result vector with minimal values
let mut result = iter::repeat(min_result).take(n).collect::<Vec<_>>();
for m in (2..n).rev() {
let cmin: f64;
let m_as_float = m as f64;
let mut a = p_values.clone();
// println!("\nn: {}", m);
{
// split p-values into two group
let (_, second) = p_values.split_at(n - m + 1);
// calculate minumum of m*p/i for this second group
cmin = second
.iter()
.zip(2..=m)
.map(|(p, i)| (m_as_float * p) / i as f64)
.fold(1. / 0. /* inf */, f64::min);
}
// replace p values if p<cmin in the second group
((n - m + 1)..n).for_each(|i| a[i] = a[i].max(cmin));
// replace p values if min(cmin, m*p) > p
(0..=(n - m)).for_each(|i| a[i] = a[i].max(f64::min(cmin, m_as_float * p_values[i])));
// store in the result vector if any adjusted p is higher than the current one
(0..n).for_each(|i| result[i] = result[i].max(a[i]));
}
// re-sort into the original order
let mut result = result
.into_iter()
.zip(order.into_iter())
.map(|(p, idx)| (p, idx))
.collect::<Vec<_>>();
result.sort_unstable_by(|a: &(f64, usize), b: &(f64, usize)| a.1.cmp(&b.1));
let (result, _): (Vec<_>, Vec<_>) = result.iter().cloned().unzip();
result
}
#[allow(clippy::cast_precision_loss)]
fn p_value_correction(p_values: &[f64], ctype: &CorrectionType) -> Vec<f64> {
let p_vec = p_values.to_vec();
if p_values.is_empty() {
return p_vec;
}
let fsize = p_values.len() as f64;
match ctype {
CorrectionType::BenjaminiHochberg => {
let multiplier = (0..p_values.len())
.map(|index| fsize / (fsize - index as f64))
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Increasing)
}
CorrectionType::BenjaminiYekutieli => {
let q: f64 = (1..=p_values.len()).map(|index| 1. / index as f64).sum();
let multiplier = (0..p_values.len())
.map(|index| q * fsize / (fsize - index as f64))
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Increasing)
}
CorrectionType::Bonferroni => p_vec
.iter()
.map(|p| f64::min(p * fsize, 1.0))
.collect::<Vec<_>>(),
CorrectionType::Hochberg => {
let multiplier = (0..p_values.len())
.map(|index| 1. + index as f64)
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Increasing)
}
CorrectionType::Holm => {
let multiplier = (0..p_values.len())
.map(|index| fsize - index as f64)
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Decreasing)
}
CorrectionType::Sidak => p_vec
.iter()
.map(|x| 1. - (1. - x).powf(fsize))
.collect::<Vec<_>>(),
CorrectionType::Hommel => hommel(&p_vec),
}
}
// prints array into a nice table, max 5 floats/row
fn array_to_string(a: &[f64]) -> String {
a.chunks(5)
.enumerate()
.map(|(index, e)| {
format!(
"[{:>2}]: {}",
index * 5,
e.iter()
.map(|x| format!("{:>1.10}", x))
.collect::<Vec<_>>()
.join(", ")
)
})
.collect::<Vec<_>>()
.join("\n")
}
fn main() {
let ctypes = [
CorrectionType::BenjaminiHochberg,
CorrectionType::BenjaminiYekutieli,
CorrectionType::Bonferroni,
CorrectionType::Hochberg,
CorrectionType::Holm,
CorrectionType::Sidak,
CorrectionType::Hommel,
];
for ctype in &ctypes {
println!("\n{:?}:", ctype);
println!("{}", array_to_string(&p_value_correction(&PVALUES, ctype)));
}
}
</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">
BenjaminiHochberg:
[ 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
BenjaminiYekutieli:
[ 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
Sidak:
[ 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
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
</pre>
=={{header|SAS}}==
<
input raw_p @@;
cards;
Line 4,719 ⟶ 5,802:
proc multtest pdata=pvalues bon sid hom hoc holm;
run;</
'''output'''
Line 4,796 ⟶ 5,879:
First, install the package with:
<syntaxhighlight lang
Given a dataset containing the p-values in a variable, the qqvalue command generates another variable with the adjusted p-values. Here is an example showing the result with all implemented methods:
<
#delimit ;
Line 4,822 ⟶ 5,905:
}
list</
'''output'''
Line 4,889 ⟶ 5,972:
50. | .00573549 .2867745 .24993848 .21794862 .19633763 .21794862 .02205958 .09925057 |
+-----------------------------------------------------------------------------------------------+</pre>
=={{header|Wren}}==
{{trans|Kotlin (version 2)}}
{{libheader|Wren-dynamic}}
{{libheader|Wren-fmt}}
{{libheader|Wren-seq}}
{{libheader|Wren-math}}
{{libheader|Wren-sort}}
<syntaxhighlight lang="wren">import "./dynamic" for Enum
import "./fmt" for Fmt
import "./seq" for Lst
import "./math" for Nums
import "./sort" for Sort
var Direction = Enum.create("Direction", ["UP", "DOWN"])
// test also for 'Unknown' correction type
var types = [
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
]
var pFormat = Fn.new { |p, cols|
var i = -cols
var fmt = "$1.10f"
return Lst.chunks(p, cols).map { |chunk|
i = i + cols
return Fmt.swrite("[$2d $s", i, chunk.map { |v| Fmt.swrite(fmt, v) }.join(" "))
}.join("\n")
}
var check = Fn.new { |p|
if (p.count == 0 || Nums.min(p) < 0 || Nums.max(p) > 1) {
Fiber.abort("p-values must be in range 0 to 1")
}
return p
}
var ratchet = Fn.new { |p, dir|
var pp = p.toList
var m = pp[0]
if (dir == Direction.UP) {
for (i in 1...pp.count) {
if (pp[i] > m) pp[i] = m
m = pp[i]
}
} else {
for (i in 1...pp.count) {
if (pp[i] < m) pp[i] = m
m = pp[i]
}
}
return pp.map { |v| (v < 1) ? v : 1 }.toList
}
var schwartzian = Fn.new { |p, mult, dir|
var size = p.count
var pwi = List.filled(size, null)
for (i in 0...size) pwi[i] = [i, p[i]]
var cmp = (dir == Direction.UP) ? Fn.new { |a, b| (b[1] - a[1]).sign } :
Fn.new { |a, b| (a[1] - b[1]).sign }
var order = Sort.merge(pwi, cmp).map { |e| e[0] }.toList
var pa = List.filled(size, 0)
for (i in 0...size) pa[i] = mult[i] * p[order[i]]
pa = ratchet.call(pa, dir)
var owi = List.filled(order.count, null)
for (i in 0...order.count) owi[i] = [i, order[i]]
cmp = Fn.new { |a, b| (a[1] - b[1]).sign }
var order2 = Sort.merge(owi, cmp).map { |e| e[0] }.toList
var res = List.filled(size, 0)
for (i in 0...size) res[i] = pa[order2[i]]
return res
}
var adjust = Fn.new { |p, type|
var size = p.count
if (size == 0) Fiber.abort("List cannot be empty.")
if (type == "Benjamini-Hochberg") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = size / (size - i)
return schwartzian.call(p, mult, Direction.UP)
} else if (type == "Benjamini-Yekutieli") {
var q = (1..size).reduce { |acc, i| acc + 1/i }
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = q * size / (size - i)
return schwartzian.call(p, mult, Direction.UP)
} else if (type == "Bonferroni") {
return p.map { |v| (v * size).min(1) }.toList
} else if (type == "Hochberg") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = i + 1
return schwartzian.call(p, mult, Direction.UP)
} else if (type == "Holm") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = size - i
return schwartzian.call(p, mult, Direction.DOWN)
} else if (type == "Hommel") {
var pwi = List.filled(size, null)
for (i in 0...size) pwi[i] = [i, p[i]]
var cmp = Fn.new { |a, b| (a[1] - b[1]).sign }
var order = Sort.merge(pwi, cmp).map { |e| e[0] }.toList
var s = List.filled(size, 0)
for (i in 0...size) s[i] = p[order[i]]
var m = List.filled(size, 0)
for (i in 0...size) m[i] = s[i] * size / (i + 1)
var min = Nums.min(m)
var q = List.filled(size, min)
var pa = List.filled(size, min)
for (j in size-1..2) {
var lower = List.filled(size - j + 1, 0) // lower indices
for (i in 0...lower.count) lower[i] = i
var upper = List.filled(j - 1, 0) // upper indices
for (i in 0...upper.count) upper[i] = size - j + 1 + i
var qmin = j * s[upper[0]] / 2
for (i in 1...upper.count) {
var temp = s[upper[i]] * j / (2 + i)
if (temp < qmin) qmin = temp
}
for (i in 0...lower.count) {
q[lower[i]] = qmin.min(s[lower[i]] * j)
}
for (i in 0...upper.count) q[upper[i]] = q[size - j]
for (i in 0...size) if (pa[i] < q[i]) pa[i] = q[i]
}
var owi = List.filled(order.count, null)
for (i in 0...order.count) owi[i] = [i, order[i]]
var order2 = Sort.merge(owi, cmp).map { |e| e[0] }.toList
var res = List.filled(size, 0)
for (i in 0...size) res[i] = pa[order2[i]]
return res
} else if (type == "Šidák") {
return p.map { |v| 1 - (1 - v).pow(size) }.toList
} else {
System.print("\nSorry, do not know how to do '%(type)' correction.\n" +
"Perhaps you want one of these?:\n" +
types[0...-1].map { |t| " %(t)" }.join("\n")
)
Fiber.suspend()
}
}
var adjusted = Fn.new { |p, type| "\n%(type)\n%(pFormat.call(adjust.call(check.call(p), type), 5))" }
var 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
]
types.each { |type| System.print(adjusted.call(pValues, type)) }</syntaxhighlight>
{{out}}
<pre>
Same as Kotlin (version 2) entry.
</pre>
=={{header|zkl}}==
Line 4,894 ⟶ 6,145:
''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 [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<
psz,pszf := pvalues.len(), psz.toFloat();
n_i := psz.pump(List,'wrap(n){ pszf/(psz - n) }); # N/(N-0),N/(N-1),..
Line 4,958 ⟶ 6,209:
}
psz.pump(List,'wrap(n){ pa[ro[n]] }); // Hommel q-values
}</
<
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
Line 4,984 ⟶ 6,235:
}
println();
}</
{{out}}
<pre style="height:45ex">
|