P-value correction: Difference between revisions
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{{
Given a list of [[wp:p-value|p-values]], adjust the p-values for multiple comparisons. This is done in order to control the false positive, or Type 1 error rate.
The adjusted p-values are sometimes called "q-values".
;Task:
Given one list of [
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,
Line 19 ⟶ 23:
There are
* Yoav Benjamini, Yosef Hochberg "[http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_hochberg1995.pdf
* Yoav Benjamini, Daniel Yekutieli, "[http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_yekutieli_ANNSTAT2001.pdf
* 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.
<br><br>
=={{header|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.
Line 46 ⟶ 53:
Link with <code>-lm</code>
<
#include <stdlib.h>//qsort
#include <math.h>//fabs
#include <stdbool.h>//bool data type
#include <strings.h>//strcasecmp
#include <assert.h>//assert, necessary for random integer selection
unsigned int *
//named after R function of same name, but simpler function
if (START == END) {
unsigned int *restrict sequence = malloc( (end+1) * sizeof(unsigned int));
Line 63 ⟶ 71:
exit(EXIT_FAILURE);
}
for (
sequence[i] = i+1;
}
Line 69 ⟶ 77:
}
if (START > END) {
end = (unsigned)START;
start = (unsigned)END;
}
const
unsigned int *restrict sequence = malloc( (1+LENGTH) * sizeof(unsigned int));
if (sequence == NULL) {
Line 80 ⟶ 88:
}
if (START < END) {
for (
sequence[index] = start + index;
}
} else {
for (
sequence[index] = end - index;
}
Line 117 ⟶ 125:
}
unsigned int *
//this has the same name as the same R function
unsigned int *restrict idx = malloc(SIZE * sizeof(unsigned int));
Line 144 ⟶ 152:
}
double *
//this takes the same name of the R function which it copies
//this requires a free() afterward where it is used
Line 168 ⟶ 176:
}
double *
//this takes the same name of the R function which it copies
//this requires a free() afterward where it is used
Line 183 ⟶ 191:
}
double cumulative_max = ARRAY[0];
for (
if (ARRAY[i] > cumulative_max) {
cumulative_max = ARRAY[i];
Line 192 ⟶ 200:
}
double *
//named after the R function pmin
if (NO_OF_ARRAY_ELEMENTS < 1) {
Line 217 ⟶ 225:
void double_say (const double *restrict ARRAY, const size_t NO_OF_ARRAY_ELEMENTS) {
printf("[1] %e", ARRAY[0]);
for (
printf(" %.10f", ARRAY[i]);
if (((i+1) % 5) == 0) {
printf("\n[%
}
}
Line 235 ⟶ 243:
}*/
double *
double *restrict doubleArray = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (doubleArray == NULL) {
Line 242 ⟶ 250:
exit(EXIT_FAILURE);
}
for (
doubleArray[index] = (double)ARRAY[index];
}
Line 256 ⟶ 264:
}
double *
//this function is a translation of R's p.adjust "BH" method
// i is always i[index] = NO_OF_ARRAY_ELEMENTS - index - 1
Line 265 ⟶ 273:
}
short int TYPE = -1;
if
TYPE = 0;
} else if (strcasecmp(STRING, "BH") == 0) {
TYPE = 0;
} else if (strcasecmp(STRING, "fdr") == 0) {
Line 293 ⟶ 303:
exit(EXIT_FAILURE);
}
for (
const double BONFERRONI = PVALUES[index] * NO_OF_ARRAY_ELEMENTS;
if (BONFERRONI >= 1.0) {
Line 315 ⟶ 325:
double *restrict o2double = uint2double(o, NO_OF_ARRAY_ELEMENTS);
double *restrict cummax_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
for (
cummax_input[index] = (NO_OF_ARRAY_ELEMENTS - index ) * (double)PVALUES[o[index]];
// printf("cummax_input[%zu] = %e\n", index, cummax_input[index]);
}
Line 329 ⟶ 339:
free(cummax_output); cummax_output = NULL;
double *restrict qvalues = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
for (
qvalues[index] = pmin[ro[index]];
}
Line 348 ⟶ 358:
exit(EXIT_FAILURE);
}
for (
p[index] = PVALUES[o[index]];
}
Line 371 ⟶ 381:
}
double min = (double)NO_OF_ARRAY_ELEMENTS * p[0];
for (
const double TEMP = (double)NO_OF_ARRAY_ELEMENTS * p[index] / (double)(1+index);
if (TEMP < min) {
min = TEMP;
}
}
for (
pa[index] = min;
q[index] = min;
Line 392 ⟶ 402:
}
*/
for (
// printf("j = %zu\n", j);
unsigned int *restrict ij = seq_len(
const size_t I2_LENGTH = j - 1;
unsigned int *restrict i2 = malloc(I2_LENGTH * sizeof(unsigned int));
for (
i2[i] = NO_OF_ARRAY_ELEMENTS-j+2+i-1;
//R's indices are 1-based, C's are 0-based, I added the -1
}
double q1 = (double)j * p[i2[0]] / 2.0;
for (
const double TEMP_Q1 = (double)j * p[i2[i]] / (double)(2 + i);
if (TEMP_Q1 < q1) {
q1 = TEMP_Q1;
Line 413 ⟶ 420:
}
for (
q[ij[i]] = min2( (double)j*p[ij[i]], q1);
}
free(ij); ij = NULL;
for (
q[i2[i]] = q[NO_OF_ARRAY_ELEMENTS - j];//subtract 1 because of starting index difference
}
free(i2); i2 = NULL;
for (
if (pa[i] < q[i]) {
pa[i] = q[i];
Line 432 ⟶ 439:
}//end j loop
free(p); p = NULL;
for (
q[index] = pa[ro[index]];//Hommel q-values
}
Line 465 ⟶ 472:
double *restrict cummin_input = malloc(sizeof(double) * NO_OF_ARRAY_ELEMENTS);
if (TYPE == 0) {//BH method
for (
const double NI = (double)NO_OF_ARRAY_ELEMENTS / (double)(NO_OF_ARRAY_ELEMENTS - index);// n/i simplified
cummin_input[index] = NI * PVALUES[o[index]];//PVALUES[o[index]] is p[o]
}
} else if (TYPE == 1) {//BY method
double q = 1.0;
for (
q +=
}
for (
const double NI = (double)NO_OF_ARRAY_ELEMENTS / (double)(NO_OF_ARRAY_ELEMENTS - index);// n/i simplified
cummin_input[index] = q * NI * PVALUES[o[index]];//PVALUES[o[index]] is p[o]
}
} else if (TYPE == 3) {//Hochberg method
for (
// pmin(1, cummin((n - i + 1L) * p[o]))[ro]
cummin_input[index] = (double)(index + 1) * PVALUES[o[index]];
}
}
Line 499 ⟶ 506:
return q_array;
}
int main(void) {
Line 593 ⟶ 601:
return 0;
}
</syntaxhighlight>
{{out}}
Line 680 ⟶ 688:
type 5 = 'hommel' has cumulative error of 4.35302e-07</pre>
===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 Raku entry. If using gcc, you need to link to the math library (-lm).
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define SIZE 50
#define each_i(start, end) for (i = start; i < end; ++i)
typedef enum { UP, DOWN } direction;
typedef struct { int index; double value; } iv1;
typedef struct { int index; int value; } iv2;
/* test also for 'Unknown' correction type */
const char *types[8] = {
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
};
int compare_iv1(const void *a, const void *b) {
double aa = ((iv1 *)a) -> value;
double bb = ((iv1 *)b) -> value;
if (aa > bb) return 1;
if (aa < bb) return -1;
return 0;
}
int compare_iv1_desc(const void *a, const void *b) {
return -compare_iv1(a, b);
}
int compare_iv2(const void *a, const void *b) {
return ((iv2 *)a) -> value - ((iv2 *)b) -> value;
}
void ratchet(double *pa, direction dir) {
int i;
double m = pa[0];
if (dir == UP) {
each_i(1, SIZE) {
if (pa[i] > m) pa[i] = m;
m = pa[i];
}
}
else {
each_i(1, SIZE) {
if (pa[i] < m) pa[i] = m;
m = pa[i];
}
}
each_i(0, SIZE) if (pa[i] > 1.0) pa[i] = 1.0;
}
void schwartzian(const double *p, double *pa, direction dir) {
int i;
int order[SIZE];
int order2[SIZE];
iv1 iv1s[SIZE];
iv2 iv2s[SIZE];
double pa2[SIZE];
each_i(0, SIZE) { iv1s[i].index = i; iv1s[i].value = p[i]; }
if (dir == UP)
qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1_desc);
else
qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1);
each_i(0, SIZE) order[i] = iv1s[i].index;
each_i(0, SIZE) pa[i] *= p[order[i]];
ratchet(pa, dir);
each_i(0, SIZE) { iv2s[i].index = i; iv2s[i].value = order[i]; }
qsort(iv2s, SIZE, sizeof(iv2s[0]), compare_iv2);
each_i(0, SIZE) order2[i] = iv2s[i].index;
each_i(0, SIZE) pa2[i] = pa[order2[i]];
each_i(0, SIZE) pa[i] = pa2[i];
}
void adjust(const double *p, double *pa, const char *type) {
int i;
if (!strcmp(type, "Benjamini-Hochberg")) {
each_i(0, SIZE) pa[i] = (double)SIZE / (SIZE - i);
schwartzian(p, pa, UP);
}
else if (!strcmp(type, "Benjamini-Yekutieli")) {
double q = 0.0;
each_i(1, SIZE + 1) q += 1.0 / i;
each_i(0, SIZE) pa[i] = q * SIZE / (SIZE - i);
schwartzian(p, pa, UP);
}
else if (!strcmp(type, "Bonferroni")) {
each_i(0, SIZE) pa[i] = (p[i] * SIZE > 1.0) ? 1.0 : p[i] * SIZE;
}
else if (!strcmp(type, "Hochberg")) {
each_i(0, SIZE) pa[i] = i + 1.0;
schwartzian(p, pa, UP);
}
else if (!strcmp(type, "Holm")) {
each_i(0, SIZE) pa[i] = SIZE - i;
schwartzian(p, pa, DOWN);
}
else if (!strcmp(type, "Hommel")) {
int i, j;
int order[SIZE];
int order2[SIZE];
iv1 iv1s[SIZE];
iv2 iv2s[SIZE];
double s[SIZE];
double q[SIZE];
double pa2[SIZE];
int indices[SIZE];
each_i(0, SIZE) { iv1s[i].index = i; iv1s[i].value = p[i]; }
qsort(iv1s, SIZE, sizeof(iv1s[0]), compare_iv1);
each_i(0, SIZE) order[i] = iv1s[i].index;
each_i(0, SIZE) s[i] = p[order[i]];
double min = s[0] * SIZE;
each_i(1, SIZE) {
double temp = s[i] / (i + 1.0);
if (temp < min) min = temp;
}
each_i(0, SIZE) q[i] = min;
each_i(0, SIZE) pa2[i] = min;
for (j = SIZE - 1; j >= 2; --j) {
each_i(0, SIZE) indices[i] = i;
int upper_start = SIZE - j + 1; /* upper indices start index */
int upper_size = j - 1; /* size of upper indices */
int lower_size = SIZE - upper_size; /* size of lower indices */
double qmin = j * s[indices[upper_start]] / 2.0;
each_i(1, upper_size) {
double temp = s[indices[upper_start + i]] * j / (2.0 + i);
if (temp < qmin) qmin = temp;
}
each_i(0, lower_size) {
double temp = s[indices[i]] * j;
q[indices[i]] = (temp < qmin) ? temp : qmin;
}
each_i(0, upper_size) q[indices[upper_start + i]] = q[SIZE - j];
each_i(0, SIZE) if (pa2[i] < q[i]) pa2[i] = q[i];
}
each_i(0, SIZE) { iv2s[i].index = i; iv2s[i].value = order[i]; }
qsort(iv2s, SIZE, sizeof(iv2s[0]), compare_iv2);
each_i(0, SIZE) order2[i] = iv2s[i].index;
each_i(0, SIZE) pa[i] = pa2[order2[i]];
}
else if (!strcmp(type, "Šidák")) {
each_i(0, SIZE) pa[i] = 1.0 - pow(1.0 - p[i], SIZE);
}
else {
printf("\nSorry, do not know how to do '%s' correction.\n", type);
printf("Perhaps you want one of these?:\n");
each_i(0, 7) printf(" %s\n", types[i]);
exit(1);
}
}
void adjusted(const double *p, const char *type) {
int i;
double pa[SIZE] = { 0.0 };
if (check(p)) {
adjust(p, pa, type);
printf("\n%s", type);
each_i(0, SIZE) {
if (!(i % 5)) printf("\n[%2d] ", i);
printf("%1.10f ", pa[i]);
}
printf("\n");
}
else {
printf("p-values must be in range 0.0 to 1.0\n");
exit(1);
}
}
int check(const double* p) {
int i;
each_i(0, SIZE) {
if (p[i] < 0.0 || p[i] > 1.0) return 0;
}
return 1;
}
int main() {
int i;
double p_values[SIZE] = {
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
each_i(0, 8) adjusted(p_values, types[i]);
return 0;
}</syntaxhighlight>
{{output}}
<pre>
Same as Kotlin (Version 2) output.
</pre>
=={{header|C sharp|C#}}==
{{trans|Java}}
<syntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.Linq;
namespace PValueCorrection {
class Program {
static List<int> SeqLen(int start, int end) {
var result = new List<int>();
if (start == end) {
for (int i = 0; i < end + 1; ++i) {
result.Add(i + 1);
}
} else if (start < end) {
for (int i = 0; i < end - start + 1; ++i) {
result.Add(start + i);
}
} else {
for (int i = 0; i < start - end + 1; ++i) {
result.Add(start - i);
}
}
return result;
}
static List<int> Order(List<double> array, bool decreasing) {
List<int> idx = new List<int>();
for (int i = 0; i < array.Count; ++i) {
idx.Add(i);
}
IComparer<int> cmp;
if (decreasing) {
cmp = Comparer<int>.Create((a, b) => array[a] < array[b] ? 1 : array[b] < array[a] ? -1 : 0);
} else {
cmp = Comparer<int>.Create((a, b) => array[b] < array[a] ? 1 : array[a] < array[b] ? -1 : 0);
}
idx.Sort(cmp);
return idx;
}
static List<double> Cummin(List<double> array) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("cummin requires at least one element");
var output = new List<double>();
double cumulativeMin = array[0];
for (int i = 0; i < array.Count; ++i) {
if (array[i] < cumulativeMin) cumulativeMin = array[i];
output.Add(cumulativeMin);
}
return output;
}
static List<double> Cummax(List<double> array) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("cummax requires at least one element");
var output = new List<double>();
double cumulativeMax = array[0];
for (int i = 0; i < array.Count; ++i) {
if (array[i] > cumulativeMax) cumulativeMax = array[i];
output.Add(cumulativeMax);
}
return output;
}
static List<double> Pminx(List<double> array, double x) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("pmin requires at least one element");
var result = new List<double>();
for (int i = 0; i < array.Count; ++i) {
if (array[i] < x) {
result.Add(array[i]);
} else {
result.Add(x);
}
}
return result;
}
static void Say(List<double> array) {
Console.Write("[ 1] {0:E}", array[0]);
for (int i = 1; i < array.Count; ++i) {
Console.Write(" {0:E}", array[i]);
if ((i + 1) % 5 == 0) Console.Write("\n[{0,2}]", i + 1);
}
Console.WriteLine();
}
static List<double> PAdjust(List<double> pvalues, string str) {
var size = pvalues.Count;
if (size < 1) throw new ArgumentOutOfRangeException("pAdjust requires at least one element");
int type;
switch (str.ToLower()) {
case "bh":
case "fdr":
type = 0;
break;
case "by":
type = 1;
break;
case "bonferroni":
type = 2;
break;
case "hochberg":
type = 3;
break;
case "holm":
type = 4;
break;
case "hommel":
type = 5;
break;
default:
throw new ArgumentException(str + " doesn't match any accepted FDR types");
}
if (2 == type) { // Bonferroni method
var result2 = new List<double>();
for (int i = 0; i < size; ++i) {
double b = pvalues[i] * size;
if (b >= 1) {
result2.Add(1);
} else if (0 <= b && b < 1) {
result2.Add(b);
} else {
throw new Exception(b + " is outside [0, 1)");
}
}
return result2;
} else if (4 == type) { // Holm method
var o4 = Order(pvalues, false);
var o4d = o4.ConvertAll(x => (double)x);
var cummaxInput = new List<double>();
for (int i = 0; i < size; ++i) {
cummaxInput.Add((size - i) * pvalues[o4[i]]);
}
var ro4 = Order(o4d, false);
var cummaxOutput = Cummax(cummaxInput);
var pmin4 = Pminx(cummaxOutput, 1.0);
var hr = new List<double>();
for (int i = 0; i < size; ++i) {
hr.Add(pmin4[ro4[i]]);
}
return hr;
} else if (5 == type) { // Hommel method
var indices = SeqLen(size, size);
var o5 = Order(pvalues, false);
var p = new List<double>();
for (int i = 0; i < size; ++i) {
p.Add(pvalues[o5[i]]);
}
var o5d = o5.ConvertAll(x => (double)x);
var ro5 = Order(o5d, false);
var q = new List<double>();
var pa = new List<double>();
var npi = new List<double>();
for (int i = 0; i < size; ++i) {
npi.Add(p[i] * size / indices[i]);
}
double min = npi.Min();
q.AddRange(Enumerable.Repeat(min, size));
pa.AddRange(Enumerable.Repeat(min, size));
for (int j = size; j >= 2; --j) {
var ij = SeqLen(1, size - j + 1);
for (int i = 0; i < size - j + 1; ++i) {
ij[i]--;
}
int i2Length = j - 1;
var i2 = new List<int>();
for (int i = 0; i < i2Length; ++i) {
i2.Add(size - j + 2 + i - 1);
}
double q1 = j * p[i2[0]] / 2.0;
for (int i = 1; i < i2Length; ++i) {
double temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
for (int i = 0; i < size - j + 1; ++i) {
q[ij[i]] = Math.Min(p[ij[i]] * j, q1);
}
for (int i = 0; i < i2Length; ++i) {
q[i2[i]] = q[size - j];
}
for (int i = 0; i < size; ++i) {
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
}
for (int i = 0; i < size; ++i) {
q[i] = pa[ro5[i]];
}
return q;
}
var ni = new List<double>();
var o = Order(pvalues, true);
var od = o.ConvertAll(x => (double)x);
for (int i = 0; i < size; ++i) {
if (pvalues[i] < 0 || pvalues[i] > 1) {
throw new Exception("array[" + i + "] = " + pvalues[i] + " is outside [0, 1]");
}
ni.Add((double)size / (size - i));
}
var ro = Order(od, false);
var cumminInput = new List<double>();
if (0 == type) { // BH method
for (int i = 0; i < size; ++i) {
cumminInput.Add(ni[i] * pvalues[o[i]]);
}
} else if (1 == type) { // BY method
double q = 0;
for (int i = 1; i < size + 1; ++i) {
q += 1.0 / i;
}
for (int i = 0; i < size; ++i) {
cumminInput.Add(q * ni[i] * pvalues[o[i]]);
}
} else if (3 == type) { // Hochberg method
for (int i = 0; i < size; ++i) {
cumminInput.Add((i + 1) * pvalues[o[i]]);
}
}
var cumminArray = Cummin(cumminInput);
var pmin = Pminx(cumminArray, 1.0);
var result = new List<double>();
for (int i = 0; i < size; ++i) {
result.Add(pmin[ro[i]]);
}
return result;
}
static void Main(string[] args) {
var pvalues = new List<double> {
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
var correctAnswers = new List<List<double>> {
new List<double> { // Benjamini-Hochberg
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
},
new List<double> { // Benjamini & Yekutieli
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
},
new List<double> { // Bonferroni
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
},
new List<double> { // Hochberg
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new List<double> { // Holm
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new List<double> { // Hommel
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
}
};
string[] types = { "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
for (int type = 0; type < types.Length; ++type) {
var q = PAdjust(pvalues, types[type]);
double error = 0.0;
for (int i = 0; i < pvalues.Count; ++i) {
error += Math.Abs(q[i] - correctAnswers[type][i]);
}
Say(q);
Console.WriteLine("type {0} = '{1}' has a cumulative error of {2:E}", type, types[type], error);
Console.WriteLine();
}
}
}
}</syntaxhighlight>
{{out}}
<pre>[ 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</pre>
=={{header|C++}}==
{{trans|Java}}
<syntaxhighlight lang="cpp">#include <algorithm>
#include <functional>
#include <iostream>
#include <numeric>
#include <vector>
std::vector<int> seqLen(int start, int end) {
std::vector<int> result;
if (start == end) {
result.resize(end + 1);
std::iota(result.begin(), result.end(), 1);
} else if (start < end) {
result.resize(end - start + 1);
std::iota(result.begin(), result.end(), start);
} else {
result.resize(start - end + 1);
std::iota(result.rbegin(), result.rend(), end);
}
return result;
}
std::vector<int> order(const std::vector<double>& arr, bool decreasing) {
std::vector<int> idx(arr.size());
std::iota(idx.begin(), idx.end(), 0);
std::function<bool(int, int)> cmp;
if (decreasing) {
cmp = [&arr](int a, int b) { return arr[b] < arr[a]; };
} else {
cmp = [&arr](int a, int b) { return arr[a] < arr[b]; };
}
std::sort(idx.begin(), idx.end(), cmp);
return idx;
}
std::vector<double> cummin(const std::vector<double>& arr) {
if (arr.empty()) throw std::runtime_error("cummin requries at least one element");
std::vector<double> output(arr.size());
double cumulativeMin = arr[0];
std::transform(arr.cbegin(), arr.cend(), output.begin(), [&cumulativeMin](double a) {
if (a < cumulativeMin) cumulativeMin = a;
return cumulativeMin;
});
return output;
}
std::vector<double> cummax(const std::vector<double>& arr) {
if (arr.empty()) throw std::runtime_error("cummax requries at least one element");
std::vector<double> output(arr.size());
double cumulativeMax = arr[0];
std::transform(arr.cbegin(), arr.cend(), output.begin(), [&cumulativeMax](double a) {
if (cumulativeMax < a) cumulativeMax = a;
return cumulativeMax;
});
return output;
}
std::vector<double> pminx(const std::vector<double>& arr, double x) {
if (arr.empty()) throw std::runtime_error("pmin requries at least one element");
std::vector<double> result(arr.size());
std::transform(arr.cbegin(), arr.cend(), result.begin(), [&x](double a) {
if (a < x) return a;
return x;
});
return result;
}
void doubleSay(const std::vector<double>& arr) {
printf("[ 1] %.10f", arr[0]);
for (size_t i = 1; i < arr.size(); ++i) {
printf(" %.10f", arr[i]);
if ((i + 1) % 5 == 0) printf("\n[%2d]", i + 1);
}
}
std::vector<double> pAdjust(const std::vector<double>& pvalues, const std::string& str) {
if (pvalues.empty()) throw std::runtime_error("pAdjust requires at least one element");
size_t size = pvalues.size();
int type;
if ("bh" == str || "fdr" == str) {
type = 0;
} else if ("by" == str) {
type = 1;
} else if ("bonferroni" == str) {
type = 2;
} else if ("hochberg" == str) {
type = 3;
} else if ("holm" == str) {
type = 4;
} else if ("hommel" == str) {
type = 5;
} else {
throw std::runtime_error(str + " doesn't match any accepted FDR types");
}
// Bonferroni method
if (2 == type) {
std::vector<double> result(size);
for (size_t i = 0; i < size; ++i) {
double b = pvalues[i] * size;
if (b >= 1) {
result[i] = 1;
} else if (0 <= b && b < 1) {
result[i] = b;
} else {
throw std::runtime_error("a value is outside [0, 1)");
}
}
return result;
}
// Holm method
else if (4 == type) {
auto o = order(pvalues, false);
std::vector<double> o2Double(o.begin(), o.end());
std::vector<double> cummaxInput(size);
for (size_t i = 0; i < size; ++i) {
cummaxInput[i] = (size - i) * pvalues[o[i]];
}
auto ro = order(o2Double, false);
auto cummaxOutput = cummax(cummaxInput);
auto pmin = pminx(cummaxOutput, 1.0);
std::vector<double> result(size);
std::transform(ro.cbegin(), ro.cend(), result.begin(), [&pmin](int a) { return pmin[a]; });
return result;
}
// Hommel
else if (5 == type) {
auto indices = seqLen(size, size);
auto o = order(pvalues, false);
std::vector<double> p(size);
std::transform(o.cbegin(), o.cend(), p.begin(), [&pvalues](int a) { return pvalues[a]; });
std::vector<double> o2Double(o.begin(), o.end());
auto ro = order(o2Double, false);
std::vector<double> q(size);
std::vector<double> pa(size);
std::vector<double> npi(size);
for (size_t i = 0; i < size; ++i) {
npi[i] = p[i] * size / indices[i];
}
double min = *std::min_element(npi.begin(), npi.end());
std::fill(q.begin(), q.end(), min);
std::fill(pa.begin(), pa.end(), min);
for (int j = size; j >= 2; --j) {
auto ij = seqLen(1, size - j + 1);
std::transform(ij.cbegin(), ij.cend(), ij.begin(), [](int a) { return a - 1; });
int i2Length = j - 1;
std::vector<int> i2(i2Length);
for (int i = 0; i < i2Length; ++i) {
i2[i] = size - j + 2 + i - 1;
}
double q1 = j * p[i2[0]] / 2.0;
for (int i = 1; i < i2Length; ++i) {
double temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
for (size_t i = 0; i < size - j + 1; ++i) {
q[ij[i]] = std::min(p[ij[i]] * j, q1);
}
for (int i = 0; i < i2Length; ++i) {
q[i2[i]] = q[size - j];
}
for (size_t i = 0; i < size; ++i) {
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
}
std::transform(ro.cbegin(), ro.cend(), q.begin(), [&pa](int a) { return pa[a]; });
return q;
}
std::vector<double> ni(size);
std::vector<int> o = order(pvalues, true);
std::vector<double> od(o.begin(), o.end());
for (size_t i = 0; i < size; ++i) {
if (pvalues[i] < 0 || pvalues[i]>1) {
throw std::runtime_error("a value is outside [0, 1]");
}
ni[i] = (double)size / (size - i);
}
auto ro = order(od, false);
std::vector<double> cumminInput(size);
if (0 == type) { // BH method
for (size_t i = 0; i < size; ++i) {
cumminInput[i] = ni[i] * pvalues[o[i]];
}
} else if (1 == type) { // BY method
double q = 0;
for (size_t i = 1; i < size + 1; ++i) {
q += 1.0 / i;
}
for (size_t i = 0; i < size; ++i) {
cumminInput[i] = q * ni[i] * pvalues[o[i]];
}
} else if (3 == type) { // Hochberg method
for (size_t i = 0; i < size; ++i) {
cumminInput[i] = (i + 1) * pvalues[o[i]];
}
}
auto cumminArray = cummin(cumminInput);
auto pmin = pminx(cumminArray, 1.0);
std::vector<double> result(size);
for (size_t i = 0; i < size; ++i) {
result[i] = pmin[ro[i]];
}
return result;
}
int main() {
using namespace std;
vector<double> pvalues{
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
vector<vector<double>> correctAnswers{
// Benjamini-Hochberg
{
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
},
// Benjamini & Yekutieli
{
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
},
// Bonferroni
{
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
},
// Hochberg
{
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
// Holm
{
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
// Hommel
{
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
}
};
vector<string> types{ "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
for (size_t type = 0; type < types.size(); ++type) {
auto q = pAdjust(pvalues, types[type]);
double error = 0.0;
for (size_t i = 0; i < pvalues.size(); ++i) {
error += abs(q[i] - correctAnswers[type][i]);
}
doubleSay(q);
printf("\ntype = %d = '%s' has a cumulative error of %g\n\n\n", type, types[type].c_str(), error);
}
return 0;
}</syntaxhighlight>
{{out}}
<pre>[ 1] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
[50]
type = 0 = 'bh' has a cumulative error of 8.03053e-07
[ 1] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
[50]
type = 1 = 'by' has a cumulative error of 3.64072e-07
[ 1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
[50]
type = 2 = 'bonferroni' has a cumulative error of 6.5e-08
[ 1] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type = 3 = 'hochberg' has a cumulative error of 2.7375e-07
[ 1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
[50]
type = 4 = 'holm' has a cumulative error of 2.8095e-07
[ 1] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
[50]
type = 5 = 'hommel' has a cumulative error of 4.35302e-07</pre>
=={{header|D}}==
{{trans|Kotlin}}
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<syntaxhighlight lang="d">import std.algorithm;
import std.conv;
import std.math;
Line 1,022 ⟶ 2,057:
writefln("\ntype %d = '%s' has a cumulative error of %g", type, types[type], error);
}
}</
{{out}}
<pre>[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
Line 1,102 ⟶ 2,137:
type 5 = 'hommel' has a cumulative error of 4.35302e-07</pre>
=={{header|Go}}==
{{trans|Kotlin (Version 2)}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"log"
"math"
"os"
"sort"
"strconv"
"strings"
)
type pvalues = []float64
type iv1 struct {
index int
value float64
}
type iv2 struct{ index, value int }
type direction int
const (
up direction = iota
down
)
// Test also for 'Unknown' correction type.
var ctypes = []string{
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown",
}
func minimum(p pvalues) float64 {
m := p[0]
for i := 1; i < len(p); i++ {
if p[i] < m {
m = p[i]
}
}
return m
}
func maximum(p pvalues) float64 {
m := p[0]
for i := 1; i < len(p); i++ {
if p[i] > m {
m = p[i]
}
}
return m
}
func adjusted(p pvalues, ctype string) (string, error) {
err := check(p)
if err != nil {
return "", err
}
temp := pformat(adjust(p, ctype), 5)
return fmt.Sprintf("\n%s\n%s", ctype, temp), nil
}
func pformat(p pvalues, cols int) string {
var lines []string
for i := 0; i < len(p); i += cols {
fchunk := p[i : i+cols]
schunk := make([]string, cols)
for j := 0; j < cols; j++ {
schunk[j] = strconv.FormatFloat(fchunk[j], 'f', 10, 64)
}
lines = append(lines, fmt.Sprintf("[%2d] %s", i, strings.Join(schunk, " ")))
}
return strings.Join(lines, "\n")
}
func check(p []float64) error {
cond := len(p) > 0 && minimum(p) >= 0 && maximum(p) <= 1
if !cond {
return fmt.Errorf("p-values must be in range 0.0 to 1.0")
}
return nil
}
func ratchet(p pvalues, dir direction) {
size := len(p)
m := p[0]
if dir == up {
for i := 1; i < size; i++ {
if p[i] > m {
p[i] = m
}
m = p[i]
}
} else {
for i := 1; i < size; i++ {
if p[i] < m {
p[i] = m
}
m = p[i]
}
}
for i := 0; i < size; i++ {
if p[i] > 1.0 {
p[i] = 1.0
}
}
}
func schwartzian(p pvalues, mult pvalues, dir direction) pvalues {
size := len(p)
order := make([]int, size)
iv1s := make([]iv1, size)
for i := 0; i < size; i++ {
iv1s[i] = iv1{i, p[i]}
}
if dir == up {
sort.Slice(iv1s, func(i, j int) bool {
return iv1s[i].value > iv1s[j].value
})
} else {
sort.Slice(iv1s, func(i, j int) bool {
return iv1s[i].value < iv1s[j].value
})
}
for i := 0; i < size; i++ {
order[i] = iv1s[i].index
}
pa := make(pvalues, size)
for i := 0; i < size; i++ {
pa[i] = mult[i] * p[order[i]]
}
ratchet(pa, dir)
order2 := make([]int, size)
iv2s := make([]iv2, size)
for i := 0; i < size; i++ {
iv2s[i] = iv2{i, order[i]}
}
sort.Slice(iv2s, func(i, j int) bool {
return iv2s[i].value < iv2s[j].value
})
for i := 0; i < size; i++ {
order2[i] = iv2s[i].index
}
pa2 := make(pvalues, size)
for i := 0; i < size; i++ {
pa2[i] = pa[order2[i]]
}
return pa2
}
func adjust(p pvalues, ctype string) pvalues {
size := len(p)
if size == 0 {
return p
}
fsize := float64(size)
switch ctype {
case "Benjamini-Hochberg":
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = fsize / float64(size-i)
}
return schwartzian(p, mult, up)
case "Benjamini-Yekutieli":
q := 0.0
for i := 1; i <= size; i++ {
q += 1.0 / float64(i)
}
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = q * fsize / (fsize - float64(i))
}
return schwartzian(p, mult, up)
case "Bonferroni":
p2 := make(pvalues, size)
for i := 0; i < size; i++ {
p2[i] = math.Min(p[i]*fsize, 1.0)
}
return p2
case "Hochberg":
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = float64(i) + 1
}
return schwartzian(p, mult, up)
case "Holm":
mult := make(pvalues, size)
for i := 0; i < size; i++ {
mult[i] = fsize - float64(i)
}
return schwartzian(p, mult, down)
case "Hommel":
order := make([]int, size)
iv1s := make([]iv1, size)
for i := 0; i < size; i++ {
iv1s[i] = iv1{i, p[i]}
}
sort.Slice(iv1s, func(i, j int) bool {
return iv1s[i].value < iv1s[j].value
})
for i := 0; i < size; i++ {
order[i] = iv1s[i].index
}
s := make(pvalues, size)
for i := 0; i < size; i++ {
s[i] = p[order[i]]
}
m := make(pvalues, size)
for i := 0; i < size; i++ {
m[i] = s[i] * fsize / (float64(i) + 1)
}
min := minimum(m)
q := make(pvalues, size)
for i := 0; i < size; i++ {
q[i] = min
}
pa := make(pvalues, size)
for i := 0; i < size; i++ {
pa[i] = min
}
for j := size - 1; j >= 2; j-- {
lower := make([]int, size-j+1) // lower indices
for i := 0; i < len(lower); i++ {
lower[i] = i
}
upper := make([]int, j-1) // upper indices
for i := 0; i < len(upper); i++ {
upper[i] = size - j + 1 + i
}
qmin := float64(j) * s[upper[0]] / 2.0
for i := 1; i < len(upper); i++ {
temp := s[upper[i]] * float64(j) / (2.0 + float64(i))
if temp < qmin {
qmin = temp
}
}
for i := 0; i < len(lower); i++ {
q[lower[i]] = math.Min(s[lower[i]]*float64(j), qmin)
}
for i := 0; i < len(upper); i++ {
q[upper[i]] = q[size-j]
}
for i := 0; i < size; i++ {
if pa[i] < q[i] {
pa[i] = q[i]
}
}
}
order2 := make([]int, size)
iv2s := make([]iv2, size)
for i := 0; i < size; i++ {
iv2s[i] = iv2{i, order[i]}
}
sort.Slice(iv2s, func(i, j int) bool {
return iv2s[i].value < iv2s[j].value
})
for i := 0; i < size; i++ {
order2[i] = iv2s[i].index
}
pa2 := make(pvalues, size)
for i := 0; i < size; i++ {
pa2[i] = pa[order2[i]]
}
return pa2
case "Šidák":
p2 := make(pvalues, size)
for i := 0; i < size; i++ {
p2[i] = 1.0 - math.Pow(1.0-float64(p[i]), fsize)
}
return p2
default:
fmt.Printf("\nSorry, do not know how to do '%s' correction.\n", ctype)
fmt.Println("Perhaps you want one of these?:")
temp := make([]string, len(ctypes)-1)
for i := 0; i < len(temp); i++ {
temp[i] = fmt.Sprintf(" %s", ctypes[i])
}
fmt.Println(strings.Join(temp, "\n"))
os.Exit(1)
}
return p
}
func main() {
p := pvalues{
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03,
}
for _, ctype := range ctypes {
s, err := adjusted(p, ctype)
if err != nil {
log.Fatal(err)
}
fmt.Println(s)
}
}</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">
Benjamini-Hochberg
[ 0] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
Benjamini-Yekutieli
[ 0] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
Bonferroni
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
Hochberg
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Holm
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Hommel
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
Šidák
[ 0] 1.0000000000 1.0000000000 0.9946598274 0.9914285749 0.9999515274
[ 5] 1.0000000000 0.9999999688 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 0.9999999995 1.0000000000 0.9999998801
[15] 1.0000000000 1.0000000000 1.0000000000 0.9999999855 0.9231179729
[20] 0.9999999956 1.0000000000 1.0000000000 0.9999317605 1.0000000000
[25] 0.9983109511 1.0000000000 0.5068253940 1.0000000000 0.9703301333
[30] 0.1832692440 0.0150545753 0.4320729669 0.6993672225 0.0286818157
[35] 0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
[40] 0.0009001752 0.0000125222 0.8142104886 0.3772612062 0.0430222116
[45] 0.0108312558 0.0473319661 0.0032997780 0.7705015898 0.2499384839
Sorry, do not know how to do 'Unknown' correction.
Perhaps you want one of these?:
Benjamini-Hochberg
Benjamini-Yekutieli
Bonferroni
Hochberg
Holm
Hommel
Šidák
</pre>
=={{header|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]''.
<syntaxhighlight lang="java">import java.util.Arrays;
import java.util.Comparator;
Line 1,455 ⟶ 2,895:
}
}
}</
{{out}}
<pre>[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
Line 1,537 ⟶ 2,977:
=={{header|Julia}}==
<syntaxhighlight lang="julia">using MultipleTesting, IterTools, Printf
p = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
Line 1,564 ⟶ 3,001:
println("\n", corr)
printpvalues(adjust(p, corr))
end</
{{out}}
Line 1,617 ⟶ 3,054:
=={{header|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]''.
<syntaxhighlight lang="scala">// version 1.1.51
import java.util.Arrays
Line 1,899 ⟶ 3,339:
println(f.format(type, types[type], error))
}
}</
{{out}}
Line 1,983 ⟶ 3,423:
</pre>
==
{{trans|
To avoid licensing issues, this version follows the approach of the Raku entry of which it is a partial translation. However, the correction routines themselves have been coded independently, common code factored out into separate functions (analogous to Raku) and (apart from the Šidák method) agree with the Raku results.
<syntaxhighlight lang="scala">// version 1.2.21
typealias DList = List<Double>
enum class Direction { UP, DOWN }
// test also for 'Unknown' correction type
val types = listOf(
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
)
fun adjusted(p: DList, type: String) = "\n$type\n${pFormat(adjust(check(p), type))}"
fun pFormat(p: DList, cols: Int = 5): String {
var i = -cols
val fmt = "%1.10f"
return p.chunked(cols).map { chunk ->
i += cols
"[%2d] %s".format(i, chunk.map { fmt.format(it) }.joinToString(" "))
}.joinToString("\n")
}
fun check(p: DList): DList {
require(p.size > 0 && p.min()!! >= 0.0 && p.max()!! <= 1.0) {
"p-values must be in range 0.0 to 1.0"
}
return p
}
fun ratchet(p: DList, dir: Direction): DList {
val pp = p.toMutableList()
var m = pp[0]
if (dir == Direction.UP) {
for (i in 1 until pp.size) {
if (pp[i] > m) pp[i] = m
m = pp[i]
}
}
else {
for (i in 1 until pp.size) {
if (pp[i] < m) pp[i] = m
m = pp[i]
}
}
return pp.map { if (it < 1.0) it else 1.0 }
}
fun schwartzian(p: DList, mult: DList, dir: Direction): DList {
val size = p.size
val order = if (dir == Direction.UP)
p.withIndex().sortedByDescending { it.value }.map { it.index }
else
p.withIndex().sortedBy { it.value }.map { it.index }
var pa = List(size) { mult[it] * p[order[it]] }
pa = ratchet(pa, dir)
val order2 = order.withIndex().sortedBy{ it.value }.map { it.index }
return List(size) { pa[order2[it]] }
}
fun adjust(p: DList, type: String): DList {
val size = p.size
require(size > 0)
when (type) {
"Benjamini-Hochberg" -> {
val mult = List(size) { size.toDouble() / (size - it) }
return schwartzian(p, mult, Direction.UP)
}
"Benjamini-Yekutieli" -> {
val q = (1..size).sumByDouble { 1.0 / it }
val mult = List(size) { q * size / (size - it) }
return schwartzian(p, mult, Direction.UP)
}
"Bonferroni" -> {
return p.map { minOf(it * size, 1.0) }
}
"Hochberg" -> {
val mult = List(size) { (it + 1).toDouble() }
return schwartzian(p, mult, Direction.UP)
}
"Holm" -> {
val mult = List(size) { (size - it).toDouble() }
return schwartzian(p, mult, Direction.DOWN)
}
"Hommel" -> {
val order = p.withIndex().sortedBy { it.value }.map { it.index }
val s = List(size) { p[order[it]] }
val min = List(size){ s[it] * size / ( it + 1) }.min()!!
val q = MutableList(size) { min }
val pa = MutableList(size) { min }
for (j in size - 1 downTo 2) {
val lower = IntArray(size - j + 1) { it } // lower indices
val upper = IntArray(j - 1) { size - j + 1 + it } // upper indices
var qmin = j * s[upper[0]] / 2.0
for (i in 1 until upper.size) {
val temp = s[upper[i]] * j / (2.0 + i)
if (temp < qmin) qmin = temp
}
for (i in 0 until lower.size) {
q[lower[i]] = minOf(s[lower[i]] * j, qmin)
}
for (i in 0 until upper.size) q[upper[i]] = q[size - j]
for (i in 0 until size) if (pa[i] < q[i]) pa[i] = q[i]
}
val order2 = order.withIndex().sortedBy{ it.value }.map { it.index }
return List(size) { pa[order2[it]] }
}
"Šidák" -> {
val m = size.toDouble()
return p.map { 1.0 - Math.pow(1.0 - it, m) }
}
else -> {
println(
"\nSorry, do not know how to do '$type' correction.\n" +
"Perhaps you want one of these?:\n" +
types.dropLast(1).map { " $it" }.joinToString("\n")
)
System.exit(1)
}
}
return p
}
fun main(args: Array<String>) {
val pValues = listOf(
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
)
types.forEach { println(adjusted(pValues, it)) }
}</syntaxhighlight>
{{out}}
Same as Raku entry except:
<pre>
....
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
</pre>
=={{header|Nim}}==
{{trans|Kotlin (Version 2)}}
<syntaxhighlight lang="nim">import algorithm, math, sequtils, strformat, strutils, sugar
type
CorrectionType {.pure.} = enum
BenjaminiHochberg = "Benjamini-Hochberg"
BenjaminiYekutieli = "Benjamini-Yekutieli"
Bonferroni = "Bonferroni"
Hochberg = "Hochberg"
Holm = "Holm"
Hommel = "Hommel"
Šidák = "Šidák"
Direction {.pure.} = enum Up, Down
PValues = seq[float]
template newPValues(length: Natural): PValues =
## Create a PValues object of given length.
newSeq[float](length)
func ratchet(p: var PValues; dir: Direction) =
var m = p[0]
case dir
of Up:
for i in 1..p.high:
if p[i] > m: p[i] = m
m = p[i]
of Down:
for i in 1..p.high:
if p[i] < m: p[i] = m
m = p[i]
for i in 0..p.high:
if p[i] > 1: p[i] = 1
func schwartzian(p, mult: PValues; dir: Direction): PValues =
let length = p.len
let sortOrder = if dir == Up: Descending else: Ascending
let order1 = toSeq(p.pairs).sorted((x, y) => cmp(x.val, y.val), sortOrder).mapIt(it.key)
var pa = newPValues(length)
for i in 0..pa.high:
pa[i] = mult[i] * p[order1[i]]
ratchet(pa, dir)
let order2 = toSeq(order1.pairs).sortedByIt(it.val).mapIt(it.key)
for idx in order2:
result.add pa[idx]
proc adjust(p: PValues; ctype: CorrectionType): PValues =
let length = p.len
assert length > 0
let flength = length.toFloat
case ctype
of BenjaminiHochberg:
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = flength / (flength - i.toFloat)
return schwartzian(p, mult, Up)
of BenjaminiYekutieli:
var q = 0.0
for i in 1..length: q += 1 / i
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = (q * flength) / (flength - i.toFloat)
return schwartzian(p, mult, Up)
of Bonferroni:
result = newPValues(length)
for i in 0..result.high:
result[i] = min(p[i] * flength, 1)
return
of Hochberg:
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = i.toFloat + 1
return schwartzian(p, mult, Up)
of Holm:
var mult = newPValues(length)
for i in 0..mult.high:
mult[i] = flength - i.toFloat
return schwartzian(p, mult, Down)
of Hommel:
let order1 = toSeq(p.pairs).sortedByIt(it.val).mapIt(it.key)
let s = order1.mapIt(p[it])
var m = Inf
for i in 0..s.high:
m = min(m, s[i] * flength / (i + 1).toFloat)
var q, pa = repeat(m, length)
for j in countdown(length - 1, 2):
let lower = toSeq(0..length - j)
let upper = toSeq((length - j + 1)..<length)
var qmin = j.toFloat * s[upper[0]] / 2
for i in 1..upper.high:
let val = s[upper[i]] * j.toFloat / (i + 2).toFloat
if val < qmin: qmin = val
for idx in lower: q[idx] = min(s[idx] * j.toFloat, qmin)
for idx in upper: q[idx] = q[^j]
for i, val in q:
if pa[i] < val: pa[i] = val
let order2 = toSeq(order1.pairs).sortedByIt(it.val).mapIt(it.key)
return order2.mapIt(pa[it])
of Šidák:
result = newPValues(length)
for i in 0..result.high:
result[i] = 1 - (1 - p[i])^length
return
func pformat(p: PValues; cols = 5): string =
var lines: seq[string]
for i in countup(0, p.high, cols):
let fchunk = p[i..<(i + cols)]
var schunk = newSeq[string](fchunk.len)
for j in 0..<cols:
schunk[j] = fchunk[j].formatFloat(ffDecimal, 10)
lines.add &"[{i:2}] {schunk.join(\" \")}"
result = lines.join("\n")
func adjusted(p: PValues; ctype: CorrectionType): string =
doAssert p.len > 0 and min(p) >= 0 and max(p) <= 1, "p-values must be in range 0.0 to 1.0."
result = &"\n{ctype}\n{pformat(p.adjust(ctype))}"
when isMainModule:
const PVals = @[
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03]
for ctype in CorrectionType:
echo adjusted(PVals, ctype)</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">
Benjamini-Hochberg
[ 0] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608437 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502862 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
Benjamini-Yekutieli
[ 0] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
Bonferroni
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
Hochberg
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Holm
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825610 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Hommel
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825610 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
Šidák
[ 0] 1.0000000000 1.0000000000 0.9946598274 0.9914285749 0.9999515274
[ 5] 1.0000000000 0.9999999688 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 0.9999999995 1.0000000000 0.9999998801
[15] 1.0000000000 1.0000000000 1.0000000000 0.9999999855 0.9231179729
[20] 0.9999999956 1.0000000000 1.0000000000 0.9999317605 1.0000000000
[25] 0.9983109511 1.0000000000 0.5068253940 1.0000000000 0.9703301333
[30] 0.1832692440 0.0150545753 0.4320729669 0.6993672225 0.0286818157
[35] 0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
[40] 0.0009001752 0.0000125222 0.8142104886 0.3772612062 0.0430222116
[45] 0.0108312558 0.0473319661 0.0032997780 0.7705015898 0.2499384839</pre>
=={{header|Perl}}==
{{trans|C}}
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<syntaxhighlight lang="perl">#!/usr/bin/env perl
use strict;
use warnings FATAL => 'all';
use autodie ':all';
use List::Util 'min';
use feature 'say';
sub pmin {
my $
my $x = 1;
my @pmin_array;
my $n = scalar @$
for (my $index = 0; $index < $n; $index++) {
}
}
sub cummin {
my $array_ref = shift;
my @cummin;
my $cumulative_min = @$array_ref[0];
Line 2,039 ⟶ 3,878:
push @cummin, $cumulative_min;
}
}
sub cummax {
my $array_ref = shift;
my @cummax;
my $cumulative_max = @$array_ref[0];
Line 2,056 ⟶ 3,891:
push @cummax, $cumulative_max;
}
}
Line 2,072 ⟶ 3,907:
die;
}
}
my @array;
Line 2,084 ⟶ 3,915:
@array = sort { @$array_ref[$b] <=> @$array_ref[$a] } 0..$max_index;
}
@array
}
sub p_adjust {
my $pvalues_ref = shift;
my $method;
if (defined $_[0]) {
$method = shift
} else {
$method = 'Holm'
}
my %methods = (
Line 2,137 ⟶ 3,941:
$method = $key;
$method_found = 'yes';
last
}
}
Line 2,151 ⟶ 3,955:
if ($method_found eq 'no') {
print "No method could be determined from $method.\n";
die
}
my $lp = scalar @$pvalues_ref;
Line 2,163 ⟶ 3,967:
}
my @cummin = cummin(\@cummin_input);
my @pmin = pmin(\@cummin);
my @ro = order(\@o);
@qvalues = @pmin[@ro];
} elsif ($method eq 'bh') {
Line 2,176 ⟶ 3,977:
}
my @ro = order(\@o);
my @cummin = cummin(\@cummin_input);
my @pmin = pmin(\@cummin);
@qvalues = @pmin[@ro];
} elsif ($method eq 'by') {
Line 2,193 ⟶ 3,991:
$cummin_input[$index] = $q * ($n/($n-$index)) * @$pvalues_ref[$o[$index]];#PVALUES[$o[$index]] is p[o]
}
# say join (',', @cummin_input);
# say '@cummin_input # of elements = ' . scalar @cummin_input;
my @cummin = cummin(\@cummin_input);
undef @cummin_input;
my @pmin = pmin(\@cummin);
@qvalues = @pmin[@ro];
} elsif ($method eq 'bonferroni') {
Line 2,206 ⟶ 4,005:
$qvalues[$index] = 1.0;
} else {
die;
}
Line 2,224 ⟶ 4,023:
@qvalues = @pmin[@ro];
} elsif ($method eq 'hommel') {
my @o = order($pvalues_ref);
my @p = @$pvalues_ref[@o];
my @ro = order(\@o);
undef @o;
my (@q, @pa);
my $min = $n*$p[0];
for (my $index = 0; $index < $n; $index++) {
my $temp = $n*$p[$index] / ($index + 1);
}
for (my $index = 0; $index < $n; $index++) {
Line 2,243 ⟶ 4,038:
}
for (my $j = ($n-1); $j >= 2; $j--) {
my @ij = 0..($n - $j);#ij <- seq_len(n - j + 1)
my $I2_LENGTH = $j - 1;
my @i2;
Line 2,258 ⟶ 4,049:
for (my $i = 1; $i < $I2_LENGTH; $i++) {#loop through 2:j
my $TEMP_Q1 = $j * $p[$i2[$i]] / (2 + $i);
}
for (my $i = 0; $i < ($n - $j + 1); $i++) {#q[ij] <- pmin(j * p[ij], q1)
$q[$ij[$i]] =
}
for (my $i = 0; $i < $I2_LENGTH; $i++) {#q[i2] <- q[n - j + 1]
$q[$i2[$i]] = $q[$n - $j];
}
Line 2,282 ⟶ 4,070:
} else {
print "$method doesn't fit my types.\n";
die
}
}
my @pvalues = (4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
Line 2,371 ⟶ 4,159:
printf("type $method has cumulative error of %g.\n", $error);
}
</syntaxhighlight>
{{out}}
Line 2,389 ⟶ 4,177:
</pre>
=={{header|
Translation of Kotlin (version 2), except for the Hommel part, which is translated from Go.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DOWN</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">ratchet</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">=</span><span style="color: #000000;">UP</span><span style="color: #0000FF;">?</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]></span><span style="color: #000000;">m</span><span style="color: #0000FF;">:</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sq_min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">order</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">custom_sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">=</span><span style="color: #000000;">UP</span> <span style="color: #008080;">then</span> <span style="color: #000000;">order</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">order</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">pa</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ratchet</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">order</span><span style="color: #0000FF;">)),</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">order</span><span style="color: #0000FF;">,</span><span style="color: #000000;">invert</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">adjust</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">method</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">size</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">method</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Benjamini-Hochberg"</span><span style="color: #0000FF;">:</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Benjamini-Yekutieli"</span><span style="color: #0000FF;">:</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">*</span><span style="color: #000000;">size</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Bonferroni"</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sq_min</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Hochberg"</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Holm"</span><span style="color: #0000FF;">:</span>
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">schwartzian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DOWN</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Hommel"</span><span style="color: #0000FF;">:</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ivdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">size</span> <span style="color: #008080;">do</span> <span style="color: #000000;">ivdx</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">i</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">ivdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ivdx</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ivdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">qh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">),</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">pa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">),</span><span style="color: #000000;">size</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">order</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ivdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lwr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">upr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">qmin</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]/</span><span style="color: #000000;">2</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">qmin</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]*</span><span style="color: #000000;">j</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">qmin</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lwr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">qh</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lwr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lwr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]*</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">qmin</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">qh</span><span style="color: #0000FF;">[</span><span style="color: #000000;">upr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">qh</span><span style="color: #0000FF;">[</span><span style="color: #000000;">size</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">pa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">qh</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">order</span><span style="color: #0000FF;">,</span><span style="color: #000000;">invert</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">"Sidak"</span><span style="color: #0000FF;">:</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">-</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
<span style="color: #008080;">else</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- (unknown method)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">types</span><span style="color: #0000FF;">,</span><span style="color: #000000;">correct_answers</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Benjamini-Hochberg"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">6.126681e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.521710e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.987205e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.891595e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.217789e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.301450e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.870370e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.301450e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.049731e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.826753e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">6.482629e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.253722e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.280973e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.769926e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.705703e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.241867e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.049731e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.856107e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.887526e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.136717e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.991891e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.769926e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.217789e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.301450e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.304958e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.832475e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.899547e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.521710e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.476843e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.683638e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.562902e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.516084e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.250189e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.636589e-03</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.562902e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.946883e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.166064e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.899547e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.688991e-03</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.502862e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.881555e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.142613e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.846527e-03</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.562902e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.846527e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.101708e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.252032e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.205958e-02</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Benjamini-Yekutieli"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.940844e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.510676e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.114323e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.754486e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.644618e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">7.575031e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.153102e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.581959e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.812089e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.636176e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.153102e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.325863e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.774239e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.754486e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.209832e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.025930e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.634031e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.546073e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.413926e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.180552e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.153102e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.180552e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.956812e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.262838e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.925057e-02</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Bonferroni"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.019185e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.020365e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.516674e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.625735e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.909271e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.537741e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.125636e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.782670e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.803480e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.882294e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.005725e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.713920e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.395577e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.088915e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.846527e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.305125e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.867745e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Hochberg"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.632662e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.575885e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.383967e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.938014e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.600230e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.501973e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.383967e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.052971e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.426136e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.626366e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.656419e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.825610e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.930759e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.394022e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.692284e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.023581e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.974152e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.172920e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.992520e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.179486e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Holm"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.632662e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.000000e+00</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.575885e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.395341e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.938014e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.600230e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.501973e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.395341e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.052971e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.426136e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.626366e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.656419e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.825610e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.930759e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.394022e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.692284e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.023581e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.974152e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.172920e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.992520e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.179486e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Hommel"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.987624e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.595180e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.351895e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.766522e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.414256e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.304340e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.530937e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.887709e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.385602e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.322457e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.722920e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.426136e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.218158e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.581127e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.825610e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.252228e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.743649e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.016908e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.516461e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">9.582456e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.877222e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.172920e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.122276e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.950067e-01</span><span style="color: #0000FF;">}},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Sidak"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9946598274</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9914285749</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999515274</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999999688</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999999995</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999998801</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999999855</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9231179729</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.9999999956</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9999317605</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.9983109511</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.5068253940</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0000000000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.9703301333</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.1832692440</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0150545753</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.4320729669</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.6993672225</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0286818157</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.0152621104</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3391808707</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0656206307</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.4959194266</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0186503726</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.0009001752</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0000125222</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.8142104886</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3772612062</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0430222116</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.0108312558</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0473319661</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0032997780</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.7705015898</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.2499384839</span><span style="color: #0000FF;">}}})</span>
<span style="color: #000080;font-style:italic;">-- {"Unknown",{1<nowiki>}}</nowiki>})</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">pValues</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">4.533744e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.296024e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.936026e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.079658e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.801962e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.752257e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.922222e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.115421e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.355806e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.324867e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.926798e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.802978e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.485442e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.883130e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.729308e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">8.502518e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.268138e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.442008e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.030266e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.001555e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">3.194810e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.892933e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.991834e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.745691e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.037516e-01</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.198578e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.966083e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.403837e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.328671e-01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.793476e-02</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">4.040730e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.033349e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.125147e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.375072e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.818542e-04</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">3.075482e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.251272e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.356534e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.360696e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.764588e-04</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1.801145e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.504456e-07</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.310253e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.427839e-03</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8.791153e-04</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2.177831e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.693054e-04</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.610250e-05</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.900813e-02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5.735490e-03</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">)></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"p-values must be in range 0.0 to 1.0"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">types</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ti</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">types</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">adjust</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pValues</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nSorry, do not know how to do %s correction.\n"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"Perhaps you want one of these?:\n %s\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">types</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #008000;">"\n "</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- printf(1,"%s\n",{ti})
-- res = correct_answers[i] -- (for easier comparison only)
-- pp(res,{pp_FltFmt,"%13.10f",pp_IntFmt,"%13.10f",pp_Maxlen,75,pp_Pause,0})</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">error</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_abs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">correct_answers</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s has cumulative error of %g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">error</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
Matches Kotlin (etc) when some of those lines just above are uncommented.
<pre>
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
</pre>
=={{header|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]''.
<syntaxhighlight lang="python">from __future__ import division
import sys
Line 2,809 ⟶ 4,624:
error += abs(q[i] - correct_answers[key][i])
print '%s error = %g' % (key.upper(), error)
</syntaxhighlight>
{{out}}
Line 2,822 ⟶ 4,637:
=={{header|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].
<syntaxhighlight lang="rsplus">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')
Line 2,913 ⟶ 4,667:
p.adjust(p, method = 'hommel')
writeLines("Hommel\n")</syntaxhighlight>
{{out}}
Line 2,981 ⟶ 4,734:
[46] 9.582456e-03 3.877222e-02 3.172920e-03 8.122276e-01 1.950067e-01
Hommel</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2019.03.1}}
<syntaxhighlight lang="raku" line>########################### Helper subs ###########################
sub adjusted (@p, $type) { "\n$type\n" ~ format adjust( check(@p), $type ) }
sub format ( @p, $cols = 5 ) {
my $i = -$cols;
my $fmt = "%1.10f";
join "\n", @p.rotor($cols, :partial).map:
{ sprintf "[%2d] { join ' ', $fmt xx $_ }", $i+=$cols, $_ };
}
sub check ( @p ) { die 'p-values must be in range 0.0 to 1.0' if @p.min < 0 or 1 < @p.max; @p }
multi ratchet ( 'up', @p ) { my $m; @p[$_] min= $m, $m = @p[$_] for ^@p; @p }
multi ratchet ( 'dn', @p ) { my $m; @p[$_] max= $m, $m = @p[$_] for ^@p .reverse; @p }
sub schwartzian ( @p, &transform, :$ratchet ) {
my @pa = @p.map( {[$_, $++]} ).sort( -*.[0] ).map: { [transform(.[0]), .[1]] };
@pa[*;0] = ratchet($ratchet, @pa»[0]);
@pa.sort( *.[1] )»[0]
}
############# The various p-value correction routines #############
multi adjust( @p, 'Benjamini-Hochberg' ) {
@p.&schwartzian: * * @p / (@p - $++) min 1, :ratchet('up')
}
multi adjust( @p, 'Benjamini-Yekutieli' ) {
my \r = ^@p .map( { 1 / ++$ } ).sum;
@p.&schwartzian: * * r * @p / (@p - $++) min 1, :ratchet('up')
}
multi adjust( @p, 'Hochberg' ) {
my \m = @p.max;
@p.&schwartzian: * * ++$ min m, :ratchet('up')
}
multi adjust( @p, 'Holm' ) {
@p.&schwartzian: * * ++$ min 1, :ratchet('dn')
}
multi adjust( @p, 'Šidák' ) {
@p.&schwartzian: 1 - (1 - *) ** ++$, :ratchet('dn')
}
multi adjust( @p, 'Bonferroni' ) {
@p.map: * * @p min 1
}
# Hommel correction can't be easily reduced to a one pass transform
multi adjust( @p, 'Hommel' ) {
my @s = @p.map( {[$_, $++]} ).sort: *.[0] ; # sorted
my \z = +@p; # array si(z)e
my @pa = @s»[0].map( * * z / ++$ ).min xx z; # p adjusted
my @q; # scratch array
for (1 ..^ z).reverse -> $i {
my @L = 0 .. z - $i; # lower indices
my @U = z - $i ^..^ z; # upper indices
my $q = @s[@U]»[0].map( { $_ * $i / (2 + $++) } ).min;
@q[@L] = @s[@L]»[0].map: { min $_ * $i, $q, @s[*-1][0] };
@pa = ^z .map: { max @pa[$_], @q[$_] }
}
@pa[@s[*;1].map( {[$_, $++]} ).sort( *.[0] )»[1]]
}
multi adjust ( @p, $unknown ) {
note "\nSorry, do not know how to do $unknown correction.\n" ~
"Perhaps you want one of these?:\n" ~
<Benjamini-Hochberg Benjamini-Yekutieli Bonferroni Hochberg
Holm Hommel Šidák>.join("\n");
exit
}
########################### The task ###########################
my @p-values =
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
;
for < Benjamini-Hochberg Benjamini-Yekutieli Bonferroni Hochberg Holm Hommel Šidák >
{
say adjusted @p-values, $_
}</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">Benjamini-Hochberg
[ 0] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
[ 5] 0.9301450000 0.4870370000 0.9301450000 0.6049730556 0.6826752564
[10] 0.6482628947 0.7253722500 0.5280972727 0.8769925556 0.4705703448
[15] 0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
[20] 0.4991890625 0.8769925556 0.9991834000 0.3217789286 0.9301450000
[25] 0.2304957692 0.5832475000 0.0389954722 0.8521710465 0.1476842609
[30] 0.0168363750 0.0025629017 0.0351608438 0.0625018947 0.0036365888
[35] 0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
[40] 0.0004502863 0.0000125223 0.0788155476 0.0314261300 0.0048465270
[45] 0.0025629017 0.0048465270 0.0011017083 0.0725203250 0.0220595769
Benjamini-Yekutieli
[ 0] 1.0000000000 1.0000000000 0.8940844244 0.8510676197 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 0.5114323399
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.1754486368 1.0000000000 0.6644618149
[30] 0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
[35] 0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
[40] 0.0020259303 0.0000563403 0.3546073326 0.1413926119 0.0218055202
[45] 0.0115310209 0.0218055202 0.0049568120 0.3262838334 0.0992505663
Bonferroni
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.7019185000 1.0000000000 1.0000000000
[30] 0.2020365000 0.0151667450 0.5625735000 1.0000000000 0.0290927100
[35] 0.0153774100 0.4125636000 0.0678267000 0.6803480000 0.0188229400
[40] 0.0009005725 0.0000125223 1.0000000000 0.4713919500 0.0439557650
[45] 0.0108891550 0.0484652700 0.0033051250 1.0000000000 0.2867745000
Hochberg
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4632662100 0.9991834000 0.9991834000
[30] 0.1575884700 0.0138396690 0.3938014500 0.7600230400 0.0250197306
[35] 0.0138396690 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Holm
[ 0] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[ 5] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[10] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[15] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[20] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[25] 1.0000000000 1.0000000000 0.4632662100 1.0000000000 1.0000000000
[30] 0.1575884700 0.0139534054 0.3938014500 0.7600230400 0.0250197306
[35] 0.0139534054 0.3052970640 0.0542613600 0.4626366400 0.0165641872
[40] 0.0008825611 0.0000125223 0.9930759000 0.3394022040 0.0369228426
[45] 0.0102358057 0.0397415214 0.0031729200 0.8992520300 0.2179486200
Hommel
[ 0] 0.9991834000 0.9991834000 0.9991834000 0.9987623800 0.9991834000
[ 5] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[10] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[15] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9595180000
[20] 0.9991834000 0.9991834000 0.9991834000 0.9991834000 0.9991834000
[25] 0.9991834000 0.9991834000 0.4351894700 0.9991834000 0.9766522500
[30] 0.1414255500 0.0130434007 0.3530936533 0.6887708800 0.0238560222
[35] 0.0132245726 0.2722919760 0.0542613600 0.4218157600 0.0158112696
[40] 0.0008825611 0.0000125223 0.8743649143 0.3016908480 0.0351646120
[45] 0.0095824564 0.0387722160 0.0031729200 0.8122276400 0.1950066600
Šidák
[ 0] 0.9998642526 0.9999922727 0.9341844137 0.9234670175 0.9899922294
[ 5] 0.9999922727 0.9992955735 0.9999922727 0.9998642526 0.9998909746
[10] 0.9998642526 0.9999288207 0.9995533892 0.9999922727 0.9990991210
[15] 0.9999922727 0.9998642526 0.9999674876 0.9992955735 0.7741716825
[20] 0.9993332472 0.9999922727 0.9999922727 0.9899922294 0.9999922727
[25] 0.9589019598 0.9998137104 0.3728369461 0.9999922727 0.8605248833
[30] 0.1460714182 0.0138585952 0.3270159382 0.5366136349 0.0247164330
[35] 0.0138585952 0.2640282766 0.0528503728 0.3723753774 0.0164308228
[40] 0.0008821796 0.0000125222 0.6357389664 0.2889497995 0.0362651575
[45] 0.0101847015 0.0389807074 0.0031679962 0.5985019850 0.1963376344</pre>
=={{header|Ruby}}==
{{trans|Perl}}
<syntaxhighlight lang="ruby">def pmin(array)
x = 1
pmin_array = []
array.each_index do |i|
pmin_array[i] = [array[i], x].min
abort if pmin_array[i] > 1
end
pmin_array
end
def cummin(array)
cumulative_min = array[0]
arr_cummin = []
array.each do |p|
cumulative_min = [p, cumulative_min].min
arr_cummin.push(cumulative_min)
end
arr_cummin
end
def cummax(array)
cumulative_max = array[0]
arr_cummax = []
array.each do |p|
cumulative_max = [p, cumulative_max].max
arr_cummax.push(cumulative_max)
end
arr_cummax
end
# decreasing variable is optional
def order(array, decreasing = false)
if decreasing == false
array.sort.map { |n| array.index(n) }
else
array.sort.map { |n| array.index(n) }.reverse
end
end
def p_adjust(arr_pvalues, method = 'Holm')
lp = arr_pvalues.size
n = lp
if method.casecmp('hochberg').zero?
arr_o = order(arr_pvalues, true)
arr_cummin_input = []
(0..n).each do |index|
arr_cummin_input[index] = (index + 1) * arr_pvalues[arr_o[index].to_i]
end
arr_cummin = cummin(arr_cummin_input)
arr_pmin = pmin(arr_cummin)
arr_ro = order(arr_o)
return arr_pmin.values_at(*arr_ro)
elsif method.casecmp('bh').zero? || method.casecmp('benjamini-hochberg').zero?
arr_o = order(arr_pvalues, true)
arr_cummin_input = []
(0..(n - 1)).each do |i|
arr_cummin_input[i] = (n / (n - i).to_f) * arr_pvalues[arr_o[i]]
end
arr_ro = order(arr_o)
arr_cummin = cummin(arr_cummin_input)
arr_pmin = pmin(arr_cummin)
return arr_pmin.values_at(*arr_ro)
elsif method.casecmp('by').zero? || method.casecmp('benjamini-yekutieli').zero?
q = 0.0
arr_o = order(arr_pvalues, true)
arr_ro = order(arr_o)
(1..n).each do |index|
q += 1.0 / index
end
arr_cummin_input = []
(0..(n - 1)).each do |i|
arr_cummin_input[i] = q * (n / (n - i).to_f) * arr_pvalues[arr_o[i]]
end
arr_cummin = cummin(arr_cummin_input)
arr_pmin = pmin(arr_cummin)
return arr_pmin.values_at(*arr_ro)
elsif method.casecmp('bonferroni').zero?
arr_qvalues = []
(0..(n - 1)).each do |i|
q = arr_pvalues[i] * n
if (q >= 0) && (q < 1)
arr_qvalues[i] = q
elsif q >= 1
arr_qvalues[i] = 1.0
else
puts "Falied to get Bonferroni adjusted p for #{arr_pvalues[i]}"
end
end
return arr_qvalues
elsif method.casecmp('holm').zero?
o = order(arr_pvalues)
cummax_input = []
(0..(n - 1)).each do |index|
cummax_input[index] = (n - index) * arr_pvalues[o[index]]
end
ro = order(o)
arr_cummax = cummax(cummax_input)
arr_pmin = pmin(arr_cummax)
return arr_pmin.values_at(*ro)
elsif method.casecmp('hommel').zero?
o = order(arr_pvalues)
arr_p = arr_pvalues.values_at(*o)
ro = order(o)
q = []
pa = []
min = n * arr_p[0]
(0..(n - 1)).each do |index|
temp = n * arr_p[index] / (index + 1)
min = [min, temp].min
end
(0..(n - 1)).each do |index|
pa[index] = min
q[index] = min
end
j = n - 1
while j >= 2
ij = Array 0..(n - j)
i2_length = j - 1
i2 = []
(0..(i2_length - 1)).each do |i|
i2[i] = n - j + 2 + i - 1 # R's indices are 1-based, C's are 0-based
end
q1 = j * arr_p[i2[0]] / 2.0
(1..(i2_length - 1)).each do |i|
temp_q1 = j * arr_p[i2[i]] / (2 + i)
q1 = [temp_q1, q1].min
end
(0..(n - j)).each do |i|
tmp = j * arr_p[ij[i]]
q[ij[i]] = [tmp, q1].min
end
(0..(i2_length - 1)).each do |i|
q[i2[i]] = q[n - j]
end
(0..(n - 1)).each do |i|
pa[i] = q[i] if pa[i] < q[i]
end
j -= 1
end
return pa.values_at(*ro)
else
puts "#{method} isn't accepted."
abort
end
end
pvalues =
[4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02,
1.801962e-01, 8.752257e-01, 2.922222e-01, 9.115421e-01,
4.355806e-01, 5.324867e-01, 4.926798e-01, 5.802978e-01,
3.485442e-01, 7.883130e-01, 2.729308e-01, 8.502518e-01,
4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01,
9.037516e-01, 1.198578e-01, 3.966083e-01, 1.403837e-02,
7.328671e-01, 6.793476e-02, 4.040730e-03, 3.033349e-04,
1.125147e-02, 2.375072e-02, 5.818542e-04, 3.075482e-04,
8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03,
8.791153e-04, 2.177831e-04, 9.693054e-04, 6.610250e-05,
2.900813e-02, 5.735490e-03]
correct_answers = {
'Benjamini-Hochberg' => [6.126681e-01, 8.521710e-01, 1.987205e-01,
1.891595e-01, 3.217789e-01, 9.301450e-01,
4.870370e-01, 9.301450e-01, 6.049731e-01,
6.826753e-01, 6.482629e-01, 7.253722e-01,
5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01,
4.887526e-01, 1.136717e-01, 4.991891e-01,
8.769926e-01, 9.991834e-01, 3.217789e-01,
9.301450e-01, 2.304958e-01, 5.832475e-01,
3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02,
6.250189e-02, 3.636589e-03, 2.562902e-03,
2.946883e-02, 6.166064e-03, 3.899547e-02,
2.688991e-03, 4.502862e-04, 1.252228e-05,
7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03,
7.252032e-02, 2.205958e-02],
'Benjamini-Yekutieli' => [1.000000e+00, 1.000000e+00, 8.940844e-01,
8.510676e-01, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 5.114323e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00,
1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01,
2.812089e-01, 1.636176e-02, 1.153102e-02,
1.325863e-01, 2.774239e-02, 1.754486e-01,
1.209832e-02, 2.025930e-03, 5.634031e-05,
3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03,
3.262838e-01, 9.925057e-02],
'Bonferroni' => [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 7.019185e-01,
1.000000e+00, 1.000000e+00, 2.020365e-01, 1.516674e-02,
5.625735e-01, 1.000000e+00, 2.909271e-02, 1.537741e-02,
4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01,
4.395577e-02, 1.088915e-02, 4.846527e-02, 3.305125e-03,
1.000000e+00, 2.867745e-01],
'Hochberg' => [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 4.632662e-01,
9.991834e-01, 9.991834e-01, 1.575885e-01, 1.383967e-02,
3.938014e-01, 7.600230e-01, 2.501973e-02, 1.383967e-02,
3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01,
3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03,
8.992520e-01, 2.179486e-01],
'Holm' => [1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 4.632662e-01,
1.000000e+00, 1.000000e+00, 1.575885e-01, 1.395341e-02,
3.938014e-01, 7.600230e-01, 2.501973e-02, 1.395341e-02,
3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01,
3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03,
8.992520e-01, 2.179486e-01],
'Hommel' => [9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 4.351895e-01,
9.991834e-01, 9.766522e-01, 1.414256e-01, 1.304340e-02,
3.530937e-01, 6.887709e-01, 2.385602e-02, 1.322457e-02,
2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01,
3.516461e-02, 9.582456e-03, 3.877222e-02, 3.172920e-03,
8.122276e-01, 1.950067e-01]
}
# correct_answers.each do |method, answers|
methods = ['Benjamini-Yekutieli', 'Benjamini-Hochberg', 'Hochberg',
'Bonferroni', 'Holm', 'Hommel']
methods.each do |method|
puts method
error = 0.0
arr_q = p_adjust(pvalues, method)
arr_q.each_index do |p|
error += (correct_answers[method][p] - arr_q[p])
end
puts "total error for #{method} = #{error}"
end
</syntaxhighlight>
{{out}}
<pre>Benjamini-Yekutieli
total error for Benjamini-Yekutieli = -1.7373780825929845e-07
Benjamini-Hochberg
total error for Benjamini-Hochberg = -1.4736877299143964e-08
Hochberg
total error for Hochberg = -1.2354999978398105e-07
Bonferroni
total error for Bonferroni = 4.49999999152751e-08
Holm
total error for Holm = -1.163499997815258e-07
Hommel
total error for Hommel = 1.1483094955369324e-07
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">
use std::iter;
#[rustfmt::skip]
const PVALUES:[f64;50] = [
4.533_744e-01, 7.296_024e-01, 9.936_026e-02, 9.079_658e-02, 1.801_962e-01,
8.752_257e-01, 2.922_222e-01, 9.115_421e-01, 4.355_806e-01, 5.324_867e-01,
4.926_798e-01, 5.802_978e-01, 3.485_442e-01, 7.883_130e-01, 2.729_308e-01,
8.502_518e-01, 4.268_138e-01, 6.442_008e-01, 3.030_266e-01, 5.001_555e-02,
3.194_810e-01, 7.892_933e-01, 9.991_834e-01, 1.745_691e-01, 9.037_516e-01,
1.198_578e-01, 3.966_083e-01, 1.403_837e-02, 7.328_671e-01, 6.793_476e-02,
4.040_730e-03, 3.033_349e-04, 1.125_147e-02, 2.375_072e-02, 5.818_542e-04,
3.075_482e-04, 8.251_272e-03, 1.356_534e-03, 1.360_696e-02, 3.764_588e-04,
1.801_145e-05, 2.504_456e-07, 3.310_253e-02, 9.427_839e-03, 8.791_153e-04,
2.177_831e-04, 9.693_054e-04, 6.610_250e-05, 2.900_813e-02, 5.735_490e-03
];
#[derive(Debug)]
enum CorrectionType {
BenjaminiHochberg,
BenjaminiYekutieli,
Bonferroni,
Hochberg,
Holm,
Hommel,
Sidak,
}
enum SortDirection {
Increasing,
Decreasing,
}
/// orders **input** vector by value and multiplies with **multiplier** vector
/// Finally returns the multiplied values in the original order of **input**
fn ordered_multiply(input: &[f64], multiplier: &[f64], direction: &SortDirection) -> Vec<f64> {
let order_by_value = match direction {
SortDirection::Increasing => {
|a: &(f64, usize), b: &(f64, usize)| b.0.partial_cmp(&a.0).unwrap()
}
SortDirection::Decreasing => {
|a: &(f64, usize), b: &(f64, usize)| a.0.partial_cmp(&b.0).unwrap()
}
};
let cmp_minmax = match direction {
SortDirection::Increasing => |a: f64, b: f64| a.gt(&b),
SortDirection::Decreasing => |a: f64, b: f64| a.lt(&b),
};
// add original order index
let mut input_indexed = input
.iter()
.enumerate()
.map(|(idx, &p_value)| (p_value, idx))
.collect::<Vec<_>>();
// order by value desc/asc
input_indexed.sort_unstable_by(order_by_value);
// do the multiplication in place, clamp it at 1.0,
// keep the original index in place
for i in 0..input_indexed.len() {
input_indexed[i] = (
f64::min(1.0, input_indexed[i].0 * multiplier[i]),
input_indexed[i].1,
);
}
// make vector strictly monotonous increasing/decreasing in place
for i in 1..input_indexed.len() {
if cmp_minmax(input_indexed[i].0, input_indexed[i - 1].0) {
input_indexed[i] = (input_indexed[i - 1].0, input_indexed[i].1);
}
}
// re-sort back to original order
input_indexed.sort_unstable_by(|a: &(f64, usize), b: &(f64, usize)| a.1.cmp(&b.1));
// remove ordering index
let (resorted, _): (Vec<_>, Vec<_>) = input_indexed.iter().cloned().unzip();
resorted
}
#[allow(clippy::cast_precision_loss)]
fn hommel(input: &[f64]) -> Vec<f64> {
// using algorith described:
// http://stat.wharton.upenn.edu/~steele/Courses/956/ResourceDetails/MultipleComparision/Writght92.pdf
// add original order index
let mut input_indexed = input
.iter()
.enumerate()
.map(|(idx, &p_value)| (p_value, idx))
.collect::<Vec<_>>();
// order by value asc
input_indexed
.sort_unstable_by(|a: &(f64, usize), b: &(f64, usize)| a.0.partial_cmp(&b.0).unwrap());
let (p_values, order): (Vec<_>, Vec<_>) = input_indexed.iter().cloned().unzip();
let n = input.len();
// initial minimal n*p/i values
// get the smalles of these values
let min_result = (0..n)
.map(|i| ((p_values[i] * n as f64) / (i + 1) as f64))
.fold(1. / 0. /* -inf */, f64::min);
// // initialize result vector with minimal values
let mut result = iter::repeat(min_result).take(n).collect::<Vec<_>>();
for m in (2..n).rev() {
let cmin: f64;
let m_as_float = m as f64;
let mut a = p_values.clone();
// println!("\nn: {}", m);
{
// split p-values into two group
let (_, second) = p_values.split_at(n - m + 1);
// calculate minumum of m*p/i for this second group
cmin = second
.iter()
.zip(2..=m)
.map(|(p, i)| (m_as_float * p) / i as f64)
.fold(1. / 0. /* inf */, f64::min);
}
// replace p values if p<cmin in the second group
((n - m + 1)..n).for_each(|i| a[i] = a[i].max(cmin));
// replace p values if min(cmin, m*p) > p
(0..=(n - m)).for_each(|i| a[i] = a[i].max(f64::min(cmin, m_as_float * p_values[i])));
// store in the result vector if any adjusted p is higher than the current one
(0..n).for_each(|i| result[i] = result[i].max(a[i]));
}
// re-sort into the original order
let mut result = result
.into_iter()
.zip(order.into_iter())
.map(|(p, idx)| (p, idx))
.collect::<Vec<_>>();
result.sort_unstable_by(|a: &(f64, usize), b: &(f64, usize)| a.1.cmp(&b.1));
let (result, _): (Vec<_>, Vec<_>) = result.iter().cloned().unzip();
result
}
#[allow(clippy::cast_precision_loss)]
fn p_value_correction(p_values: &[f64], ctype: &CorrectionType) -> Vec<f64> {
let p_vec = p_values.to_vec();
if p_values.is_empty() {
return p_vec;
}
let fsize = p_values.len() as f64;
match ctype {
CorrectionType::BenjaminiHochberg => {
let multiplier = (0..p_values.len())
.map(|index| fsize / (fsize - index as f64))
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Increasing)
}
CorrectionType::BenjaminiYekutieli => {
let q: f64 = (1..=p_values.len()).map(|index| 1. / index as f64).sum();
let multiplier = (0..p_values.len())
.map(|index| q * fsize / (fsize - index as f64))
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Increasing)
}
CorrectionType::Bonferroni => p_vec
.iter()
.map(|p| f64::min(p * fsize, 1.0))
.collect::<Vec<_>>(),
CorrectionType::Hochberg => {
let multiplier = (0..p_values.len())
.map(|index| 1. + index as f64)
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Increasing)
}
CorrectionType::Holm => {
let multiplier = (0..p_values.len())
.map(|index| fsize - index as f64)
.collect::<Vec<_>>();
ordered_multiply(&p_vec, &multiplier, &SortDirection::Decreasing)
}
CorrectionType::Sidak => p_vec
.iter()
.map(|x| 1. - (1. - x).powf(fsize))
.collect::<Vec<_>>(),
CorrectionType::Hommel => hommel(&p_vec),
}
}
// prints array into a nice table, max 5 floats/row
fn array_to_string(a: &[f64]) -> String {
a.chunks(5)
.enumerate()
.map(|(index, e)| {
format!(
"[{:>2}]: {}",
index * 5,
e.iter()
.map(|x| format!("{:>1.10}", x))
.collect::<Vec<_>>()
.join(", ")
)
})
.collect::<Vec<_>>()
.join("\n")
}
fn main() {
let ctypes = [
CorrectionType::BenjaminiHochberg,
CorrectionType::BenjaminiYekutieli,
CorrectionType::Bonferroni,
CorrectionType::Hochberg,
CorrectionType::Holm,
CorrectionType::Sidak,
CorrectionType::Hommel,
];
for ctype in &ctypes {
println!("\n{:?}:", ctype);
println!("{}", array_to_string(&p_value_correction(&PVALUES, ctype)));
}
}
</syntaxhighlight>
{{out}}
<pre style="height:60ex;overflow:scroll;">
BenjaminiHochberg:
[ 0]: 0.6126681081, 0.8521710465, 0.1987205200, 0.1891595417, 0.3217789286
[ 5]: 0.9301450000, 0.4870370000, 0.9301450000, 0.6049730556, 0.6826752564
[10]: 0.6482628947, 0.7253722500, 0.5280972727, 0.8769925556, 0.4705703448
[15]: 0.9241867391, 0.6049730556, 0.7856107317, 0.4887525806, 0.1136717045
[20]: 0.4991890625, 0.8769925556, 0.9991834000, 0.3217789286, 0.9301450000
[25]: 0.2304957692, 0.5832475000, 0.0389954722, 0.8521710465, 0.1476842609
[30]: 0.0168363750, 0.0025629017, 0.0351608437, 0.0625018947, 0.0036365888
[35]: 0.0025629017, 0.0294688286, 0.0061660636, 0.0389954722, 0.0026889914
[40]: 0.0004502862, 0.0000125223, 0.0788155476, 0.0314261300, 0.0048465270
[45]: 0.0025629017, 0.0048465270, 0.0011017083, 0.0725203250, 0.0220595769
BenjaminiYekutieli:
[ 0]: 1.0000000000, 1.0000000000, 0.8940844244, 0.8510676197, 1.0000000000
[ 5]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[10]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[15]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 0.5114323399
[20]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[25]: 1.0000000000, 1.0000000000, 0.1754486368, 1.0000000000, 0.6644618149
[30]: 0.0757503083, 0.0115310209, 0.1581958559, 0.2812088585, 0.0163617595
[35]: 0.0115310209, 0.1325863108, 0.0277423864, 0.1754486368, 0.0120983246
[40]: 0.0020259303, 0.0000563403, 0.3546073326, 0.1413926119, 0.0218055202
[45]: 0.0115310209, 0.0218055202, 0.0049568120, 0.3262838334, 0.0992505663
Bonferroni:
[ 0]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[ 5]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[10]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[15]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[20]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[25]: 1.0000000000, 1.0000000000, 0.7019185000, 1.0000000000, 1.0000000000
[30]: 0.2020365000, 0.0151667450, 0.5625735000, 1.0000000000, 0.0290927100
[35]: 0.0153774100, 0.4125636000, 0.0678267000, 0.6803480000, 0.0188229400
[40]: 0.0009005725, 0.0000125223, 1.0000000000, 0.4713919500, 0.0439557650
[45]: 0.0108891550, 0.0484652700, 0.0033051250, 1.0000000000, 0.2867745000
Hochberg:
[ 0]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[ 5]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[10]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[15]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[20]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[25]: 0.9991834000, 0.9991834000, 0.4632662100, 0.9991834000, 0.9991834000
[30]: 0.1575884700, 0.0138396690, 0.3938014500, 0.7600230400, 0.0250197306
[35]: 0.0138396690, 0.3052970640, 0.0542613600, 0.4626366400, 0.0165641872
[40]: 0.0008825610, 0.0000125223, 0.9930759000, 0.3394022040, 0.0369228426
[45]: 0.0102358057, 0.0397415214, 0.0031729200, 0.8992520300, 0.2179486200
Holm:
[ 0]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[ 5]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[10]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[15]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[20]: 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000, 1.0000000000
[25]: 1.0000000000, 1.0000000000, 0.4632662100, 1.0000000000, 1.0000000000
[30]: 0.1575884700, 0.0139534054, 0.3938014500, 0.7600230400, 0.0250197306
[35]: 0.0139534054, 0.3052970640, 0.0542613600, 0.4626366400, 0.0165641872
[40]: 0.0008825610, 0.0000125223, 0.9930759000, 0.3394022040, 0.0369228426
[45]: 0.0102358057, 0.0397415214, 0.0031729200, 0.8992520300, 0.2179486200
Sidak:
[ 0]: 1.0000000000, 1.0000000000, 0.9946598274, 0.9914285749, 0.9999515274
[ 5]: 1.0000000000, 0.9999999688, 1.0000000000, 1.0000000000, 1.0000000000
[10]: 1.0000000000, 1.0000000000, 0.9999999995, 1.0000000000, 0.9999998801
[15]: 1.0000000000, 1.0000000000, 1.0000000000, 0.9999999855, 0.9231179729
[20]: 0.9999999956, 1.0000000000, 1.0000000000, 0.9999317605, 1.0000000000
[25]: 0.9983109511, 1.0000000000, 0.5068253940, 1.0000000000, 0.9703301333
[30]: 0.1832692440, 0.0150545753, 0.4320729669, 0.6993672225, 0.0286818157
[35]: 0.0152621104, 0.3391808707, 0.0656206307, 0.4959194266, 0.0186503726
[40]: 0.0009001752, 0.0000125222, 0.8142104886, 0.3772612062, 0.0430222116
[45]: 0.0108312558, 0.0473319661, 0.0032997780, 0.7705015898, 0.2499384839
Hommel:
[ 0]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9987623800, 0.9991834000
[ 5]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[10]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[15]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9595180000
[20]: 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000, 0.9991834000
[25]: 0.9991834000, 0.9991834000, 0.4351894700, 0.9991834000, 0.9766522500
[30]: 0.1414255500, 0.0130434007, 0.3530936533, 0.6887708800, 0.0238560222
[35]: 0.0132245726, 0.2722919760, 0.0542613600, 0.4218157600, 0.0158112696
[40]: 0.0008825610, 0.0000125223, 0.8743649143, 0.3016908480, 0.0351646120
[45]: 0.0095824564, 0.0387722160, 0.0031729200, 0.8122276400, 0.1950066600
</pre>
=={{header|SAS}}==
<syntaxhighlight lang="sas">data pvalues;
input raw_p @@;
cards;
4.533744e-01 7.296024e-01 9.936026e-02 9.079658e-02 1.801962e-01
8.752257e-01 2.922222e-01 9.115421e-01 4.355806e-01 5.324867e-01
4.926798e-01 5.802978e-01 3.485442e-01 7.883130e-01 2.729308e-01
8.502518e-01 4.268138e-01 6.442008e-01 3.030266e-01 5.001555e-02
3.194810e-01 7.892933e-01 9.991834e-01 1.745691e-01 9.037516e-01
1.198578e-01 3.966083e-01 1.403837e-02 7.328671e-01 6.793476e-02
4.040730e-03 3.033349e-04 1.125147e-02 2.375072e-02 5.818542e-04
3.075482e-04 8.251272e-03 1.356534e-03 1.360696e-02 3.764588e-04
1.801145e-05 2.504456e-07 3.310253e-02 9.427839e-03 8.791153e-04
2.177831e-04 9.693054e-04 6.610250e-05 2.900813e-02 5.735490e-03
;
run;
proc multtest pdata=pvalues bon sid hom hoc holm;
run;</syntaxhighlight>
'''output'''
<pre> 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</pre>
=={{header|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:
<syntaxhighlight lang="stata">ssc install qqvalue</syntaxhighlight>
Given a dataset containing the p-values in a variable, the qqvalue command generates another variable with the adjusted p-values. Here is an example showing the result with all implemented methods:
<syntaxhighlight lang="stata">clear
#delimit ;
input 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;
end;
#delimit cr
loc meth bonferroni sidak holm holland hochberg simes yekutieli
foreach m in `meth' {
qqvalue p, method(`m') qvalue(`m')
}
list</syntaxhighlight>
'''output'''
<pre> +-----------------------------------------------------------------------------------------------+
| p bonferr~i sidak holm holland hochberg simes yekutieli |
|-----------------------------------------------------------------------------------------------|
1. | .4533744 1 1 1 .99986425 .9991834 .61266811 1 |
2. | .7296024 1 1 1 .99999227 .9991834 .85217105 1 |
3. | .09936026 1 .99465983 1 .93418441 .9991834 .19872052 .89408442 |
4. | .09079658 1 .99142857 1 .92346702 .9991834 .18915954 .85106762 |
5. | .1801962 1 .99995153 1 .98999223 .9991834 .32177893 1 |
|-----------------------------------------------------------------------------------------------|
6. | .8752257 1 1 1 .99999227 .9991834 .930145 1 |
7. | .2922222 1 .99999997 1 .99929557 .9991834 .487037 1 |
8. | .9115421 1 1 1 .99999227 .9991834 .930145 1 |
9. | .4355806 1 1 1 .99986425 .9991834 .60497306 1 |
10. | .5324867 1 1 1 .99989097 .9991834 .68267526 1 |
|-----------------------------------------------------------------------------------------------|
11. | .4926798 1 1 1 .99986425 .9991834 .64826289 1 |
12. | .5802978 1 1 1 .99992882 .9991834 .72537225 1 |
13. | .3485442 1 1 1 .99955339 .9991834 .52809727 1 |
14. | .788313 1 1 1 .99999227 .9991834 .87699256 1 |
15. | .2729308 1 .99999988 1 .99909912 .9991834 .47057034 1 |
|-----------------------------------------------------------------------------------------------|
16. | .8502518 1 1 1 .99999227 .9991834 .92418674 1 |
17. | .4268138 1 1 1 .99986425 .9991834 .60497306 1 |
18. | .6442008 1 1 1 .99996749 .9991834 .78561073 1 |
19. | .3030266 1 .99999999 1 .99929557 .9991834 .48875258 1 |
20. | .05001555 1 .92311797 1 .77417168 .9991834 .1136717 .51143234 |
|-----------------------------------------------------------------------------------------------|
21. | .319481 1 1 1 .99933325 .9991834 .49918906 1 |
22. | .7892933 1 1 1 .99999227 .9991834 .87699256 1 |
23. | .9991834 1 1 1 .99999227 .9991834 .9991834 1 |
24. | .1745691 1 .99993176 1 .98999223 .9991834 .32177893 1 |
25. | .9037516 1 1 1 .99999227 .9991834 .930145 1 |
|-----------------------------------------------------------------------------------------------|
26. | .1198578 1 .99831095 1 .95890196 .9991834 .23049577 1 |
27. | .3966083 1 1 1 .99981371 .9991834 .5832475 1 |
28. | .01403837 .7019185 .50682539 .46326621 .37283695 .46326621 .03899547 .17544864 |
29. | .7328671 1 1 1 .99999227 .9991834 .85217105 1 |
30. | .06793476 1 .97033013 1 .86052488 .9991834 .14768426 .66446181 |
|-----------------------------------------------------------------------------------------------|
31. | .00404073 .2020365 .18326924 .15758847 .14607142 .15758847 .01683638 .07575031 |
32. | .00030333 .01516674 .01505458 .01395341 .0138586 .01383967 .0025629 .01153102 |
33. | .01125147 .5625735 .43207297 .39380145 .32701594 .39380145 .03516084 .15819586 |
34. | .02375072 1 .69936722 .76002304 .53661363 .76002304 .06250189 .28120886 |
35. | .00058185 .02909271 .02868182 .02501973 .02471643 .02501973 .00363659 .01636176 |
|-----------------------------------------------------------------------------------------------|
36. | .00030755 .01537741 .01526211 .01395341 .0138586 .01383967 .0025629 .01153102 |
37. | .00825127 .4125636 .33918087 .30529706 .26402828 .30529706 .02946883 .13258631 |
38. | .00135653 .0678267 .06562063 .05426136 .05285037 .05426136 .00616606 .02774239 |
39. | .01360696 .680348 .49591943 .46263664 .37237538 .46263664 .03899547 .17544864 |
40. | .00037646 .01882294 .01865037 .01656419 .01643082 .01656419 .00268899 .01209832 |
|-----------------------------------------------------------------------------------------------|
41. | .00001801 .00090057 .00090018 .00088256 .00088218 .00088256 .00045029 .00202593 |
42. | 2.504e-07 .00001252 .00001252 .00001252 .00001252 .00001252 .00001252 .00005634 |
43. | .03310253 1 .81421049 .9930759 .63573897 .9930759 .07881555 .35460733 |
44. | .00942784 .47139195 .37726121 .3394022 .2889498 .3394022 .03142613 .14139261 |
45. | .00087912 .04395577 .04302221 .03692284 .03626516 .03692284 .00484653 .02180552 |
|-----------------------------------------------------------------------------------------------|
46. | .00021778 .01088915 .01083126 .01023581 .0101847 .01023581 .0025629 .01153102 |
47. | .00096931 .04846527 .04733197 .03974152 .03898071 .03974152 .00484653 .02180552 |
48. | .0000661 .00330513 .00329978 .00317292 .003168 .00317292 .00110171 .00495681 |
49. | .02900813 1 .77050159 .89925203 .59850199 .89925203 .07252032 .32628383 |
50. | .00573549 .2867745 .24993848 .21794862 .19633763 .21794862 .02205958 .09925057 |
+-----------------------------------------------------------------------------------------------+</pre>
=={{header|Wren}}==
{{trans|Kotlin (version 2)}}
{{libheader|Wren-dynamic}}
{{libheader|Wren-fmt}}
{{libheader|Wren-seq}}
{{libheader|Wren-math}}
{{libheader|Wren-sort}}
<syntaxhighlight lang="wren">import "./dynamic" for Enum
import "./fmt" for Fmt
import "./seq" for Lst
import "./math" for Nums
import "./sort" for Sort
var Direction = Enum.create("Direction", ["UP", "DOWN"])
// test also for 'Unknown' correction type
var types = [
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
]
var pFormat = Fn.new { |p, cols|
var i = -cols
var fmt = "$1.10f"
return Lst.chunks(p, cols).map { |chunk|
i = i + cols
return Fmt.swrite("[$2d $s", i, chunk.map { |v| Fmt.swrite(fmt, v) }.join(" "))
}.join("\n")
}
var check = Fn.new { |p|
if (p.count == 0 || Nums.min(p) < 0 || Nums.max(p) > 1) {
Fiber.abort("p-values must be in range 0 to 1")
}
return p
}
var ratchet = Fn.new { |p, dir|
var pp = p.toList
var m = pp[0]
if (dir == Direction.UP) {
for (i in 1...pp.count) {
if (pp[i] > m) pp[i] = m
m = pp[i]
}
} else {
for (i in 1...pp.count) {
if (pp[i] < m) pp[i] = m
m = pp[i]
}
}
return pp.map { |v| (v < 1) ? v : 1 }.toList
}
var schwartzian = Fn.new { |p, mult, dir|
var size = p.count
var pwi = List.filled(size, null)
for (i in 0...size) pwi[i] = [i, p[i]]
var cmp = (dir == Direction.UP) ? Fn.new { |a, b| (b[1] - a[1]).sign } :
Fn.new { |a, b| (a[1] - b[1]).sign }
var order = Sort.merge(pwi, cmp).map { |e| e[0] }.toList
var pa = List.filled(size, 0)
for (i in 0...size) pa[i] = mult[i] * p[order[i]]
pa = ratchet.call(pa, dir)
var owi = List.filled(order.count, null)
for (i in 0...order.count) owi[i] = [i, order[i]]
cmp = Fn.new { |a, b| (a[1] - b[1]).sign }
var order2 = Sort.merge(owi, cmp).map { |e| e[0] }.toList
var res = List.filled(size, 0)
for (i in 0...size) res[i] = pa[order2[i]]
return res
}
var adjust = Fn.new { |p, type|
var size = p.count
if (size == 0) Fiber.abort("List cannot be empty.")
if (type == "Benjamini-Hochberg") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = size / (size - i)
return schwartzian.call(p, mult, Direction.UP)
} else if (type == "Benjamini-Yekutieli") {
var q = (1..size).reduce { |acc, i| acc + 1/i }
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = q * size / (size - i)
return schwartzian.call(p, mult, Direction.UP)
} else if (type == "Bonferroni") {
return p.map { |v| (v * size).min(1) }.toList
} else if (type == "Hochberg") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = i + 1
return schwartzian.call(p, mult, Direction.UP)
} else if (type == "Holm") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = size - i
return schwartzian.call(p, mult, Direction.DOWN)
} else if (type == "Hommel") {
var pwi = List.filled(size, null)
for (i in 0...size) pwi[i] = [i, p[i]]
var cmp = Fn.new { |a, b| (a[1] - b[1]).sign }
var order = Sort.merge(pwi, cmp).map { |e| e[0] }.toList
var s = List.filled(size, 0)
for (i in 0...size) s[i] = p[order[i]]
var m = List.filled(size, 0)
for (i in 0...size) m[i] = s[i] * size / (i + 1)
var min = Nums.min(m)
var q = List.filled(size, min)
var pa = List.filled(size, min)
for (j in size-1..2) {
var lower = List.filled(size - j + 1, 0) // lower indices
for (i in 0...lower.count) lower[i] = i
var upper = List.filled(j - 1, 0) // upper indices
for (i in 0...upper.count) upper[i] = size - j + 1 + i
var qmin = j * s[upper[0]] / 2
for (i in 1...upper.count) {
var temp = s[upper[i]] * j / (2 + i)
if (temp < qmin) qmin = temp
}
for (i in 0...lower.count) {
q[lower[i]] = qmin.min(s[lower[i]] * j)
}
for (i in 0...upper.count) q[upper[i]] = q[size - j]
for (i in 0...size) if (pa[i] < q[i]) pa[i] = q[i]
}
var owi = List.filled(order.count, null)
for (i in 0...order.count) owi[i] = [i, order[i]]
var order2 = Sort.merge(owi, cmp).map { |e| e[0] }.toList
var res = List.filled(size, 0)
for (i in 0...size) res[i] = pa[order2[i]]
return res
} else if (type == "Šidák") {
return p.map { |v| 1 - (1 - v).pow(size) }.toList
} else {
System.print("\nSorry, do not know how to do '%(type)' correction.\n" +
"Perhaps you want one of these?:\n" +
types[0...-1].map { |t| " %(t)" }.join("\n")
)
Fiber.suspend()
}
}
var adjusted = Fn.new { |p, type| "\n%(type)\n%(pFormat.call(adjust.call(check.call(p), type), 5))" }
var pValues = [
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
]
types.each { |type| System.print(adjusted.call(pValues, type)) }</syntaxhighlight>
{{out}}
<pre>
Same as Kotlin (version 2) entry.
</pre>
=={{header|zkl}}==
{{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]''.
<syntaxhighlight lang="zkl">fcn bh(pvalues){ // Benjamini-Hochberg
psz,pszf := pvalues.len(), psz.toFloat();
n_i := psz.pump(List,'wrap(n){ pszf/(psz - n) }); # N/(N-0),N/(N-1),..
Line 3,048 ⟶ 5,949:
}
psz.pump(List,'wrap(n){ pa[ro[n]] }); // Hommel q-values
}</
<
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
Line 3,074 ⟶ 5,975:
}
println();
}</
{{out}}
<pre style="height:45ex">
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