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{{task|Probability and statistics}}
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: Given one list of [[Welch's_t-test|p-values]], return the p-values correcting for multiple comparisons
p = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03}
There are several methods to do this, see:
- Yoav Benjamini, Yosef Hochberg "[http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_hochberg1995.pdf Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing]", ''Journal of the Royal Statistical Society. Series B'', Vol. 57, No. 1 (1995), pp. 289-300, JSTOR:[http://www.jstor.org/stable/2346101 2346101]
- Yoav Benjamini, Daniel Yekutieli, "[http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_yekutieli_ANNSTAT2001.pdf The control of the false discovery rate in multiple testing under dependency]", ''Ann. Statist.'', Vol. 29, No. 4 (2001), pp. 1165-1188, DOI:[https://doi.org/10.1214/aos/1013699998 10.1214/aos/1013699998] JSTOR:[http://www.jstor.org/stable/2674075 2674075]
- Sture Holm, "A Simple Sequentially Rejective Multiple Test Procedure", ''Scandinavian Journal of Statistics'', Vol. 6, No. 2 (1979), pp. 65-70, JSTOR:[https://www.jstor.org/stable/4615733 4615733]
- 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.
C
Version 1
{{works with|C99}} {{trans|R}} ''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
This work is a translation of the R source code. In order to confirm that the new function is working correctly, each value is compared to R's output and a cumulative absolute error is returned.
The C function p_adjust is designed to work as similarly to the R function p.adjust as possible, and is able to do any one of the methods.
This program, for example, fdr.c, can be compiled by
gcc -o fdr fdr.c -Wall -pedantic -std=c11 -lm -O4
or
clang -o fdr fdr.c -Wall -pedantic -std=c11 -lm -O4.
Link with -lm
#include <stdio.h>//printf
#include <stdlib.h>//qsort
#include <math.h>//fabs
#include <stdbool.h>//bool data type
#include <strings.h>//strcasecmp
unsigned int *restrict seq_len(const size_t START, const size_t END) {
//named after R function of same name, but simpler function
size_t start = START;
size_t end = END;
if (START == END) {
unsigned int *restrict sequence = malloc( (end+1) * sizeof(unsigned int));
if (sequence == NULL) {
printf("malloc failed at %s line %u\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
for (size_t i = 0; i < end; i++) {
sequence[i] = i+1;
}
return sequence;
}
if (START > END) {
end = START;
start = END;
}
const size_t LENGTH = end - start ;
unsigned int *restrict sequence = malloc( (1+LENGTH) * sizeof(unsigned int));
if (sequence == NULL) {
printf("malloc failed at %s line %u\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
if (START < END) {
for (size_t index = 0; index <= LENGTH; index++) {
sequence[index] = start + index;
}
} else {
for (size_t index = 0; index <= LENGTH; index++) {
sequence[index] = end - index;
}
}
return sequence;
}
//modified from https://phoxis.org/2012/07/12/get-sorted-index-orderting-of-an-array/
double *restrict base_arr = NULL;
static int compar_increase (const void *restrict a, const void *restrict b) {
int aa = *((int *restrict ) a), bb = *((int *restrict) b);
if (base_arr[aa] < base_arr[bb]) {
return 1;
} else if (base_arr[aa] == base_arr[bb]) {
return 0;
} else {
return -1;
}
}
static int compar_decrease (const void *restrict a, const void *restrict b) {
int aa = *((int *restrict ) a), bb = *((int *restrict) b);
if (base_arr[aa] < base_arr[bb]) {
return -1;
} else if (base_arr[aa] == base_arr[bb]) {
return 0;
} else {
return 1;
}
}
unsigned int *restrict order (const double *restrict ARRAY, const unsigned int SIZE, const bool DECREASING) {
//this has the same name as the same R function
unsigned int *restrict idx = malloc(SIZE * sizeof(unsigned int));
if (idx == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
base_arr = malloc(sizeof(double) * SIZE);
if (base_arr == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
for (unsigned int i = 0; i < SIZE; i++) {
base_arr[i] = ARRAY[i];
idx[i] = i;
}
if (DECREASING == false) {
qsort(idx, SIZE, sizeof(unsigned int), compar_decrease);
} else if (DECREASING == true) {
qsort(idx, SIZE, sizeof(unsigned int), compar_increase);
}
free(base_arr); base_arr = NULL;
return idx;
}
double *restrict cummin(const double *restrict ARRAY, const unsigned int NO_OF_ARRAY_ELEMENTS) {
//this takes the same name of the R function which it copies
//this requires a free() afterward where it is used
if (NO_OF_ARRAY_ELEMENTS < 1) {
puts("cummin function requires at least one element.\n");
printf("Failed at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
double *restrict output = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (output == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
double cumulative_min = ARRAY[0];
for (unsigned int i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) {
if (ARRAY[i] < cumulative_min) {
cumulative_min = ARRAY[i];
}
output[i] = cumulative_min;
}
return output;
}
double *restrict cummax(const double *restrict ARRAY, const unsigned int NO_OF_ARRAY_ELEMENTS) {
//this takes the same name of the R function which it copies
//this requires a free() afterward where it is used
if (NO_OF_ARRAY_ELEMENTS < 1) {
puts("function requires at least one element.\n");
printf("Failed at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
double *restrict output = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (output == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
double cumulative_max = ARRAY[0];
for (size_t i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) {
if (ARRAY[i] > cumulative_max) {
cumulative_max = ARRAY[i];
}
output[i] = cumulative_max;
}
return output;
}
double *restrict pminx(const double *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS, const double X) {
//named after the R function pmin
if (NO_OF_ARRAY_ELEMENTS < 1) {
puts("pmin requires at least one element.\n");
printf("Failed at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
double *restrict pmin_array = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (pmin_array == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
if (ARRAY[index] < X) {
pmin_array[index] = ARRAY[index];
} else {
pmin_array[index] = X;
}
}
return pmin_array;
}
void double_say (const double *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) {
printf("[1] %e", ARRAY[0]);
for (size_t i = 1; i < NO_OF_ARRAY_ELEMENTS; i++) {
printf(" %.10f", ARRAY[i]);
if (((i+1) % 5) == 0) {
printf("\n[%zu]", i+1);
}
}
puts("\n");
}
/*void uint_say (const unsigned int *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) {
//for debugging
printf("%u", ARRAY[0]);
for (size_t i = 1; i < NO_OF_ARRAY_ELEMENTS; i++) {
printf(",%u", ARRAY[i]);
}
puts("\n");
}*/
double *restrict uint2double (const unsigned int *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) {
double *restrict doubleArray = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (doubleArray == NULL) {
printf("Failure to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
doubleArray[index] = (double)ARRAY[index];
}
return doubleArray;
}
double min2 (const double N1, const double N2) {
if (N1 < N2) {
return N1;
} else {
return N2;
}
}
double *restrict p_adjust (const double *restrict PVALUES, const size_t NO_OF_ARRAY_ELEMENTS, const char *restrict STRING) {
//this function is a translation of R's p.adjust "BH" method
// i is always i[index] = NO_OF_ARRAY_ELEMENTS - index - 1
if (NO_OF_ARRAY_ELEMENTS < 1) {
puts("p_adjust requires at least one element.\n");
printf("Failed at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
short int TYPE = -1;
if (strcasecmp(STRING, "BH") == 0) {
TYPE = 0;
} else if (strcasecmp(STRING, "fdr") == 0) {
TYPE = 0;
} else if (strcasecmp(STRING, "by") == 0) {
TYPE = 1;
} else if (strcasecmp(STRING, "Bonferroni") == 0) {
TYPE = 2;
} else if (strcasecmp(STRING, "hochberg") == 0) {
TYPE = 3;
} else if (strcasecmp(STRING, "holm") == 0) {
TYPE = 4;
} else if (strcasecmp(STRING, "hommel") == 0) {
TYPE = 5;
} else {
printf("%s doesn't match any accepted FDR methods.\n", STRING);
printf("Failed at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
if (TYPE == 2) {//Bonferroni method
double *restrict bonferroni = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (bonferroni == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double BONFERRONI = PVALUES[index] * NO_OF_ARRAY_ELEMENTS;
if (BONFERRONI >= 1.0) {
bonferroni[index] = 1.0;
} else if ((0.0 <= BONFERRONI) && (BONFERRONI < 1.0)) {
bonferroni[index] = BONFERRONI;
} else {
printf("%g is outside of the interval I planned.\n", BONFERRONI);
printf("Failure at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
}
return bonferroni;
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
} else if (TYPE == 4) {//Holm method
/*these values are computed separately from BH, BY, and Hochberg because they are
computed differently*/
unsigned int *restrict o = order(PVALUES, NO_OF_ARRAY_ELEMENTS, false);
//sorted in reverse of methods 0-3
double *restrict o2double = uint2double(o, NO_OF_ARRAY_ELEMENTS);
double *restrict cummax_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
cummax_input[index] = (NO_OF_ARRAY_ELEMENTS - index ) * PVALUES[o[index]];
// printf("cummax_input[%zu] = %e\n", index, cummax_input[index]);
}
free(o); o = NULL;
unsigned int *restrict ro = order(o2double, NO_OF_ARRAY_ELEMENTS, false);
free(o2double); o2double = NULL;
double *restrict cummax_output = cummax(cummax_input, NO_OF_ARRAY_ELEMENTS);
free(cummax_input); cummax_input = NULL;
double *restrict pmin = pminx(cummax_output, NO_OF_ARRAY_ELEMENTS, 1);
free(cummax_output); cummax_output = NULL;
double *restrict qvalues = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
qvalues[index] = pmin[ro[index]];
}
free(pmin); pmin = NULL;
free(ro); ro = NULL;
return qvalues;
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
} else if (TYPE == 5) {//Hommel method
//i <- seq_len(n)
//o <- order(p)
unsigned int *restrict o = order(PVALUES, NO_OF_ARRAY_ELEMENTS, false);//false is R's default
//p <- p[o]
double *restrict p = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (p == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
p[index] = PVALUES[o[index]];
}
//ro <- order(o)
double *restrict o2double = uint2double(o, NO_OF_ARRAY_ELEMENTS);
free(o); o = NULL;
unsigned int *restrict ro = order(o2double, NO_OF_ARRAY_ELEMENTS, false);
free(o2double); o2double = NULL;
// puts("ro");
//q <- pa <- rep.int(min(n * p/i), n)
double *restrict q = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (q == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
double *restrict pa = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (pa == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
double min = (double)NO_OF_ARRAY_ELEMENTS * p[0];
for (size_t index = 1; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double TEMP = (double)NO_OF_ARRAY_ELEMENTS * p[index] / (1+index);
if (TEMP < min) {
min = TEMP;
}
}
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
pa[index] = min;
q[index] = min;
}
// puts("q & pa");
// double_say(q, NO_OF_ARRAY_ELEMENTS);
/*for (j in (n - 1):2) {
ij <- seq_len(n - j + 1)
i2 <- (n - j + 2):n
q1 <- min(j * p[i2]/(2:j))
q[ij] <- pmin(j * p[ij], q1)
q[i2] <- q[n - j + 1]
pa <- pmax(pa, q)
}
*/
for (size_t j = (NO_OF_ARRAY_ELEMENTS-1); j >= 2; j--) {
// printf("j = %zu\n", j);
unsigned int *restrict ij = seq_len(1,NO_OF_ARRAY_ELEMENTS - j + 1);
for (size_t i = 0; i < NO_OF_ARRAY_ELEMENTS - j + 1; i++) {
ij[i]--;//R's indices are 1-based, C's are 0-based
}
const size_t I2_LENGTH = j - 1;
unsigned int *restrict i2 = malloc(I2_LENGTH * sizeof(unsigned int));
for (size_t i = 0; i < I2_LENGTH; i++) {
i2[i] = NO_OF_ARRAY_ELEMENTS-j+2+i-1;
//R's indices are 1-based, C's are 0-based, I added the -1
}
double q1 = j * p[i2[0]] / 2.0;
for (size_t i = 1; i < I2_LENGTH; i++) {//loop through 2:j
const double TEMP_Q1 = (double)j * p[i2[i]] / (2 + i);
if (TEMP_Q1 < q1) {
q1 = TEMP_Q1;
}
}
for (size_t i = 0; i < (NO_OF_ARRAY_ELEMENTS - j + 1); i++) {//q[ij] <- pmin(j * p[ij], q1)
q[ij[i]] = min2( j*p[ij[i]], q1);
}
free(ij); ij = NULL;
for (size_t i = 0; i < I2_LENGTH; i++) {//q[i2] <- q[n - j + 1]
q[i2[i]] = q[NO_OF_ARRAY_ELEMENTS - j];//subtract 1 because of starting index difference
}
free(i2); i2 = NULL;
for (size_t i = 0; i < NO_OF_ARRAY_ELEMENTS; i++) {//pa <- pmax(pa, q)
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
// printf("j = %zu, pa = \n", j);
// double_say(pa, N);
}//end j loop
free(p); p = NULL;
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
q[index] = pa[ro[index]];//Hommel q-values
}
//now free memory
free(ro); ro = NULL;
free(pa); pa = NULL;
return q;
}
//The methods are similarly computed and thus can be combined for clarity
unsigned int *restrict o = order(PVALUES, NO_OF_ARRAY_ELEMENTS, true);
if (o == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
double *restrict o_double = uint2double(o, NO_OF_ARRAY_ELEMENTS);
for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
if ((PVALUES[index] < 0) || (PVALUES[index] > 1)) {
printf("array[%u] = %lf, which is outside the interval [0,1]\n", index, PVALUES[index]);
printf("died at %s line %u\n", __FILE__, __LINE__);
exit(EXIT_FAILURE);
}
}
unsigned int *restrict ro = order(o_double, NO_OF_ARRAY_ELEMENTS, false);
if (ro == NULL) {
printf("failed to malloc at %s line %u.\n", __FILE__, __LINE__);
perror("");
exit(EXIT_FAILURE);
}
free(o_double); o_double = NULL;
double *restrict cummin_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (TYPE == 0) {//BH method
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double NI = (double)NO_OF_ARRAY_ELEMENTS / (NO_OF_ARRAY_ELEMENTS - index);// n/i simplified
cummin_input[index] = NI * PVALUES[o[index]];//PVALUES[o[index]] is p[o]
}
} else if (TYPE == 1) {//BY method
double q = 1.0;
for (size_t index = 2; index < (1+NO_OF_ARRAY_ELEMENTS); index++) {
q += (double) 1.0/index;
}
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
const double NI = (double)NO_OF_ARRAY_ELEMENTS / (NO_OF_ARRAY_ELEMENTS - index);// n/i simplified
cummin_input[index] = q * NI * PVALUES[o[index]];//PVALUES[o[index]] is p[o]
}
} else if (TYPE == 3) {//Hochberg method
for (size_t index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
// pmin(1, cummin((n - i + 1L) * p[o]))[ro]
cummin_input[index] = (index + 1) * PVALUES[o[index]];
}
}
free(o); o = NULL;
double *restrict cummin_array = NULL;
cummin_array = cummin(cummin_input, NO_OF_ARRAY_ELEMENTS);
free(cummin_input); cummin_input = NULL;//I don't need this anymore
double *restrict pmin = pminx(cummin_array, NO_OF_ARRAY_ELEMENTS, 1);
free(cummin_array); cummin_array = NULL;
double *restrict q_array = malloc(NO_OF_ARRAY_ELEMENTS*sizeof(double));
for (unsigned int index = 0; index < NO_OF_ARRAY_ELEMENTS; index++) {
q_array[index] = pmin[ro[index]];
}
free(ro); ro = NULL;
free(pmin); pmin = NULL;
return q_array;
}
int main(void) {
const double PVALUES[] = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03};//just the pvalues
const double CORRECT_ANSWERS[6][50] = {//each first index is type
{6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02},//Benjamini-Hochberg
{1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02},//Benjamini & Yekutieli
{1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01},//Bonferroni
{9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01},//Hochberg
{1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01},//Holm
{ 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01}//Hommel
};
//the following loop checks each type with R's answers
const char *restrict TYPES[] = {"bh", "by", "bonferroni", "hochberg", "holm", "hommel"};
for (unsigned short int type = 0; type <= 5; type++) {
double *restrict q = p_adjust(PVALUES, sizeof(PVALUES) / sizeof(*PVALUES), TYPES[type]);
double error = fabs(q[0] - CORRECT_ANSWERS[type][0]);
// printf("%e - %e = %g\n", q[0], CORRECT_ANSWERS[type][0], error);
// puts("p q");
// printf("%g\t%g\n", pvalues[0], q[0]);
for (unsigned int i = 1; i < sizeof(PVALUES) / sizeof(*PVALUES); i++) {
const double this_error = fabs(q[i] - CORRECT_ANSWERS[type][i]);
// printf("%e - %e = %g\n", q[i], CORRECT_ANSWERS[type][i], error);
error += this_error;
}
double_say(q, sizeof(PVALUES) / sizeof(*PVALUES));
free(q); q = NULL;
printf("\ntype %u = '%s' has cumulative error of %g\n", type, TYPES[type], error);
}
return 0;
}
{{out}}
[1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type 0 = 'bh' has cumulative error of 8.03053e-07
[1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]
type 1 = 'by' has cumulative error of 3.64072e-07
[1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type 2 = 'bonferroni' has cumulative error of 6.5e-08
[1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 3 = 'hochberg' has cumulative error of 2.7375e-07
[1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 4 = 'holm' has cumulative error of 2.8095e-07
[1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type 5 = 'hommel' has cumulative error of 4.35302e-07
Version 2
{{works with|C89}} {{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 Perl 6 entry. If using gcc, you need to link to the math library (-lm).
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define SIZE 50
#define each_i(start, end) for (i = start; i < end; ++i)
typedef enum { UP, DOWN } direction;
typedef struct { int index; double value; } iv1;
typedef struct { int index; int value; } iv2;
/* test also for 'Unknown' correction type */
const char *types[8] = {
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
};
int compare_iv1(const void *a, const void *b) {
double aa = ((iv1 *)a) -> value;
double bb = ((iv1 *)b) -> value;
if (aa > bb) return 1;
if (aa < bb) return -1;
return 0;
}
int compare_iv1_desc(const void *a, const void *b) {
return -compare_iv1(a, b);
}
int compare_iv2(const void *a, const void *b) {
return ((iv2 *)a) -> value - ((iv2 *)b) -> value;
}
void ratchet(double *pa, direction dir) {
int i;
double m = pa[0];
if (dir == UP) {
each_i(1, SIZE) {
if (pa[i] > m) pa[i] = m;
m = pa[i];
}
}
else {
each_i(1, SIZE) {
if (pa[i] < m) pa[i] = m;
m = pa[i];
}
}
each_i(0, SIZE) if (pa[i] > 1.0) pa[i] = 1.0;
}
void schwartzian(const double *p, double *pa, direction dir) {
int i;
int order[SIZE];
int order2[SIZE];
iv1 iv1s[SIZE];
iv2 iv2s[SIZE];
double pa2[SIZE];
each_i(0, SIZE) { iv1s[i].index = i; iv1s[i].value = p[i]; }
if (dir == UP)
qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1_desc);
else
qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1);
each_i(0, SIZE) order[i] = iv1s[i].index;
each_i(0, SIZE) pa[i] *= p[order[i]];
ratchet(pa, dir);
each_i(0, SIZE) { iv2s[i].index = i; iv2s[i].value = order[i]; }
qsort(iv2s, SIZE, sizeof(iv2s[0]), compare_iv2);
each_i(0, SIZE) order2[i] = iv2s[i].index;
each_i(0, SIZE) pa2[i] = pa[order2[i]];
each_i(0, SIZE) pa[i] = pa2[i];
}
void adjust(const double *p, double *pa, const char *type) {
int i;
if (!strcmp(type, "Benjamini-Hochberg")) {
each_i(0, SIZE) pa[i] = (double)SIZE / (SIZE - i);
schwartzian(p, pa, UP);
}
else if (!strcmp(type, "Benjamini-Yekutieli")) {
double q = 0.0;
each_i(1, SIZE + 1) q += 1.0 / i;
each_i(0, SIZE) pa[i] = q * SIZE / (SIZE - i);
schwartzian(p, pa, UP);
}
else if (!strcmp(type, "Bonferroni")) {
each_i(0, SIZE) pa[i] = (p[i] * SIZE > 1.0) ? 1.0 : p[i] * SIZE;
}
else if (!strcmp(type, "Hochberg")) {
each_i(0, SIZE) pa[i] = i + 1.0;
schwartzian(p, pa, UP);
}
else if (!strcmp(type, "Holm")) {
each_i(0, SIZE) pa[i] = SIZE - i;
schwartzian(p, pa, DOWN);
}
else if (!strcmp(type, "Hommel")) {
int i, j;
int order[SIZE];
int order2[SIZE];
iv1 iv1s[SIZE];
iv2 iv2s[SIZE];
double s[SIZE];
double q[SIZE];
double pa2[SIZE];
int indices[SIZE];
each_i(0, SIZE) { iv1s[i].index = i; iv1s[i].value = p[i]; }
qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1);
each_i(0, SIZE) order[i] = iv1s[i].index;
each_i(0, SIZE) s[i] = p[order[i]];
double min = s[0] * SIZE;
each_i(1, SIZE) {
double temp = s[i] / (i + 1.0);
if (temp < min) min = temp;
}
each_i(0, SIZE) q[i] = min;
each_i(0, SIZE) pa2[i] = min;
for (j = SIZE - 1; j >= 2; --j) {
each_i(0, SIZE) indices[i] = i;
int upper_start = SIZE - j + 1; /* upper indices start index */
int upper_size = j - 1; /* size of upper indices */
int lower_size = SIZE - upper_size; /* size of lower indices */
double qmin = j * s[indices[upper_start]] / 2.0;
each_i(1, upper_size) {
double temp = s[indices[upper_start + i]] * j / (2.0 + i);
if (temp < qmin) qmin = temp;
}
each_i(0, lower_size) {
double temp = s[indices[i]] * j;
q[indices[i]] = (temp < qmin) ? temp : qmin;
}
each_i(0, upper_size) q[indices[upper_start + i]] = q[SIZE - j];
each_i(0, SIZE) if (pa2[i] < q[i]) pa2[i] = q[i];
}
each_i(0, SIZE) { iv2s[i].index = i; iv2s[i].value = order[i]; }
qsort(iv2s, SIZE, sizeof(iv2s[0]), compare_iv2);
each_i(0, SIZE) order2[i] = iv2s[i].index;
each_i(0, SIZE) pa[i] = pa2[order2[i]];
}
else if (!strcmp(type, "Šidák")) {
each_i(0, SIZE) pa[i] = 1.0 - pow(1.0 - p[i], SIZE);
}
else {
printf("\nSorry, do not know how to do '%s' correction.\n", type);
printf("Perhaps you want one of these?:\n");
each_i(0, 7) printf(" %s\n", types[i]);
exit(1);
}
}
void adjusted(const double *p, const char *type) {
int i;
double pa[SIZE] = { 0.0 };
if (check(p)) {
adjust(p, pa, type);
printf("\n%s", type);
each_i(0, SIZE) {
if (!(i % 5)) printf("\n[%2d] ", i);
printf("%1.10f ", pa[i]);
}
printf("\n");
}
else {
printf("p-values must be in range 0.0 to 1.0\n");
exit(1);
}
}
int check(const double* p) {
int i;
each_i(0, SIZE) {
if (p[i] < 0.0 || p[i] > 1.0) return 0;
}
return 1;
}
int main() {
int i;
double p_values[SIZE] = {
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
each_i(0, 8) adjusted(p_values, types[i]);
return 0;
}
{{output}}
Same as Kotlin (Version 2) output.
C++
{{trans|Java}}
#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;
}
{{out}}
[ 1] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type = 0 = 'bh' has a cumulative error of 8.03053e-07
[ 1] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]
type = 1 = 'by' has a cumulative error of 3.64072e-07
[ 1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type = 2 = 'bonferroni' has a cumulative error of 6.5e-08
[ 1] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type = 3 = 'hochberg' has a cumulative error of 2.7375e-07
[ 1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type = 4 = 'holm' has a cumulative error of 2.8095e-07
[ 1] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type = 5 = 'hommel' has a cumulative error of 4.35302e-07
C#
{{trans|Java}}
using System;
using System.Collections.Generic;
using System.Linq;
namespace PValueCorrection {
class Program {
static List<int> SeqLen(int start, int end) {
var result = new List<int>();
if (start == end) {
for (int i = 0; i < end + 1; ++i) {
result.Add(i + 1);
}
} else if (start < end) {
for (int i = 0; i < end - start + 1; ++i) {
result.Add(start + i);
}
} else {
for (int i = 0; i < start - end + 1; ++i) {
result.Add(start - i);
}
}
return result;
}
static List<int> Order(List<double> array, bool decreasing) {
List<int> idx = new List<int>();
for (int i = 0; i < array.Count; ++i) {
idx.Add(i);
}
IComparer<int> cmp;
if (decreasing) {
cmp = Comparer<int>.Create((a, b) => array[a] < array[b] ? 1 : array[b] < array[a] ? -1 : 0);
} else {
cmp = Comparer<int>.Create((a, b) => array[b] < array[a] ? 1 : array[a] < array[b] ? -1 : 0);
}
idx.Sort(cmp);
return idx;
}
static List<double> Cummin(List<double> array) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("cummin requires at least one element");
var output = new List<double>();
double cumulativeMin = array[0];
for (int i = 0; i < array.Count; ++i) {
if (array[i] < cumulativeMin) cumulativeMin = array[i];
output.Add(cumulativeMin);
}
return output;
}
static List<double> Cummax(List<double> array) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("cummax requires at least one element");
var output = new List<double>();
double cumulativeMax = array[0];
for (int i = 0; i < array.Count; ++i) {
if (array[i] > cumulativeMax) cumulativeMax = array[i];
output.Add(cumulativeMax);
}
return output;
}
static List<double> Pminx(List<double> array, double x) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("pmin requires at least one element");
var result = new List<double>();
for (int i = 0; i < array.Count; ++i) {
if (array[i] < x) {
result.Add(array[i]);
} else {
result.Add(x);
}
}
return result;
}
static void Say(List<double> array) {
Console.Write("[ 1] {0:E}", array[0]);
for (int i = 1; i < array.Count; ++i) {
Console.Write(" {0:E}", array[i]);
if ((i + 1) % 5 == 0) Console.Write("\n[{0,2}]", i + 1);
}
Console.WriteLine();
}
static List<double> PAdjust(List<double> pvalues, string str) {
var size = pvalues.Count;
if (size < 1) throw new ArgumentOutOfRangeException("pAdjust requires at least one element");
int type;
switch (str.ToLower()) {
case "bh":
case "fdr":
type = 0;
break;
case "by":
type = 1;
break;
case "bonferroni":
type = 2;
break;
case "hochberg":
type = 3;
break;
case "holm":
type = 4;
break;
case "hommel":
type = 5;
break;
default:
throw new ArgumentException(str + " doesn't match any accepted FDR types");
}
if (2 == type) { // Bonferroni method
var result2 = new List<double>();
for (int i = 0; i < size; ++i) {
double b = pvalues[i] * size;
if (b >= 1) {
result2.Add(1);
} else if (0 <= b && b < 1) {
result2.Add(b);
} else {
throw new Exception(b + " is outside [0, 1)");
}
}
return result2;
} else if (4 == type) { // Holm method
var o4 = Order(pvalues, false);
var o4d = o4.ConvertAll(x => (double)x);
var cummaxInput = new List<double>();
for (int i = 0; i < size; ++i) {
cummaxInput.Add((size - i) * pvalues[o4[i]]);
}
var ro4 = Order(o4d, false);
var cummaxOutput = Cummax(cummaxInput);
var pmin4 = Pminx(cummaxOutput, 1.0);
var hr = new List<double>();
for (int i = 0; i < size; ++i) {
hr.Add(pmin4[ro4[i]]);
}
return hr;
} else if (5 == type) { // Hommel method
var indices = SeqLen(size, size);
var o5 = Order(pvalues, false);
var p = new List<double>();
for (int i = 0; i < size; ++i) {
p.Add(pvalues[o5[i]]);
}
var o5d = o5.ConvertAll(x => (double)x);
var ro5 = Order(o5d, false);
var q = new List<double>();
var pa = new List<double>();
var npi = new List<double>();
for (int i = 0; i < size; ++i) {
npi.Add(p[i] * size / indices[i]);
}
double min = npi.Min();
q.AddRange(Enumerable.Repeat(min, size));
pa.AddRange(Enumerable.Repeat(min, size));
for (int j = size; j >= 2; --j) {
var ij = SeqLen(1, size - j + 1);
for (int i = 0; i < size - j + 1; ++i) {
ij[i]--;
}
int i2Length = j - 1;
var i2 = new List<int>();
for (int i = 0; i < i2Length; ++i) {
i2.Add(size - j + 2 + i - 1);
}
double q1 = j * p[i2[0]] / 2.0;
for (int i = 1; i < i2Length; ++i) {
double temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
for (int i = 0; i < size - j + 1; ++i) {
q[ij[i]] = Math.Min(p[ij[i]] * j, q1);
}
for (int i = 0; i < i2Length; ++i) {
q[i2[i]] = q[size - j];
}
for (int i = 0; i < size; ++i) {
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
}
for (int i = 0; i < size; ++i) {
q[i] = pa[ro5[i]];
}
return q;
}
var ni = new List<double>();
var o = Order(pvalues, true);
var od = o.ConvertAll(x => (double)x);
for (int i = 0; i < size; ++i) {
if (pvalues[i] < 0 || pvalues[i] > 1) {
throw new Exception("array[" + i + "] = " + pvalues[i] + " is outside [0, 1]");
}
ni.Add((double)size / (size - i));
}
var ro = Order(od, false);
var cumminInput = new List<double>();
if (0 == type) { // BH method
for (int i = 0; i < size; ++i) {
cumminInput.Add(ni[i] * pvalues[o[i]]);
}
} else if (1 == type) { // BY method
double q = 0;
for (int i = 1; i < size + 1; ++i) {
q += 1.0 / i;
}
for (int i = 0; i < size; ++i) {
cumminInput.Add(q * ni[i] * pvalues[o[i]]);
}
} else if (3 == type) { // Hochberg method
for (int i = 0; i < size; ++i) {
cumminInput.Add((i + 1) * pvalues[o[i]]);
}
}
var cumminArray = Cummin(cumminInput);
var pmin = Pminx(cumminArray, 1.0);
var result = new List<double>();
for (int i = 0; i < size; ++i) {
result.Add(pmin[ro[i]]);
}
return result;
}
static void Main(string[] args) {
var pvalues = new List<double> {
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
var correctAnswers = new List<List<double>> {
new List<double> { // Benjamini-Hochberg
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
},
new List<double> { // Benjamini & Yekutieli
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
},
new List<double> { // Bonferroni
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
},
new List<double> { // Hochberg
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new List<double> { // Holm
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new List<double> { // Hommel
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
}
};
string[] types = { "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
for (int type = 0; type < types.Length; ++type) {
var q = PAdjust(pvalues, types[type]);
double error = 0.0;
for (int i = 0; i < pvalues.Count; ++i) {
error += Math.Abs(q[i] - correctAnswers[type][i]);
}
Say(q);
Console.WriteLine("type {0} = '{1}' has a cumulative error of {2:E}", type, types[type], error);
Console.WriteLine();
}
}
}
}
{{out}}
[ 1] 6.126681E-001 8.521710E-001 1.987205E-001 1.891595E-001 3.217789E-001
[ 5] 9.301450E-001 4.870370E-001 9.301450E-001 6.049731E-001 6.826753E-001
[10] 6.482629E-001 7.253723E-001 5.280973E-001 8.769926E-001 4.705703E-001
[15] 9.241867E-001 6.049731E-001 7.856107E-001 4.887526E-001 1.136717E-001
[20] 4.991891E-001 8.769926E-001 9.991834E-001 3.217789E-001 9.301450E-001
[25] 2.304958E-001 5.832475E-001 3.899547E-002 8.521710E-001 1.476843E-001
[30] 1.683638E-002 2.562902E-003 3.516084E-002 6.250189E-002 3.636589E-003
[35] 2.562902E-003 2.946883E-002 6.166064E-003 3.899547E-002 2.688991E-003
[40] 4.502863E-004 1.252228E-005 7.881555E-002 3.142613E-002 4.846527E-003
[45] 2.562902E-003 4.846527E-003 1.101708E-003 7.252033E-002 2.205958E-002
[50]
type 0 = 'bh' has a cumulative error of 8.030529E-007
[ 1] 1.000000E+000 1.000000E+000 8.940844E-001 8.510676E-001 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 5.114323E-001
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 1.754486E-001 1.000000E+000 6.644618E-001
[30] 7.575031E-002 1.153102E-002 1.581959E-001 2.812089E-001 1.636176E-002
[35] 1.153102E-002 1.325863E-001 2.774239E-002 1.754486E-001 1.209832E-002
[40] 2.025930E-003 5.634031E-005 3.546073E-001 1.413926E-001 2.180552E-002
[45] 1.153102E-002 2.180552E-002 4.956812E-003 3.262838E-001 9.925057E-002
[50]
type 1 = 'by' has a cumulative error of 3.640716E-007
[ 1] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 7.019185E-001 1.000000E+000 1.000000E+000
[30] 2.020365E-001 1.516675E-002 5.625735E-001 1.000000E+000 2.909271E-002
[35] 1.537741E-002 4.125636E-001 6.782670E-002 6.803480E-001 1.882294E-002
[40] 9.005725E-004 1.252228E-005 1.000000E+000 4.713920E-001 4.395577E-002
[45] 1.088916E-002 4.846527E-002 3.305125E-003 1.000000E+000 2.867745E-001
[50]
type 2 = 'bonferroni' has a cumulative error of 6.500000E-008
[ 1] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[ 5] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[10] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[15] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[20] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[25] 9.991834E-001 9.991834E-001 4.632662E-001 9.991834E-001 9.991834E-001
[30] 1.575885E-001 1.383967E-002 3.938015E-001 7.600230E-001 2.501973E-002
[35] 1.383967E-002 3.052971E-001 5.426136E-002 4.626366E-001 1.656419E-002
[40] 8.825611E-004 1.252228E-005 9.930759E-001 3.394022E-001 3.692284E-002
[45] 1.023581E-002 3.974152E-002 3.172920E-003 8.992520E-001 2.179486E-001
[50]
type 3 = 'hochberg' has a cumulative error of 2.737500E-007
[ 1] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 4.632662E-001 1.000000E+000 1.000000E+000
[30] 1.575885E-001 1.395341E-002 3.938015E-001 7.600230E-001 2.501973E-002
[35] 1.395341E-002 3.052971E-001 5.426136E-002 4.626366E-001 1.656419E-002
[40] 8.825611E-004 1.252228E-005 9.930759E-001 3.394022E-001 3.692284E-002
[45] 1.023581E-002 3.974152E-002 3.172920E-003 8.992520E-001 2.179486E-001
[50]
type 4 = 'holm' has a cumulative error of 2.809500E-007
[ 1] 9.991834E-001 9.991834E-001 9.991834E-001 9.987624E-001 9.991834E-001
[ 5] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[10] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[15] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.595180E-001
[20] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[25] 9.991834E-001 9.991834E-001 4.351895E-001 9.991834E-001 9.766523E-001
[30] 1.414256E-001 1.304340E-002 3.530937E-001 6.887709E-001 2.385602E-002
[35] 1.322457E-002 2.722920E-001 5.426136E-002 4.218158E-001 1.581127E-002
[40] 8.825611E-004 1.252228E-005 8.743649E-001 3.016908E-001 3.516461E-002
[45] 9.582456E-003 3.877222E-002 3.172920E-003 8.122276E-001 1.950067E-001
[50]
type 5 = 'hommel' has a cumulative error of 4.353024E-007
D
{{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.algorithm;
import std.conv;
import std.math;
import std.stdio;
import std.string;
int[] seqLen(int start, int end) {
int[] result;
if (start == end) {
result.length = end+1;
for (int i; i<result.length; i++) {
result[i] = i+1;
}
} else if (start < end) {
result.length = end - start + 1;
for (int i; i<result.length; i++) {
result[i] = start+i;
}
} else {
result.length = start - end + 1;
for (int i; i<result.length; i++) {
result[i] = start-i;
}
}
return result;
}
int[] order(double[] array, bool decreasing) {
int size = array.length;
int[] idx;
idx.length = size;
double[] baseArr;
baseArr.length = size;
for (int i; i<size; i++) {
baseArr[i] = array[i];
idx[i] = i;
}
if (!decreasing) {
alias comp = (a,b) => baseArr[a] < baseArr[b];
idx.sort!comp;
} else {
alias comp = (a,b) => baseArr[b] < baseArr[a];
idx.sort!comp;
}
return idx;
}
double[] cummin(double[] array) {
int size = array.length;
if (size < 1) throw new Exception("cummin requires at least one element");
double[] output;
output.length = size;
auto cumulativeMin = array[0];
foreach (i; 0..size) {
if (array[i] < cumulativeMin) cumulativeMin = array[i];
output[i] = cumulativeMin;
}
return output;
}
double[] cummax(double[] array) {
auto size = array.length;
if (size < 1) throw new Exception("cummax requires at least one element");
double[] output;
output.length = size;
auto cumulativeMax = array[0];
foreach (i; 0..size) {
if (array[i] > cumulativeMax) cumulativeMax = array[i];
output[i] = cumulativeMax;
}
return output;
}
double[] pminx(double[] array, double x) {
auto size = array.length;
if (size < 1) throw new Exception("pmin requires at least one element");
double[] result;
result.length = size;
foreach (i; 0..size) {
if (array[i] < x) {
result[i] = array[i];
} else {
result[i] = x;
}
}
return result;
}
void doubleSay(double[] array) {
writef("[ 1] %e", array[0]);
foreach (i; 1..array.length) {
writef(" %.10f", array[i]);
if ((i+1) % 5 == 0) writef("\n[%2d]", i+1);
}
writeln;
}
auto toArray(T,U)(U[] array) {
T[] result;
result.length = array.length;
foreach(i; 0..array.length) {
result[i] = to!T(array[i]);
}
return result;
}
double[] pAdjust(double[] pvalues, string str) {
auto size = pvalues.length;
if (size < 1) throw new Exception("pAdjust requires at least one element");
int type = str.toLower.predSwitch!"a==b"(
"bh", 0,
"fdr", 0,
"by", 1,
"bonferroni", 2,
"hochberg", 3,
"holm", 4,
"hommel", 5,
{ throw new Exception(text("'",str,"' doesn't match any accepted FDR types")); }()
);
if (type == 2) { // Bonferroni method
double[] result;
result.length = size;
foreach (i; 0..size) {
auto b = pvalues[i] * size;
if (b >= 1) {
result[i] = 1;
} else if (0 <= b && b < 1) {
result[i] = b;
} else {
throw new Exception(text(b," is outside [0, 1)"));
}
}
return result;
} else if (type == 4) { // Holm method
auto o = order(pvalues, false);
auto o2Double = toArray!(double,int)(o);
double[] cummaxInput;
cummaxInput.length = size;
foreach (i; 0..size) {
cummaxInput[i] = (size-i) * pvalues[o[i]];
}
auto ro = order(o2Double, false);
auto cummaxOutput = cummax(cummaxInput);
auto pmin = pminx(cummaxOutput, 1.0);
double[] result;
result.length = size;
foreach (i; 0..size) {
result[i] = pmin[ro[i]];
}
return result;
} else if (type == 5) {
auto indices = seqLen(size, size);
auto o = order(pvalues, false);
double[] p;
p.length = size;
foreach (i; 0..size) {
p[i] = pvalues[o[i]];
}
auto o2Double = toArray!double(o);
auto ro = order(o2Double, false);
double[] q;
q.length = size;
double[] pa;
pa.length = size;
double[] npi;
npi.length = size;
foreach (i; 0..size) {
npi[i] = p[i] * size / indices[i];
}
auto min_ = reduce!min(npi);
q[] = min_;
pa[] = min_;
foreach_reverse (j; 2..size) {
auto ij = seqLen(1, size - j + 1);
foreach (i; 0..size-j+1) {
ij[i]--;
}
auto i2Length = j-1;
int[] i2;
i2.length = i2Length;
foreach(i; 0..i2Length) {
i2[i] = size-j+2+i-1;
}
auto pi2Length = i2Length;
double q1 = j*p[i2[0]] / 2.0;
foreach (i; 1..pi2Length) {
auto temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
foreach (i; 0..size-j+1) {
q[ij[i]] = min(p[ij[i]] * j, q1);
}
foreach(i; 0..i2Length) {
q[i2[i]] = q[size-j];
}
foreach(i; 0..size) if (pa[i] < q[i]) pa[i] = q[i];
}
foreach (index; 0..size) {
q[index] = pa[ro[index]];
}
return q;
}
double[] ni;
ni.length = size;
auto o = order(pvalues, true);
auto oDouble = toArray!double(o);
foreach (index; 0..size) {
if (pvalues[index] < 0 || pvalues[index] > 1) {
throw new Exception(text("array[", index, "] = ", pvalues[index], " is outside [0, 1]"));
}
ni[index] = cast(double) size / (size - index);
}
auto ro = order(oDouble, false);
double[] cumminInput;
cumminInput.length = size;
if (type == 0) { // BH method
foreach (index; 0..size) {
cumminInput[index] = ni[index] * pvalues[o[index]];
}
} else if (type == 1) { // BY method
double q = 0;
foreach (index; 1..size+1) q += 1.0 / index;
foreach (index; 0..size) {
cumminInput[index] = q * ni[index] * pvalues[o[index]];
}
} else if (type == 3) { // Hochberg method
foreach (index; 0..size) {
cumminInput[index] = (index + 1) * pvalues[o[index]];
}
}
auto cumminArray =cummin(cumminInput);
auto pmin = pminx(cumminArray, 1.0);
double[] result;
result.length = size;
foreach (i; 0..size) {
result[i] = pmin[ro[i]];
}
return result;
}
void main() {
double[] pvalues = [
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
];
double[][] correctAnswers = [
[ // Benjamini-Hochberg
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
],
[ // Benjamini & Yekutieli
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
],
[ // Bonferroni
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
],
[ // Hochberg
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
],
[ // Holm
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
],
[ // Hommel
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
]
];
auto types = ["bh", "by", "bonferroni", "hochberg", "holm", "hommel"];
foreach (type; 0..types.length) {
auto q = pAdjust(pvalues, types[type]);
double error = 0.0;
foreach (i; 0..pvalues.length) {
error += abs(q[i] - correctAnswers[type][i]);
}
doubleSay(q);
writefln("\ntype %d = '%s' has a cumulative error of %g", type, types[type], error);
}
}
{{out}}
[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629016 0.0351608437 0.0625018947 0.0036365887
[35] 0.0025629016 0.0294688285 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125222 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629016 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type 0 = 'bh' has a cumulative error of 8.03053e-07
[ 1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503082 0.0115310208 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310208 0.1325863108 0.0277423864 0.1754486368 0.0120983245
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055201
[45] 0.0115310208 0.0218055201 0.0049568120 0.3262838334 0.0992505662
[50]
type 1 = 'by' has a cumulative error of 3.64072e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125222 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type 2 = 'bonferroni' has a cumulative error of 6.5e-08
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125222 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 3 = 'hochberg' has a cumulative error of 2.7375e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125222 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 4 = 'holm' has a cumulative error of 2.8095e-07
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125222 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type 5 = 'hommel' has a cumulative error of 4.35302e-07
Go
{{trans|Kotlin (Version 2)}}
package main
import (
"fmt"
"log"
"math"
"os"
"sort"
"strconv"
"strings"
)
type pvalues = []float64
type iv1 struct {
index int
value float64
}
type iv2 struct{ index, value int }
type direction int
const (
up direction = iota
down
)
// Test also for 'Unknown' correction type.
var ctypes = []string{
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown",
}
func minimum(p pvalues) float64 {
m := p[0]
for i := 1; i < len(p); i++ {
if p[i] < m {
m = p[i]
}
}
return m
}
func maximum(p pvalues) float64 {
m := p[0]
for i := 1; i < len(p); i++ {
if p[i] > m {
m = p[i]
}
}
return m
}
func adjusted(p pvalues, ctype string) (string, error) {
err := check(p)
if err != nil {
return "", err
}
temp := pformat(adjust(p, ctype), 5)
return fmt.Sprintf("\n%s\n%s", ctype, temp), nil
}
func pformat(p pvalues, cols int) string {
var lines []string
for i := 0; i < len(p); i += cols {
fchunk := p[i : i+cols]
schunk := make([]string, cols)
for j := 0; j < cols; j++ {
schunk[j] = strconv.FormatFloat(fchunk[j], 'f', 10, 64)
}
lines = append(lines, fmt.Sprintf("[%2d] %s", i, strings.Join(schunk, " ")))
}
return strings.Join(lines, "\n")
}
func check(p []float64) error {
cond := len(p) > 0 && minimum(p) >= 0 && maximum(p) <= 1
if !cond {
return fmt.Errorf("p-values must be in range 0.0 to 1.0")
}
return nil
}
func ratchet(p pvalues, dir direction) {
size := len(p)
m := p[0]
if dir == up {
for i := 1; i < size; i++ {
if p[i] > m {
p[i] = m
}
m = p[i]
}
} else {
for i := 1; i < size; i++ {
if p[i] < m {
p[i] = m
}
m = p[i]
}
}
for i := 0; i < size; i++ {
if p[i] > 1.0 {
p[i] = 1.0
}
}
}
func schwartzian(p pvalues, mult pvalues, dir direction) pvalues {
size := len(p)
order := make([]int, size)
iv1s := make([]iv1, size)
for i := 0; i < size; i++ {
iv1s[i] = iv1{i, p[i]}
}
if dir == up {
sort.Slice(iv1s, func(i, j int) bool {
return iv1s[i].value > iv1s[j].value
})
} else {
sort.Slice(iv1s, func(i, j int) bool {
return iv1s[i].value < iv1s[j].value
})
}
for i := 0; i < size; i++ {
order[i] = iv1s[i].index
}
pa := make(pvalues, size)
for i := 0; i < size; i++ {
pa[i] = mult[i] * p[order[i]]
}
ratchet(pa, dir)
order2 := make([]int, size)
iv2s := make([]iv2, size)
for i := 0; i < size; i++ {
iv2s[i] = iv2{i, order[i]}
}
sort.Slice(iv2s, func(i, j int) bool {
return iv2s[i].value < iv2s[j].value
})
for i := 0; i < size; i++ {
order2[i] = iv2s[i].index
}
pa2 := make(pvalues, size)
for i := 0; i < size; i++ {
pa2[i] = pa[order2[i]]
}
return pa2
}
func adjust(p pvalues, ctype string) pvalues {
size := len(p)
if size == 0 {
return p
}
fsize := float64(size)
switch ctype {
case "Benjamini-Hochberg":
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = fsize / float64(size-i)
}
return schwartzian(p, mult, up)
case "Benjamini-Yekutieli":
q := 0.0
for i := 1; i <= size; i++ {
q += 1.0 / float64(i)
}
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = q * fsize / (fsize - float64(i))
}
return schwartzian(p, mult, up)
case "Bonferroni":
p2 := make(pvalues, size)
for i := 0; i < size; i++ {
p2[i] = math.Min(p[i]*fsize, 1.0)
}
return p2
case "Hochberg":
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = float64(i) + 1
}
return schwartzian(p, mult, up)
case "Holm":
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = fsize - float64(i)
}
return schwartzian(p, mult, down)
case "Hommel":
order := make([]int, size)
iv1s := make([]iv1, size)
for i := 0; i < size; i++ {
iv1s[i] = iv1{i, p[i]}
}
sort.Slice(iv1s, func(i, j int) bool {
return iv1s[i].value < iv1s[j].value
})
for i := 0; i < size; i++ {
order[i] = iv1s[i].index
}
s := make(pvalues, size)
for i := 0; i < size; i++ {
s[i] = p[order[i]]
}
m := make(pvalues, size)
for i := 0; i < size; i++ {
m[i] = s[i] * fsize / (float64(i) + 1)
}
min := minimum(m)
q := make(pvalues, size)
for i := 0; i < size; i++ {
q[i] = min
}
pa := make(pvalues, size)
for i := 0; i < size; i++ {
pa[i] = min
}
for j := size - 1; j >= 2; j-- {
lower := make([]int, size-j+1) // lower indices
for i := 0; i < len(lower); i++ {
lower[i] = i
}
upper := make([]int, j-1) // upper indices
for i := 0; i < len(upper); i++ {
upper[i] = size - j + 1 + i
}
qmin := float64(j) * s[upper[0]] / 2.0
for i := 1; i < len(upper); i++ {
temp := s[upper[i]] * float64(j) / (2.0 + float64(i))
if temp < qmin {
qmin = temp
}
}
for i := 0; i < len(lower); i++ {
q[lower[i]] = math.Min(s[lower[i]]*float64(j), qmin)
}
for i := 0; i < len(upper); i++ {
q[upper[i]] = q[size-j]
}
for i := 0; i < size; i++ {
if pa[i] < q[i] {
pa[i] = q[i]
}
}
}
order2 := make([]int, size)
iv2s := make([]iv2, size)
for i := 0; i < size; i++ {
iv2s[i] = iv2{i, order[i]}
}
sort.Slice(iv2s, func(i, j int) bool {
return iv2s[i].value < iv2s[j].value
})
for i := 0; i < size; i++ {
order2[i] = iv2s[i].index
}
pa2 := make(pvalues, size)
for i := 0; i < size; i++ {
pa2[i] = pa[order2[i]]
}
return pa2
case "Šidák":
p2 := make(pvalues, size)
for i := 0; i < size; i++ {
p2[i] = 1.0 - math.Pow(1.0-float64(p[i]), fsize)
}
return p2
default:
fmt.Printf("\nSorry, do not know how to do '%s' correction.\n", ctype)
fmt.Println("Perhaps you want one of these?:")
temp := make([]string, len(ctypes)-1)
for i := 0; i < len(temp); i++ {
temp[i] = fmt.Sprintf(" %s", ctypes[i])
}
fmt.Println(strings.Join(temp, "\n"))
os.Exit(1)
}
return p
}
func main() {
p := pvalues{
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03,
}
for _, ctype := range ctypes {
s, err := adjusted(p, ctype)
if err != nil {
log.Fatal(err)
}
fmt.Println(s)
}
}
{{out}}
Benjamini-Hochberg
[ 0] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
Benjamini-Yekutieli
[ 0] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
Bonferroni
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
Hochberg
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Holm
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Hommel
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
Šidák
[ 0] 1.0000000000 1.0000000000 0.9946598274 0.9914285749 0.9999515274
[ 5] 1.0000000000 0.9999999688 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 0.9999999995 1.0000000000 0.9999998801
[15] 1.0000000000 1.0000000000 1.0000000000 0.9999999855 0.9231179729
[20] 0.9999999956 1.0000000000 1.0000000000 0.9999317605 1.0000000000
[25] 0.9983109511 1.0000000000 0.5068253940 1.0000000000 0.9703301333
[30] 0.1832692440 0.0150545753 0.4320729669 0.6993672225 0.0286818157
[35] 0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
[40] 0.0009001752 0.0000125222 0.8142104886 0.3772612062 0.0430222116
[45] 0.0108312558 0.0473319661 0.0032997780 0.7705015898 0.2499384839
Sorry, do not know how to do 'Unknown' correction.
Perhaps you want one of these?:
Benjamini-Hochberg
Benjamini-Yekutieli
Bonferroni
Hochberg
Holm
Hommel
Šidák
```
## Java
{{trans|D}}
{{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]''.
```Java
import java.util.Arrays;
import java.util.Comparator;
public class PValueCorrection {
private static int[] seqLen(int start, int end) {
int[] result;
if (start == end) {
result = new int[end + 1];
for (int i = 0; i < result.length; ++i) {
result[i] = i + 1;
}
} else if (start < end) {
result = new int[end - start + 1];
for (int i = 0; i < result.length; ++i) {
result[i] = start + i;
}
} else {
result = new int[start - end + 1];
for (int i = 0; i < result.length; ++i) {
result[i] = start - i;
}
}
return result;
}
private static int[] order(double[] array, boolean decreasing) {
int size = array.length;
int[] idx = new int[size];
double[] baseArr = new double[size];
for (int i = 0; i < size; ++i) {
baseArr[i] = array[i];
idx[i] = i;
}
Comparator cmp;
if (!decreasing) {
cmp = Comparator.comparingDouble(a -> baseArr[a]);
} else {
cmp = (a, b) -> Double.compare(baseArr[b], baseArr[a]);
}
return Arrays.stream(idx)
.boxed()
.sorted(cmp)
.mapToInt(a -> a)
.toArray();
}
private static double[] cummin(double[] array) {
if (array.length < 1) throw new IllegalArgumentException("cummin requires at least one element");
double[] output = new double[array.length];
double cumulativeMin = array[0];
for (int i = 0; i < array.length; ++i) {
if (array[i] < cumulativeMin) cumulativeMin = array[i];
output[i] = cumulativeMin;
}
return output;
}
private static double[] cummax(double[] array) {
if (array.length < 1) throw new IllegalArgumentException("cummax requires at least one element");
double[] output = new double[array.length];
double cumulativeMax = array[0];
for (int i = 0; i < array.length; ++i) {
if (array[i] > cumulativeMax) cumulativeMax = array[i];
output[i] = cumulativeMax;
}
return output;
}
private static double[] pminx(double[] array, double x) {
if (array.length < 1) throw new IllegalArgumentException("pmin requires at least one element");
double[] result = new double[array.length];
for (int i = 0; i < array.length; ++i) {
if (array[i] < x) {
result[i] = array[i];
} else {
result[i] = x;
}
}
return result;
}
private static void doubleSay(double[] array) {
System.out.printf("[ 1] %e", array[0]);
for (int i = 1; i < array.length; ++i) {
System.out.printf(" %.10f", array[i]);
if ((i + 1) % 5 == 0) System.out.printf("\n[%2d]", i + 1);
}
System.out.println();
}
private static double[] intToDouble(int[] array) {
double[] result = new double[array.length];
for (int i = 0; i < array.length; i++) {
result[i] = array[i];
}
return result;
}
private static double doubleArrayMin(double[] array) {
if (array.length < 1) throw new IllegalArgumentException("pAdjust requires at least one element");
return Arrays.stream(array).min().orElse(Double.NaN);
}
private static double[] pAdjust(double[] pvalues, String str) {
int size = pvalues.length;
if (size < 1) throw new IllegalArgumentException("pAdjust requires at least one element");
int type;
switch (str.toLowerCase()) {
case "bh":
case "fdr":
type = 0;
break;
case "by":
type = 1;
break;
case "bonferroni":
type = 2;
break;
case "hochberg":
type = 3;
break;
case "holm":
type = 4;
break;
case "hommel":
type = 5;
break;
default:
throw new IllegalArgumentException(str + " doesn't match any accepted FDR types");
}
if (type == 2) { // Bonferroni method
double[] result = new double[size];
for (int i = 0; i < size; ++i) {
double b = pvalues[i] * size;
if (b >= 1) {
result[i] = 1;
} else if (0 <= b && b < 1) {
result[i] = b;
} else {
throw new RuntimeException("" + b + " is outside [0, 1)");
}
}
return result;
} else if (type == 4) { // Holm method
int[] o = order(pvalues, false);
double[] o2Double = intToDouble(o);
double[] cummaxInput = new double[size];
for (int i = 0; i < size; ++i) {
cummaxInput[i] = (size - i) * pvalues[o[i]];
}
int[] ro = order(o2Double, false);
double[] cummaxOutput = cummax(cummaxInput);
double[] pmin = pminx(cummaxOutput, 1.0);
double[] result = new double[size];
for (int i = 0; i < size; ++i) {
result[i] = pmin[ro[i]];
}
return result;
} else if (type == 5) {
int[] indices = seqLen(size, size);
int[] o = order(pvalues, false);
double[] p = new double[size];
for (int i = 0; i < size; ++i) {
p[i] = pvalues[o[i]];
}
double[] o2Double = intToDouble(o);
int[] ro = order(o2Double, false);
double[] q = new double[size];
double[] pa = new double[size];
double[] npi = new double[size];
for (int i = 0; i < size; ++i) {
npi[i] = p[i] * size / indices[i];
}
double min = doubleArrayMin(npi);
Arrays.fill(q, min);
Arrays.fill(pa, min);
for (int j = size; j >= 2; --j) {
int[] ij = seqLen(1, size - j + 1);
for (int i = 0; i < size - j + 1; ++i) {
ij[i]--;
}
int i2Length = j - 1;
int[] i2 = new int[i2Length];
for (int i = 0; i < i2Length; ++i) {
i2[i] = size - j + 2 + i - 1;
}
double q1 = j * p[i2[0]] / 2.0;
for (int i = 1; i < i2Length; ++i) {
double temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
for (int i = 0; i < size - j + 1; ++i) {
q[ij[i]] = Math.min(p[ij[i]] * j, q1);
}
for (int i = 0; i < i2Length; ++i) {
q[i2[i]] = q[size - j];
}
for (int i = 0; i < size; ++i) {
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
}
for (int i = 0; i < size; ++i) {
q[i] = pa[ro[i]];
}
return q;
}
double[] ni = new double[size];
int[] o = order(pvalues, true);
double[] oDouble = intToDouble(o);
for (int i = 0; i < size; ++i) {
if (pvalues[i] < 0 || pvalues[i] > 1) {
throw new RuntimeException("array[" + i + "] = " + pvalues[i] + " is outside [0, 1]");
}
ni[i] = (double) size / (size - i);
}
int[] ro = order(oDouble, false);
double[] cumminInput = new double[size];
if (type == 0) { // BH method
for (int i = 0; i < size; ++i) {
cumminInput[i] = ni[i] * pvalues[o[i]];
}
} else if (type == 1) { // BY method
double q = 0;
for (int i = 1; i < size + 1; ++i) {
q += 1.0 / i;
}
for (int i = 0; i < size; ++i) {
cumminInput[i] = q * ni[i] * pvalues[o[i]];
}
} else if (type == 3) { // Hochberg method
for (int i = 0; i < size; ++i) {
cumminInput[i] = (i + 1) * pvalues[o[i]];
}
}
double[] cumminArray = cummin(cumminInput);
double[] pmin = pminx(cumminArray, 1.0);
double[] result = new double[size];
for (int i = 0; i < size; ++i) {
result[i] = pmin[ro[i]];
}
return result;
}
public static void main(String[] args) {
double[] pvalues = new double[]{
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
double[][] correctAnswers = new double[][]{
new double[]{ // Benjamini-Hochberg
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
},
new double[]{ // Benjamini & Yekutieli
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
},
new double[]{ // Bonferroni
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
},
new double[]{ // Hochberg
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new double[]{ // Holm
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new double[]{ // Hommel
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
}
};
String[] types = new String[]{"bh", "by", "bonferroni", "hochberg", "holm", "hommel"};
for (int type = 0; type < types.length; ++type) {
double[] q = pAdjust(pvalues, types[type]);
double error = 0.0;
for (int i = 0; i < pvalues.length; ++i) {
error += Math.abs(q[i] - correctAnswers[type][i]);
}
doubleSay(q);
System.out.printf("\ntype %d = '%s' has a cumulative error of %g\n", type, types[type], error);
}
}
}
```
{{out}}
```txt
[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type 0 = 'bh' has a cumulative error of 8.03053e-07
[ 1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]
type 1 = 'by' has a cumulative error of 3.64072e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type 2 = 'bonferroni' has a cumulative error of 6.50000e-08
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 3 = 'hochberg' has a cumulative error of 2.73750e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 4 = 'holm' has a cumulative error of 2.80950e-07
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type 5 = 'hommel' has a cumulative error of 4.35302e-07
```
## Julia
{{works with|Julia|0.6}}
```julia
using MultipleTesting
using IterTools
p = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03]
function printpvalues(v)
for chunk in partition(v, 10)
println(join((@sprintf("%4.7f", p) for p in chunk), ", "))
end
end
println("Original p-values:")
printpvalues(p)
for corr in (Bonferroni(), BenjaminiHochberg(), BenjaminiYekutieli(), Holm(), Hochberg(), Hommel())
println("\n", corr)
printpvalues(adjust(p, corr))
end
```
{{out}}
```txt
Original p-values:
0.4533744, 0.7296024, 0.0993603, 0.0907966, 0.1801962, 0.8752257, 0.2922222, 0.9115421, 0.4355806, 0.5324867
0.4926798, 0.5802978, 0.3485442, 0.7883130, 0.2729308, 0.8502518, 0.4268138, 0.6442008, 0.3030266, 0.0500155
0.3194810, 0.7892933, 0.9991834, 0.1745691, 0.9037516, 0.1198578, 0.3966083, 0.0140384, 0.7328671, 0.0679348
0.0040407, 0.0003033, 0.0112515, 0.0237507, 0.0005819, 0.0003075, 0.0082513, 0.0013565, 0.0136070, 0.0003765
0.0000180, 0.0000003, 0.0331025, 0.0094278, 0.0008791, 0.0002178, 0.0009693, 0.0000661, 0.0290081, 0.0057355
MultipleTesting.Bonferroni()
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.7019185, 1.0000000, 1.0000000
0.2020365, 0.0151667, 0.5625735, 1.0000000, 0.0290927, 0.0153774, 0.4125636, 0.0678267, 0.6803480, 0.0188229
0.0009006, 0.0000125, 1.0000000, 0.4713920, 0.0439558, 0.0108892, 0.0484653, 0.0033051, 1.0000000, 0.2867745
MultipleTesting.BenjaminiHochberg()
0.6126681, 0.8521710, 0.1987205, 0.1891595, 0.3217789, 0.9301450, 0.4870370, 0.9301450, 0.6049731, 0.6826753
0.6482629, 0.7253722, 0.5280973, 0.8769926, 0.4705703, 0.9241867, 0.6049731, 0.7856107, 0.4887526, 0.1136717
0.4991891, 0.8769926, 0.9991834, 0.3217789, 0.9301450, 0.2304958, 0.5832475, 0.0389955, 0.8521710, 0.1476843
0.0168364, 0.0025629, 0.0351608, 0.0625019, 0.0036366, 0.0025629, 0.0294688, 0.0061661, 0.0389955, 0.0026890
0.0004503, 0.0000125, 0.0788155, 0.0314261, 0.0048465, 0.0025629, 0.0048465, 0.0011017, 0.0725203, 0.0220596
MultipleTesting.BenjaminiYekutieli()
1.0000000, 1.0000000, 0.8940844, 0.8510676, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.5114323
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.1754486, 1.0000000, 0.6644618
0.0757503, 0.0115310, 0.1581959, 0.2812089, 0.0163618, 0.0115310, 0.1325863, 0.0277424, 0.1754486, 0.0120983
0.0020259, 0.0000563, 0.3546073, 0.1413926, 0.0218055, 0.0115310, 0.0218055, 0.0049568, 0.3262838, 0.0992506
MultipleTesting.Holm()
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000
1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 1.0000000, 0.4632662, 1.0000000, 1.0000000
0.1575885, 0.0139534, 0.3938014, 0.7600230, 0.0250197, 0.0139534, 0.3052971, 0.0542614, 0.4626366, 0.0165642
0.0008826, 0.0000125, 0.9930759, 0.3394022, 0.0369228, 0.0102358, 0.0397415, 0.0031729, 0.8992520, 0.2179486
MultipleTesting.Hochberg()
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.4632662, 0.9991834, 0.9991834
0.1575885, 0.0138397, 0.3938014, 0.7600230, 0.0250197, 0.0138397, 0.3052971, 0.0542614, 0.4626366, 0.0165642
0.0008826, 0.0000125, 0.9930759, 0.3394022, 0.0369228, 0.0102358, 0.0397415, 0.0031729, 0.8992520, 0.2179486
MultipleTesting.Hommel()
0.9991834, 0.9991834, 0.9991834, 0.9987624, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9595180
0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.9991834, 0.4351895, 0.9991834, 0.9766522
0.1414256, 0.0130434, 0.3530937, 0.6887709, 0.0238560, 0.0132246, 0.2722920, 0.0542614, 0.4218158, 0.0158113
0.0008826, 0.0000123, 0.8743649, 0.3016908, 0.0351646, 0.0095825, 0.0387722, 0.0031729, 0.8122276, 0.1950067
```
## Kotlin
### Version 1
{{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]''.
```scala
// version 1.1.51
import java.util.Arrays
typealias IAE = IllegalArgumentException
fun seqLen(start: Int, end: Int) =
when {
start == end -> IntArray(end + 1) { it + 1 }
start < end -> IntArray(end - start + 1) { start + it }
else -> IntArray(start - end + 1) { start - it }
}
var baseArr: DoubleArray? = null
fun compareIncrease(a: Int, b: Int): Int = baseArr!![b].compareTo(baseArr!![a])
fun compareDecrease(a: Int, b: Int): Int = baseArr!![a].compareTo(baseArr!![b])
fun order(array: DoubleArray, decreasing: Boolean): IntArray {
val size = array.size
var idx = IntArray(size) { it }
baseArr = array.copyOf()
if (!decreasing) {
idx = Arrays.stream(idx)
.boxed()
.sorted { a, b -> compareDecrease(a, b) }
.mapToInt { it }
.toArray()
}
else {
idx = Arrays.stream(idx)
.boxed()
.sorted { a, b -> compareIncrease(a, b) }
.mapToInt { it }
.toArray()
}
baseArr = null
return idx
}
fun cummin(array: DoubleArray): DoubleArray {
val size = array.size
if (size < 1) throw IAE("cummin requires at least one element")
val output = DoubleArray(size)
var cumulativeMin = array[0]
for (i in 0 until size) {
if (array[i] < cumulativeMin) cumulativeMin = array[i]
output[i] = cumulativeMin
}
return output
}
fun cummax(array: DoubleArray): DoubleArray {
val size = array.size
if (size < 1) throw IAE("cummax requires at least one element")
val output = DoubleArray(size)
var cumulativeMax = array[0]
for (i in 0 until size) {
if (array[i] > cumulativeMax) cumulativeMax = array[i]
output[i] = cumulativeMax
}
return output
}
fun pminx(array: DoubleArray, x: Double): DoubleArray {
val size = array.size
if (size < 1) throw IAE("pmin requires at least one element")
return DoubleArray(size) { if (array[it] < x) array[it] else x }
}
fun doubleSay(array: DoubleArray) {
print("[ 1] %e".format(array[0]))
for (i in 1 until array.size) {
print(" %.10f".format(array[i]))
if ((i + 1) % 5 == 0) print("\n[%2d]".format(i + 1))
}
println()
}
fun intToDouble(array: IntArray) = DoubleArray(array.size) { array[it].toDouble() }
fun doubleArrayMin(array: DoubleArray) =
if (array.size < 1) throw IAE("pAdjust requires at least one element")
else array.min()!!
fun pAdjust(pvalues: DoubleArray, str: String): DoubleArray {
val size = pvalues.size
if (size < 1) throw IAE("pAdjust requires at least one element")
val type = when(str.toLowerCase()) {
"bh", "fdr" -> 0
"by" -> 1
"bonferroni" -> 2
"hochberg" -> 3
"holm" -> 4
"hommel" -> 5
else -> throw IAE("'$str' doesn't match any accepted FDR types")
}
if (type == 2) { // Bonferroni method
return DoubleArray(size) {
val b = pvalues[it] * size
when {
b >= 1 -> 1.0
0 <= b && b < 1 -> b
else -> throw RuntimeException("$b is outside [0, 1)")
}
}
}
else if (type == 4) { // Holm method
val o = order(pvalues, false)
val o2Double = intToDouble(o)
val cummaxInput = DoubleArray(size) { (size - it) * pvalues[o[it]] }
val ro = order(o2Double, false)
val cummaxOutput = cummax(cummaxInput)
val pmin = pminx(cummaxOutput, 1.0)
return DoubleArray(size) { pmin[ro[it]] }
}
else if (type == 5) { // Hommel method
val indices = seqLen(size, size)
val o = order(pvalues, false)
val p = DoubleArray(size) { pvalues[o[it]] }
val o2Double = intToDouble(o)
val ro = order(o2Double, false)
val q = DoubleArray(size)
val pa = DoubleArray(size)
val npi = DoubleArray(size) { p[it] * size / indices[it] }
val min = doubleArrayMin(npi)
q.fill(min)
pa.fill(min)
for (j in size - 1 downTo 2) {
val ij = seqLen(1, size - j + 1)
for (i in 0 until size - j + 1) ij[i]--
val i2Length = j - 1
val i2 = IntArray(i2Length) { size - j + 2 + it - 1 }
val pi2Length = i2Length
var q1 = j * p[i2[0]] / 2.0
for (i in 1 until pi2Length) {
val temp_q1 = p[i2[i]] * j / (2.0 + i)
if(temp_q1 < q1) q1 = temp_q1
}
for (i in 0 until size - j + 1) {
q[ij[i]] = minOf(p[ij[i]] * j, q1)
}
for (i in 0 until i2Length) q[i2[i]] = q[size - j]
for (i in 0 until size) if (pa[i] < q[i]) pa[i] = q[i]
}
for (index in 0 until size) q[index] = pa[ro[index]]
return q
}
val ni = DoubleArray(size)
val o = order(pvalues, true)
val oDouble = intToDouble(o)
for (index in 0 until size) {
if (pvalues[index] !in 0.0 .. 1.0) {
throw RuntimeException("array[$index] = ${pvalues[index]} is outside [0, 1]")
}
ni[index] = size.toDouble() / (size - index)
}
val ro = order(oDouble, false)
val cumminInput = DoubleArray(size)
if (type == 0) { // BH method
for (index in 0 until size) {
cumminInput[index] = ni[index] * pvalues[o[index]]
}
}
else if (type == 1) { // BY method
var q = 0.0
for (index in 1 until size + 1) q += 1.0 / index
for (index in 0 until size) {
cumminInput[index] = q * ni[index] * pvalues[o[index]]
}
}
else if (type == 3) { // Hochberg method
for (index in 0 until size) {
cumminInput[index] = (index + 1) * pvalues[o[index]]
}
}
val cumminArray = cummin(cumminInput)
val pmin = pminx(cumminArray, 1.0)
return DoubleArray(size) { pmin[ro[it]] }
}
fun main(args: Array) {
val pvalues = doubleArrayOf(
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
)
val correctAnswers = listOf(
doubleArrayOf( // Benjamini-Hochberg
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
),
doubleArrayOf( // Benjamini & Yekutieli
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
),
doubleArrayOf( // Bonferroni
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
),
doubleArrayOf( // Hochberg
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
),
doubleArrayOf( // Holm
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
),
doubleArrayOf( // Hommel
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
)
)
val types = listOf("bh", "by", "bonferroni", "hochberg", "holm", "hommel")
val f = "\ntype %d = '%s' has cumulative error of %g"
for (type in 0 until types.size) {
val q = pAdjust(pvalues, types[type])
var error = 0.0
for (i in 0 until pvalues.size) {
error += Math.abs(q[i] - correctAnswers[type][i])
}
doubleSay(q)
println(f.format(type, types[type], error))
}
}
```
{{out}}
```txt
[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type 0 = 'bh' has cumulative error of 8.03053e-07
[ 1] 1.000000e+00 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]
type 1 = 'by' has cumulative error of 3.64072e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type 2 = 'bonferroni' has cumulative error of 6.50000e-08
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 3 = 'hochberg' has cumulative error of 2.73750e-07
[ 1] 1.000000e+00 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type 4 = 'holm' has cumulative error of 2.80950e-07
[ 1] 9.991834e-01 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type 5 = 'hommel' has cumulative error of 4.35302e-07
```
### Version 2
{{trans|Perl 6}}
To avoid licensing issues, this version follows the approach of the Perl 6 entry of which it is a partial translation. However, the correction routines themselves have been coded independently, common code factored out into separate functions (analogous to Perl 6) and (apart from the Šidák method) agree with the Perl 6 results.
```scala
// version 1.2.21
typealias DList = List
enum class Direction { UP, DOWN }
// test also for 'Unknown' correction type
val types = listOf(
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
)
fun adjusted(p: DList, type: String) = "\n$type\n${pFormat(adjust(check(p), type))}"
fun pFormat(p: DList, cols: Int = 5): String {
var i = -cols
val fmt = "%1.10f"
return p.chunked(cols).map { chunk ->
i += cols
"[%2d] %s".format(i, chunk.map { fmt.format(it) }.joinToString(" "))
}.joinToString("\n")
}
fun check(p: DList): DList {
require(p.size > 0 && p.min()!! >= 0.0 && p.max()!! <= 1.0) {
"p-values must be in range 0.0 to 1.0"
}
return p
}
fun ratchet(p: DList, dir: Direction): DList {
val pp = p.toMutableList()
var m = pp[0]
if (dir == Direction.UP) {
for (i in 1 until pp.size) {
if (pp[i] > m) pp[i] = m
m = pp[i]
}
}
else {
for (i in 1 until pp.size) {
if (pp[i] < m) pp[i] = m
m = pp[i]
}
}
return pp.map { if (it < 1.0) it else 1.0 }
}
fun schwartzian(p: DList, mult: DList, dir: Direction): DList {
val size = p.size
val order = if (dir == Direction.UP)
p.withIndex().sortedByDescending { it.value }.map { it.index }
else
p.withIndex().sortedBy { it.value }.map { it.index }
var pa = List(size) { mult[it] * p[order[it]] }
pa = ratchet(pa, dir)
val order2 = order.withIndex().sortedBy{ it.value }.map { it.index }
return List(size) { pa[order2[it]] }
}
fun adjust(p: DList, type: String): DList {
val size = p.size
require(size > 0)
when (type) {
"Benjamini-Hochberg" -> {
val mult = List(size) { size.toDouble() / (size - it) }
return schwartzian(p, mult, Direction.UP)
}
"Benjamini-Yekutieli" -> {
val q = (1..size).sumByDouble { 1.0 / it }
val mult = List(size) { q * size / (size - it) }
return schwartzian(p, mult, Direction.UP)
}
"Bonferroni" -> {
return p.map { minOf(it * size, 1.0) }
}
"Hochberg" -> {
val mult = List(size) { (it + 1).toDouble() }
return schwartzian(p, mult, Direction.UP)
}
"Holm" -> {
val mult = List(size) { (size - it).toDouble() }
return schwartzian(p, mult, Direction.DOWN)
}
"Hommel" -> {
val order = p.withIndex().sortedBy { it.value }.map { it.index }
val s = List(size) { p[order[it]] }
val min = List(size){ s[it] * size / ( it + 1) }.min()!!
val q = MutableList(size) { min }
val pa = MutableList(size) { min }
for (j in size - 1 downTo 2) {
val lower = IntArray(size - j + 1) { it } // lower indices
val upper = IntArray(j - 1) { size - j + 1 + it } // upper indices
var qmin = j * s[upper[0]] / 2.0
for (i in 1 until upper.size) {
val temp = s[upper[i]] * j / (2.0 + i)
if (temp < qmin) qmin = temp
}
for (i in 0 until lower.size) {
q[lower[i]] = minOf(s[lower[i]] * j, qmin)
}
for (i in 0 until upper.size) q[upper[i]] = q[size - j]
for (i in 0 until size) if (pa[i] < q[i]) pa[i] = q[i]
}
val order2 = order.withIndex().sortedBy{ it.value }.map { it.index }
return List(size) { pa[order2[it]] }
}
"Šidák" -> {
val m = size.toDouble()
return p.map { 1.0 - Math.pow(1.0 - it, m) }
}
else -> {
println(
"\nSorry, do not know how to do '$type' correction.\n" +
"Perhaps you want one of these?:\n" +
types.dropLast(1).map { " $it" }.joinToString("\n")
)
System.exit(1)
}
}
return p
}
fun main(args: Array) {
val pValues = listOf(
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
)
types.forEach { println(adjusted(pValues, it)) }
}
```
{{out}}
Same as Perl 6 entry except:
```txt
....
Šidák
[ 0] 1.0000000000 1.0000000000 0.9946598274 0.9914285749 0.9999515274
[ 5] 1.0000000000 0.9999999688 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 0.9999999995 1.0000000000 0.9999998801
[15] 1.0000000000 1.0000000000 1.0000000000 0.9999999855 0.9231179729
[20] 0.9999999956 1.0000000000 1.0000000000 0.9999317605 1.0000000000
[25] 0.9983109511 1.0000000000 0.5068253940 1.0000000000 0.9703301333
[30] 0.1832692440 0.0150545753 0.4320729669 0.6993672225 0.0286818157
[35] 0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
[40] 0.0009001752 0.0000125222 0.8142104886 0.3772612062 0.0430222116
[45] 0.0108312558 0.0473319661 0.0032997780 0.7705015898 0.2499384839
Sorry, do not know how to do 'Unknown' correction.
Perhaps you want one of these?:
Benjamini-Hochberg
Benjamini-Yekutieli
Bonferroni
Hochberg
Holm
Hommel
Šidák
```
## Perl
{{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]''.
```perl
#!/usr/bin/env perl
use strict;
use warnings;
sub pmin {
my $array_ref = shift;
my $x = 1;
unless ((ref $array_ref) =~ m/ARRAY/) {
print "cummin requires an array.\n";
die;
}
my @pmin_array;
my $n = scalar @$array_ref;
for (my $index = 0; $index < $n; $index++) {
if (@$array_ref[$index] < $x) {
$pmin_array[$index] = @$array_ref[$index];
} else {
$pmin_array[$index] = $x;
}
}
return @pmin_array;
}
sub cummin {
my $array_ref = shift;
unless ((ref $array_ref) =~ m/ARRAY/) {
print "cummin requires an array.\n";
die;
}
my @cummin;
my $cumulative_min = @$array_ref[0];
foreach my $p (@$array_ref) {
if ($p < $cumulative_min) {
$cumulative_min = $p;
}
push @cummin, $cumulative_min;
}
return @cummin;
}
sub cummax {
my $array_ref = shift;
unless ((ref $array_ref) =~ m/ARRAY/) {
print "cummin requires an array.\n";
die;
}
my @cummax;
my $cumulative_max = @$array_ref[0];
foreach my $p (@$array_ref) {
if ($p > $cumulative_max) {
$cumulative_max = $p;
}
push @cummax, $cumulative_max;
}
return @cummax;
}
sub order {#made to match R's "order"
my $array_ref = shift;
my $decreasing = 'false';
if (defined $_[0]) {
my $option = shift;
if ($option =~ m/true/i) {
$decreasing = 'true';
} elsif ($option =~ m/false/i) {
#do nothing, it's already set to false
} else {
print "2nd option should only be case-insensitive 'true' or 'false'";
die;
}
}
unless ((ref $array_ref) =~ m/ARRAY/) {
print "You should have entered an array.\n";
die;
}
my @array;
my $max_index = scalar @$array_ref-1;
if ($decreasing eq 'false') {
@array = sort { @$array_ref[$a] <=> @$array_ref[$b] } 0..$max_index;
} elsif ($decreasing eq 'true') {
@array = sort { @$array_ref[$b] <=> @$array_ref[$a] } 0..$max_index;
}
}
use List::Util 'min';
sub p_adjust {
my $pvalues_ref = shift;
unless ((ref $pvalues_ref) =~ m/ARRAY/) {
print "p_adjust requires an array.\n";
die;
}
my $method;
if (defined $_[0]) {
$method = shift;
} else {
$method = 'Holm';
}
my %methods = (
'bh' => 1,
'fdr' => 1,
'by' => 1,
'holm' => 1,
'hommel' => 1,
'bonferroni' => 1,
'hochberg' => 1
);
my $method_found = 'no';
foreach my $key (keys %methods) {
if ((uc $method) eq (uc $key)) {
$method = $key;
$method_found = 'yes';
last;
}
}
if ($method_found eq 'no') {
if ($method =~ m/benjamini-?\s*hochberg/i) {
$method = 'bh';
$method_found = 'yes';
} elsif ($method =~ m/benjamini-?\s*yekutieli/i) {
$method = 'by';
$method_found = 'yes';
}
}
if ($method_found eq 'no') {
print "No method could be determined from $method.\n";
die;
}
my $lp = scalar @$pvalues_ref;
my $n = $lp;
my @qvalues;
if ($method eq 'hochberg') {
my @o = order($pvalues_ref, 'TRUE');
my @cummin_input;
for (my $index = 0; $index < $n; $index++) {
$cummin_input[$index] = ($index+1)* @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o]
}
my @cummin = cummin(\@cummin_input);
undef @cummin_input;
my @pmin = pmin(\@cummin);
undef @cummin;
my @ro = order(\@o);
undef @o;
@qvalues = @pmin[@ro];
} elsif ($method eq 'bh') {
my @o = order($pvalues_ref, 'TRUE');
my @cummin_input;
for (my $index = 0; $index < $n; $index++) {
$cummin_input[$index] = ($n/($n-$index))* @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o]
}
my @ro = order(\@o);
undef @o;
my @cummin = cummin(\@cummin_input);
undef @cummin_input;
my @pmin = pmin(\@cummin);
undef @cummin;
@qvalues = @pmin[@ro];
} elsif ($method eq 'by') {
my $q = 0.0;
my @o = order($pvalues_ref, 'TRUE');
my @ro = order(\@o);
for (my $index = 1; $index < ($n+1); $index++) {
$q += 1.0 / $index;
}
my @cummin_input;
for (my $index = 0; $index < $n; $index++) {
$cummin_input[$index] = $q * ($n/($n-$index)) * @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o]
}
my @cummin = cummin(\@cummin_input);
undef @cummin_input;
my @pmin = pmin(\@cummin);
undef @cummin;
@qvalues = @pmin[@ro];
} elsif ($method eq 'bonferroni') {
for (my $index = 0; $index < $n; $index++) {
my $q = @$pvalues_ref[$index]*$n;
if ((0 <= $q) && ($q < 1)) {
$qvalues[$index] = $q;
} elsif ($q >= 1) {
$qvalues[$index] = 1.0;
} else {
print "Failed to get Bonferroni adjusted p.";
die;
}
}
} elsif ($method eq 'holm') {
my @o = order($pvalues_ref);
my @cummax_input;
for (my $index = 0; $index < $n; $index++) {
$cummax_input[$index] = ($n - $index) * @$pvalues_ref[$o[$index]];
}
my @ro = order(\@o);
undef @o;
my @cummax = cummax(\@cummax_input);
undef @cummax_input;
my @pmin = pmin(\@cummax);
undef @cummax;
@qvalues = @pmin[@ro];
} elsif ($method eq 'hommel') {
my @i = 1..$n;
my @o = order($pvalues_ref);
my @p = @$pvalues_ref[@o];
my @ro = order(\@o);
undef @o;
my @pa;
my @q;
my $min = $n*$p[0];
for (my $index = 0; $index < $n; $index++) {
my $temp = $n*$p[$index] / ($index + 1);
if ($temp < $min) {
$min = $temp;
}
}
for (my $index = 0; $index < $n; $index++) {
$pa[$index] = $min;#q <- pa <- rep.int(min(n * p/i), n)
$q[$index] = $min;#q <- pa <- rep.int(min(n * p/i), n)
}
for (my $j = ($n-1); $j >= 2; $j--) {
# printf("j = %zu\n", j);
my @ij = 1..($n - $j + 1);#ij <- seq_len(n - j + 1)
for (my $i = 0; $i < $n - $j + 1; $i++) {
$ij[$i]--;#R's indices are 1-based, C's are 0-based
}
my $I2_LENGTH = $j - 1;
my @i2;
for (my $i = 0; $i < $I2_LENGTH; $i++) {
$i2[$i] = $n-$j+2+$i-1;
#R's indices are 1-based, C's are 0-based, I added the -1
}
my $q1 = $j * $p[$i2[0]] / 2.0;
for (my $i = 1; $i < $I2_LENGTH; $i++) {#loop through 2:j
my $TEMP_Q1 = $j * $p[$i2[$i]] / (2 + $i);
if ($TEMP_Q1 < $q1) {
$q1 = $TEMP_Q1;
}
}
for (my $i = 0; $i < ($n - $j + 1); $i++) {#q[ij] <- pmin(j * p[ij], q1)
$q[$ij[$i]] = min( $j*$p[$ij[$i]], $q1);
}
for (my $i = 0; $i < $I2_LENGTH; $i++) {#q[i2] <- q[n - j + 1]
$q[$i2[$i]] = $q[$n - $j];#subtract 1 because of starting index difference
}
for (my $i = 0; $i < $n; $i++) {#pa <- pmax(pa, q)
if ($pa[$i] < $q[$i]) {
$pa[$i] = $q[$i];
}
}
# printf("j = %zu, pa = \n", j);
# double_say(pa, N);
}#end j loop
@qvalues = @pa[@ro];
} else {
print "$method doesn't fit my types.\n";
die;
}
return @qvalues;
}
my @pvalues = (4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03);
my %correct_answers = (
'Benjamini-Hochberg' => [6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02],
'Benjamini-Yekutieli' => [1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02],
'Bonferroni' => [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01],
'Hochberg' => [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01],
'Holm' => [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01],
'Hommel' => [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01]);
foreach my $method ('Hochberg','Benjamini-Hochberg','Benjamini-Yekutieli', 'Bonferroni', 'Holm', 'Hommel') {
print "$method\n";
my @qvalues = p_adjust(\@pvalues, $method);
my $error = 0.0;
foreach my $q (0..$#qvalues) {
$error += abs($qvalues[$q] - $correct_answers{$method}[$q]);
}
printf("type $method has cumulative error of %g.\n", $error);
}
```
{{out}}
```txt
Hochberg
type Hochberg has cumulative error of 2.7375e-07.
Benjamini-Hochberg
type Benjamini-Hochberg has cumulative error of 8.03053e-07.
Benjamini-Yekutieli
type Benjamini-Yekutieli has cumulative error of 3.64072e-07.
Bonferroni
type Bonferroni has cumulative error of 6.5e-08.
Holm
type Holm has cumulative error of 2.8095e-07.
Hommel
type Hommel has cumulative error of 4.35302e-07.
```
## Perl 6
{{works with|Rakudo|2019.03.1}}
```perl6
########################### Helper subs ###########################
sub adjusted (@p, $type) { "\n$type\n" ~ format adjust( check(@p), $type ) }
sub format ( @p, $cols = 5 ) {
my $i = -$cols;
my $fmt = "%1.10f";
join "\n", @p.rotor($cols, :partial).map:
{ sprintf "[%2d] { join ' ', $fmt xx $_ }", $i+=$cols, $_ };
}
sub check ( @p ) { die 'p-values must be in range 0.0 to 1.0' if @p.min < 0 or 1 < @p.max; @p }
multi ratchet ( 'up', @p ) { my $m; @p[$_] min= $m, $m = @p[$_] for ^@p; @p }
multi ratchet ( 'dn', @p ) { my $m; @p[$_] max= $m, $m = @p[$_] for ^@p .reverse; @p }
sub schwartzian ( @p, &transform, :$ratchet ) {
my @pa = @p.map( {[$_, $++]} ).sort( -*.[0] ).map: { [transform(.[0]), .[1]] };
@pa[*;0] = ratchet($ratchet, @pa»[0]);
@pa.sort( *.[1] )»[0]
}
############# 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" ~
.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, $_
}
```
{{out}}
Benjamini-Hochberg
[ 0] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502863 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
Benjamini-Yekutieli
[ 0] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
Bonferroni
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
Hochberg
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Holm
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Hommel
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825611 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
Šidák
[ 0] 0.9998642526 0.9999922727 0.9341844137 0.9234670175 0.9899922294
[ 5] 0.9999922727 0.9992955735 0.9999922727 0.9998642526 0.9998909746
[10] 0.9998642526 0.9999288207 0.9995533892 0.9999922727 0.9990991210
[15] 0.9999922727 0.9998642526 0.9999674876 0.9992955735 0.7741716825
[20] 0.9993332472 0.9999922727 0.9999922727 0.9899922294 0.9999922727
[25] 0.9589019598 0.9998137104 0.3728369461 0.9999922727 0.8605248833
[30] 0.1460714182 0.0138585952 0.3270159382 0.5366136349 0.0247164330
[35] 0.0138585952 0.2640282766 0.0528503728 0.3723753774 0.0164308228
[40] 0.0008821796 0.0000125222 0.6357389664 0.2889497995 0.0362651575
[45] 0.0101847015 0.0389807074 0.0031679962 0.5985019850 0.1963376344
```
## Phix
Translation of Kotlin (version 2), except for the Hommel part, which is translated from Go.
Note that sq_min(), extract(), and custom_sort() as used below require 0.8.0+
```Phix
enum UP, DOWN
function ratchet(sequence p, integer direction)
atom m = p[1]
for i=1 to length(p) do
if iff(direction=UP?p[i]>m:p[i]1 then
crash("p-values must be in range 0.0 to 1.0")
end if
for i=1 to length(types) do
string ti = types[i]
sequence res = adjust(pValues,ti)
if res={} then
printf(1,"\nSorry, do not know how to do %s correction.\n"&
"Perhaps you want one of these?:\n %s\n",
{ti,join(types[1..$-1],"\n ")})
exit
end if
-- printf(1,"%s\n",{ti})
-- res = correct_answers[i] -- (for easier comparison only)
-- pp(res,{pp_FltFmt,"%13.10f",pp_IntFmt,"%13.10f",pp_Maxlen,75,pp_Pause,0})
atom error = sum(sq_abs(sq_sub(res,correct_answers[i])))
printf(1,"%s has cumulative error of %g\n", {ti,error})
end for
```
{{out}}
Matches Kotlin (etc) when some of those lines just above are uncommented.
```txt
Benjamini-Hochberg has cumulative error of 8.03052e-7
Benjamini-Yekutieli has cumulative error of 3.64071e-7
Bonferroni has cumulative error of 6.5e-8
Hochberg has cumulative error of 2.7375e-7
Holm has cumulative error of 2.8095e-7
Hommel has cumulative error of 4.35302e-7
Sidak has cumulative error of 7.26897e-10
```
## Python
{{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]''.
```python
from __future__ import division
import sys
def pminf(array):
x = 1
pmin_list = []
N = len(array)
for index in range(N):
if array[index] < x:
pmin_list.insert(index, array[index])
else:
pmin_list.insert(index, x)
return pmin_list
#end function
def cumminf(array):
cummin = []
cumulative_min = array[0]
for p in array:
if p < cumulative_min:
cumulative_min = p
cummin.append(cumulative_min)
return cummin
#end
def cummaxf(array):
cummax = []
cumulative_max = array[0]
for e in array:
if e > cumulative_max:
cumulative_max = e
cummax.append(cumulative_max)
return cummax
#end
def order(*args):
if len(args) > 1:
if args[1].lower() == 'false':# if ($string1 eq $string2) {
return sorted(range(len(args[0])), key = lambda k: args[0][k])
elif list(args[1].lower()) == list('true'):
return sorted(range(len(args[0])), key = lambda k: args[0][k], reverse = True)
else:
print "%s isn't a recognized parameter" % args[1]
sys.exit()
elif len(args) == 1:
return sorted(range(len(args[0])), key = lambda k: args[0][k])
#end
def p_adjust(*args):
method = "bh"
pvalues = args[0]
if len(args) > 1:
methods = {"bh", "fdr", "by", "holm", "hommel", "bonferroni", "hochberg"}
metharg = arg[1].lower()
if metharg in methods:
method = metharg
lp = len(pvalues)
n = lp
qvalues = []
if method == 'hochberg':#already all lower case
o = order(pvalues, 'TRUE')
cummin_input = []
for index in range(n):
cummin_input.insert(index, (index+1)*pvalues[o[index]])
cummin = cumminf(cummin_input)
pmin = pminf(cummin)
ro = order(o)
qvalues = [pmin[i] for i in ro]
elif method == 'bh':
o = order(pvalues, 'TRUE')
cummin_input = []
for index in range(n):
cummin_input.insert(index, (n/(n-index))* pvalues[o[index]])
ro = order(o)
cummin = cumminf(cummin_input)
pmin = pminf(cummin)
qvalues = [pmin[i] for i in ro]
elif method == 'by':
q = 0.0
o = order(pvalues, 'TRUE')
ro = order(o)
for index in range(1, n+1):
q += 1.0 / index;
cummin_input = []
for index in range(n):
cummin_input.insert(index, q * (n/(n-index)) * pvalues[o[index]])
cummin = cumminf(cummin_input)
pmin = pminf(cummin)
qvalues = [pmin[i] for i in ro]
elif method == 'bonferroni':
for index in range(n):
q = pvalues[index] * n
if (0 <= q) and (q < 1):
qvalues.insert(index, q)
elif q >= 1:
qvalues.insert(index, 1)
else:
print '%g won\'t give a Bonferroni adjusted p' % q
sys.exit()
elif method == 'holm':
o = order(pvalues)
cummax_input = []
for index in range(n):
cummax_input.insert(index, (n - index) * pvalues[o[index]])
ro = order(o)
cummax = cummaxf(cummax_input)
pmin = pminf(cummax)
qvalues = [pmin[i] for i in ro]
elif method == 'hommel':
i = range(1,n+1)
o = order(pvalues)
p = [pvalues[index] for index in o]
ro = order(o)
pa = []
q = []
smin = n*p[0]
for index in range(n):
temp = n*p[index] / (index + 1)
if temp < smin:
smin = temp
for index in range(n):
pa.insert(index, smin)
q.insert(index, smin)
for j in range(n-1,1,-1):
ij = range(1,n-j+2)
for x in range(len(ij)):
ij[x] -= 1
I2_LENGTH = j - 1
i2 = []
for index in range(I2_LENGTH+1):
i2.insert(index, n - j + 2 + index - 1)
q1 = j * p[i2[0]] / 2.0
for index in range(1,I2_LENGTH):
TEMP_Q1 = j * p[i2[index]] / (2.0 + index)
if TEMP_Q1 < q1:
q1 = TEMP_Q1
for index in range(n - j + 1):
q[ij[index]] = min(j * p[ij[index]], q1)
for index in range(I2_LENGTH):
q[i2[index]] = q[n-j]
for index in range(n):
if pa[index] < q[index]:
pa[index] = q[index]
qvalues = [pa[index] for index in ro]
else:
print "method %s isn't defined." % method
sys.exit()
return qvalues
pvalues = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03]
correct_answers = {}
correct_answers['bh'] = [6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02]
correct_answers['by'] = [1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02]
correct_answers['bonferroni'] = [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01]
correct_answers['hochberg'] = [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01]
correct_answers['holm'] = [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01]
correct_answers['hommel'] = [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01]
for key in correct_answers.keys():
error = 0.0
q = p_adjust(pvalues, key)
for i in range(len(q)):
error += abs(q[i] - correct_answers[key][i])
print '%s error = %g' % (key.upper(), error)
```
{{out}}
```txt
BONFERRONI error = 6.5e-08
BH error = 8.03053e-07
HOLM error = 2.8095e-07
HOMMEL error = 4.35302e-07
HOCHBERG error = 2.7375e-07
BY error = 3.64072e-07
```
## R
The '''p.adjust''' function is built-in, see [https://stat.ethz.ch/R-manual/R-devel/library/stats/html/p.adjust.html R manual].
```R
p <- c(4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03)
p.adjust(p, method = 'BH')
print("Benjamini-Hochberg")
writeLines("\n")
p.adjust(p, method = 'BY')
print("Benjamini & Yekutieli")
writeLines("\n")
p.adjust(p, method = 'bonferroni')
print("Bonferroni")
writeLines("\n")
p.adjust(p, method = 'hochberg')
print("Hochberg")
writeLines("\n");
p.adjust(p, method = 'hommel')
writeLines("Hommel\n")
```
{{out}}
```txt
[1] 6.126681e-01 8.521710e-01 1.987205e-01 1.891595e-01 3.217789e-01
[6] 9.301450e-01 4.870370e-01 9.301450e-01 6.049731e-01 6.826753e-01
[11] 6.482629e-01 7.253722e-01 5.280973e-01 8.769926e-01 4.705703e-01
[16] 9.241867e-01 6.049731e-01 7.856107e-01 4.887526e-01 1.136717e-01
[21] 4.991891e-01 8.769926e-01 9.991834e-01 3.217789e-01 9.301450e-01
[26] 2.304958e-01 5.832475e-01 3.899547e-02 8.521710e-01 1.476843e-01
[31] 1.683638e-02 2.562902e-03 3.516084e-02 6.250189e-02 3.636589e-03
[36] 2.562902e-03 2.946883e-02 6.166064e-03 3.899547e-02 2.688991e-03
[41] 4.502862e-04 1.252228e-05 7.881555e-02 3.142613e-02 4.846527e-03
[46] 2.562902e-03 4.846527e-03 1.101708e-03 7.252032e-02 2.205958e-02
[1] "Benjamini-Hochberg"
[1] 1.000000e+00 1.000000e+00 8.940844e-01 8.510676e-01 1.000000e+00
[6] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 5.114323e-01
[21] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26] 1.000000e+00 1.000000e+00 1.754486e-01 1.000000e+00 6.644618e-01
[31] 7.575031e-02 1.153102e-02 1.581959e-01 2.812089e-01 1.636176e-02
[36] 1.153102e-02 1.325863e-01 2.774239e-02 1.754486e-01 1.209832e-02
[41] 2.025930e-03 5.634031e-05 3.546073e-01 1.413926e-01 2.180552e-02
[46] 1.153102e-02 2.180552e-02 4.956812e-03 3.262838e-01 9.925057e-02
[1] "Benjamini & Yekutieli"
[1] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[6] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[21] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26] 1.000000e+00 1.000000e+00 7.019185e-01 1.000000e+00 1.000000e+00
[31] 2.020365e-01 1.516674e-02 5.625735e-01 1.000000e+00 2.909271e-02
[36] 1.537741e-02 4.125636e-01 6.782670e-02 6.803480e-01 1.882294e-02
[41] 9.005725e-04 1.252228e-05 1.000000e+00 4.713920e-01 4.395577e-02
[46] 1.088915e-02 4.846527e-02 3.305125e-03 1.000000e+00 2.867745e-01
[1] "Bonferroni"
[1] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[6] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[21] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26] 9.991834e-01 9.991834e-01 4.632662e-01 9.991834e-01 9.991834e-01
[31] 1.575885e-01 1.383967e-02 3.938014e-01 7.600230e-01 2.501973e-02
[36] 1.383967e-02 3.052971e-01 5.426136e-02 4.626366e-01 1.656419e-02
[41] 8.825610e-04 1.252228e-05 9.930759e-01 3.394022e-01 3.692284e-02
[46] 1.023581e-02 3.974152e-02 3.172920e-03 8.992520e-01 2.179486e-01
[1] "Hochberg"
[1] 9.991834e-01 9.991834e-01 9.991834e-01 9.987624e-01 9.991834e-01
[6] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.595180e-01
[21] 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26] 9.991834e-01 9.991834e-01 4.351895e-01 9.991834e-01 9.766522e-01
[31] 1.414256e-01 1.304340e-02 3.530937e-01 6.887709e-01 2.385602e-02
[36] 1.322457e-02 2.722920e-01 5.426136e-02 4.218158e-01 1.581127e-02
[41] 8.825610e-04 1.252228e-05 8.743649e-01 3.016908e-01 3.516461e-02
[46] 9.582456e-03 3.877222e-02 3.172920e-03 8.122276e-01 1.950067e-01
Hommel
```
## SAS
```sas
data pvalues;
input raw_p @@;
cards;
4.533744e-01 7.296024e-01 9.936026e-02 9.079658e-02 1.801962e-01
8.752257e-01 2.922222e-01 9.115421e-01 4.355806e-01 5.324867e-01
4.926798e-01 5.802978e-01 3.485442e-01 7.883130e-01 2.729308e-01
8.502518e-01 4.268138e-01 6.442008e-01 3.030266e-01 5.001555e-02
3.194810e-01 7.892933e-01 9.991834e-01 1.745691e-01 9.037516e-01
1.198578e-01 3.966083e-01 1.403837e-02 7.328671e-01 6.793476e-02
4.040730e-03 3.033349e-04 1.125147e-02 2.375072e-02 5.818542e-04
3.075482e-04 8.251272e-03 1.356534e-03 1.360696e-02 3.764588e-04
1.801145e-05 2.504456e-07 3.310253e-02 9.427839e-03 8.791153e-04
2.177831e-04 9.693054e-04 6.610250e-05 2.900813e-02 5.735490e-03
;
run;
proc multtest pdata=pvalues bon sid hom hoc holm;
run;
```
'''output'''
```txt
The Multtest Procedure
P-Value Adjustment Information
P-Value Adjustment Bonferroni
P-Value Adjustment Stepdown Bonferroni
P-Value Adjustment Sidak
P-Value Adjustment Hochberg
P-Value Adjustment Hommel
p-Values
Stepdown
Test Raw Bonferroni Bonferroni Sidak Hochberg Hommel
1 0.4534 1.0000 1.0000 1.0000 0.9992 0.9992
2 0.7296 1.0000 1.0000 1.0000 0.9992 0.9992
3 0.0994 1.0000 1.0000 0.9947 0.9992 0.9992
4 0.0908 1.0000 1.0000 0.9914 0.9992 0.9988
5 0.1802 1.0000 1.0000 1.0000 0.9992 0.9992
6 0.8752 1.0000 1.0000 1.0000 0.9992 0.9992
7 0.2922 1.0000 1.0000 1.0000 0.9992 0.9992
8 0.9115 1.0000 1.0000 1.0000 0.9992 0.9992
9 0.4356 1.0000 1.0000 1.0000 0.9992 0.9992
10 0.5325 1.0000 1.0000 1.0000 0.9992 0.9992
11 0.4927 1.0000 1.0000 1.0000 0.9992 0.9992
12 0.5803 1.0000 1.0000 1.0000 0.9992 0.9992
13 0.3485 1.0000 1.0000 1.0000 0.9992 0.9992
14 0.7883 1.0000 1.0000 1.0000 0.9992 0.9992
15 0.2729 1.0000 1.0000 1.0000 0.9992 0.9992
16 0.8503 1.0000 1.0000 1.0000 0.9992 0.9992
17 0.4268 1.0000 1.0000 1.0000 0.9992 0.9992
18 0.6442 1.0000 1.0000 1.0000 0.9992 0.9992
19 0.3030 1.0000 1.0000 1.0000 0.9992 0.9992
20 0.0500 1.0000 1.0000 0.9231 0.9992 0.9595
21 0.3195 1.0000 1.0000 1.0000 0.9992 0.9992
22 0.7893 1.0000 1.0000 1.0000 0.9992 0.9992
23 0.9992 1.0000 1.0000 1.0000 0.9992 0.9992
24 0.1746 1.0000 1.0000 0.9999 0.9992 0.9992
25 0.9038 1.0000 1.0000 1.0000 0.9992 0.9992
26 0.1199 1.0000 1.0000 0.9983 0.9992 0.9992
27 0.3966 1.0000 1.0000 1.0000 0.9992 0.9992
28 0.0140 0.7019 0.4633 0.5068 0.4633 0.4352
29 0.7329 1.0000 1.0000 1.0000 0.9992 0.9992
30 0.0679 1.0000 1.0000 0.9703 0.9992 0.9767
31 0.0040 0.2020 0.1576 0.1833 0.1576 0.1414
32 0.0003 0.0152 0.0140 0.0151 0.0138 0.0130
33 0.0113 0.5626 0.3938 0.4321 0.3938 0.3531
34 0.0238 1.0000 0.7600 0.6994 0.7600 0.6888
35 0.0006 0.0291 0.0250 0.0287 0.0250 0.0239
36 0.0003 0.0154 0.0140 0.0153 0.0138 0.0132
37 0.0083 0.4126 0.3053 0.3392 0.3053 0.2723
38 0.0014 0.0678 0.0543 0.0656 0.0543 0.0543
39 0.0136 0.6803 0.4626 0.4959 0.4626 0.4218
40 0.0004 0.0188 0.0166 0.0187 0.0166 0.0158
41 <.0001 0.0009 0.0009 0.0009 0.0009 0.0009
42 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
43 0.0331 1.0000 0.9931 0.8142 0.9931 0.8744
44 0.0094 0.4714 0.3394 0.3773 0.3394 0.3017
45 0.0009 0.0440 0.0369 0.0430 0.0369 0.0352
46 0.0002 0.0109 0.0102 0.0108 0.0102 0.0096
47 0.0010 0.0485 0.0397 0.0473 0.0397 0.0388
48 <.0001 0.0033 0.0032 0.0033 0.0032 0.0032
49 0.0290 1.0000 0.8993 0.7705 0.8993 0.8122
50 0.0057 0.2868 0.2179 0.2499 0.2179 0.1950
```
## Stata
The '''[https://econpapers.repec.org/software/bocbocode/s457100.htm qqvalue]''' package on SSC provides the equivalent of the R function '''p.adjust'''.
First, install the package with:
```stata>ssc install qqvalue list of mins
out,m := List.createLong(pvalues.len()), pvalues[0];
foreach pv in (pvalues){ out.append(m=m.min(pv)) }
out
}
fcn order(list,downUp){ // True==increasing, --> List(int) sorted indices
f:=(downUp) and fcn(a,b){ a[1]>b[1] } or fcn(a,b){ a[1]List
sz,r := pvalues.len(),List();
foreach pv in (pvalues){
b:=pv*sz;
if(b>=1.0) r.append(1.0);
else if(0.0<=b<1.0) r.append(b);
else throw(Exception.ValueError(
"%g is outside of the interval I planned.".fmt(b)));
}
r
}
fcn hommel(pvalues){
psz,indices := pvalues.len(), [1..psz].walk(); // 1,2,3,4...
o,ro := order(pvalues,False),order(o,False); # sort pvalues, sort indices
p := o.apply('wrap(n){ pvalues[n] }).copy(); // pvalues[*o]
npi := [1..].zip(p).apply('wrap([(n,p)]){ p*psz/n });
min := (0.0).min(npi); // min value in npi
pa,q := List.createLong(psz,min), pa.copy(); #(min,min,,,)
foreach j in ([psz - 1..2,-1]){
ij:=[0..psz - j].walk();
i2:=(j - 1).pump(List,'+(psz - j + 1));
q1:=(0.0).min((j-1).pump(List,'wrap(n){ p[i2[n]]*j/(2 + n) }));
foreach i in (psz - j + 1){ q[ij[i]] = q1.min(p[ij[i]]*j) }
foreach i in (j - 1){ q[i2[i]] = q[psz - j] }
foreach i in (psz){ pa[i] = pa[i].max(q[i]) }
}
psz.pump(List,'wrap(n){ pa[ro[n]] }); // Hommel q-values
}
```
```zkl
pvalues:=T(
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03);
bh(pvalues) : format(_,"\nBenjamini-Hochberg");
by(pvalues) : format(_,"\nBenjamini & Yekutieli");
bonferroni(pvalues) : format(_,"\nBonferroni");
hochberg(pvalues) : format(_,"\nHochberg");
hommel(pvalues) : format(_,"\nHommel");
fcn format(list,title){
print(title,":");
foreach n in ([1..list.len(),5]){
print("\n[%2d]:".fmt(n));
foreach x in (list[n-1,5]){ print(" %.6e".fmt(x)) }
}
println();
}
```
{{out}}
Benjamini-Hochberg:
[ 1]: 6.126681e-01 8.521710e-01 1.987205e-01 1.891595e-01 3.217789e-01
[ 6]: 9.301450e-01 4.870370e-01 9.301450e-01 6.049731e-01 6.826753e-01
[11]: 6.482629e-01 7.253722e-01 5.280973e-01 8.769926e-01 4.705703e-01
[16]: 9.241867e-01 6.049731e-01 7.856107e-01 4.887526e-01 1.136717e-01
[21]: 4.991891e-01 8.769926e-01 9.991834e-01 3.217789e-01 9.301450e-01
[26]: 2.304958e-01 5.832475e-01 3.899547e-02 8.521710e-01 1.476843e-01
[31]: 1.683638e-02 2.562902e-03 3.516084e-02 6.250189e-02 3.636589e-03
[36]: 2.562902e-03 2.946883e-02 6.166064e-03 3.899547e-02 2.688991e-03
[41]: 4.502862e-04 1.252228e-05 7.881555e-02 3.142613e-02 4.846527e-03
[46]: 2.562902e-03 4.846527e-03 1.101708e-03 7.252032e-02 2.205958e-02
Benjamini & Yekutieli:
[ 1]: 1.000000e+00 1.000000e+00 8.940844e-01 8.510676e-01 1.000000e+00
[ 6]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 5.114323e-01
[21]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26]: 1.000000e+00 1.000000e+00 1.754486e-01 1.000000e+00 6.644618e-01
[31]: 7.575031e-02 1.153102e-02 1.581959e-01 2.812089e-01 1.636176e-02
[36]: 1.153102e-02 1.325863e-01 2.774239e-02 1.754486e-01 1.209832e-02
[41]: 2.025930e-03 5.634031e-05 3.546073e-01 1.413926e-01 2.180552e-02
[46]: 1.153102e-02 2.180552e-02 4.956812e-03 3.262838e-01 9.925057e-02
Bonferroni:
[ 1]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[ 6]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[11]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[16]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[21]: 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[26]: 1.000000e+00 1.000000e+00 7.019185e-01 1.000000e+00 1.000000e+00
[31]: 2.020365e-01 1.516674e-02 5.625735e-01 1.000000e+00 2.909271e-02
[36]: 1.537741e-02 4.125636e-01 6.782670e-02 6.803480e-01 1.882294e-02
[41]: 9.005725e-04 1.252228e-05 1.000000e+00 4.713920e-01 4.395577e-02
[46]: 1.088915e-02 4.846527e-02 3.305125e-03 1.000000e+00 2.867745e-01
Hochberg:
[ 1]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[ 6]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[21]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26]: 9.991834e-01 9.991834e-01 4.632662e-01 9.991834e-01 9.991834e-01
[31]: 1.575885e-01 1.383967e-02 3.938014e-01 7.600230e-01 2.501973e-02
[36]: 1.383967e-02 3.052971e-01 5.426136e-02 4.626366e-01 1.656419e-02
[41]: 8.825610e-04 1.252228e-05 9.930759e-01 3.394022e-01 3.692284e-02
[46]: 1.023581e-02 3.974152e-02 3.172920e-03 8.992520e-01 2.179486e-01
Hommel:
[ 1]: 9.991834e-01 9.991834e-01 9.991834e-01 9.987624e-01 9.991834e-01
[ 6]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[11]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[16]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.595180e-01
[21]: 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01 9.991834e-01
[26]: 9.991834e-01 9.991834e-01 4.351895e-01 9.991834e-01 9.766522e-01
[31]: 1.414256e-01 1.304340e-02 3.530937e-01 6.887709e-01 2.385602e-02
[36]: 1.322457e-02 2.722920e-01 5.426136e-02 4.218158e-01 1.581127e-02
[41]: 8.825610e-04 1.252228e-05 8.743649e-01 3.016908e-01 3.516461e-02
[46]: 9.582456e-03 3.877222e-02 3.172920e-03 8.122276e-01 1.950067e-01
```