P-value correction: Difference between revisions

 
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Link with <code>-lm</code>
<langsyntaxhighlight Clang="c">#include <stdio.h>//printf
#include <stdlib.h>//qsort
#include <math.h>//fabs
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return 0;
}
</syntaxhighlight>
</lang>
 
{{out}}
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{{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).
<langsyntaxhighlight Clang="c">#include <stdio.h>
#include <stdlib.h>
#include <math.h>
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each_i(0, 8) adjusted(p_values, types[i]);
return 0;
}</langsyntaxhighlight>
 
{{output}}
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=={{header|C sharp|C#}}==
{{trans|Java}}
<langsyntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.Linq;
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}
}
}</langsyntaxhighlight>
{{out}}
<pre>[ 1] 6.126681E-001 8.521710E-001 1.987205E-001 1.891595E-001 3.217789E-001
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=={{header|C++}}==
{{trans|Java}}
<langsyntaxhighlight lang="cpp">#include <algorithm>
#include <functional>
#include <iostream>
Line 1,630:
 
return 0;
}</langsyntaxhighlight>
{{out}}
<pre>[ 1] 0.6126681081 0.8521710465 0.1987205200 0.1891595417 0.3217789286
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{{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]''.
<langsyntaxhighlight Dlang="d">import std.algorithm;
import std.conv;
import std.math;
Line 2,057:
writefln("\ntype %d = '%s' has a cumulative error of %g", type, types[type], error);
}
}</langsyntaxhighlight>
{{out}}
<pre>[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
Line 2,140:
=={{header|Go}}==
{{trans|Kotlin (Version 2)}}
<langsyntaxhighlight lang="go">package main
 
import (
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fmt.Println(s)
}
}</langsyntaxhighlight>
 
{{out}}
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{{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]''.
<langsyntaxhighlight Javalang="java">import java.util.Arrays;
import java.util.Comparator;
 
Line 2,895:
}
}
}</langsyntaxhighlight>
{{out}}
<pre>[ 1] 6.126681e-01 0.8521710465 0.1987205200 0.1891595417 0.3217789286
Line 2,975:
 
type 5 = 'hommel' has a cumulative error of 4.35302e-07</pre>
 
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
 
'''Works with jq, the C implementation of jq'''
 
'''Works with gojq, the Go implementation of jq'''
 
'''Works with jaq, the Rust implementation of jq'''
 
The def of `_nwise` is included for the sake of gojq; it may be omitted if using jq or jaq.
<syntaxhighlight lang="jq">
### For gojq
# Require $n > 0
def nwise($n):
def _n: if length <= $n then . else .[:$n] , (.[$n:] | _n) end;
if $n <= 0 then "nwise: argument should be non-negative" else _n end;
 
### Generic functions
 
def array($n): . as $in | [range(0;$n)|$in];
 
def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
 
def rpad($len): tostring | ($len - length) as $l | . + (" " * $l);
 
def round($ndec): pow(10;$ndec) as $p | . * $p | round / $p;
 
# tabular print
def tprint($columns; $width):
reduce _nwise($columns) as $row ("";
. + ($row|map(lpad($width)) | join(" ")) + "\n" );
 
# Emit the permutation p such that [range(0;length) as $i | .[$p[$i]]] is sorted
def sort_index:
[range(0;length) as $i | [$i, .[$i]]]
| sort_by(.[1])
| map(.[0]);
 
 
### p-value Corrections
 
def types: [
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák"
];
 
######################################
# The functions in this section expect
# an array of p-values as input.
######################################
 
def pFormat($cols):
map(round(10) | rpad(12)) | tprint($cols; 12);
 
def check:
if (length == 0 or min < 0 or max > 1)
then "p-values must be in the range 0 to 1 inclusive" | error
else .
end;
 
# $dir should be "UP" or "DOWN"
def ratchet($dir):
{ m: .[0], p: .}
| if $dir == "UP"
then reduce range(1; .p|length) as $i (.;
if (.p[$i] > .m) then .p[$i] = .m end
| .m = .p[$i])
else reduce range(1; .p|length) as $i (.;
if (.p[$i] < .m) then .p[$i] = .m end
| .m = .p[$i] )
end
| .p
| map( if . < 1 then . else 1 end);
 
# If $dir is "UP" then reverse is called
def schwartzian($mult; $dir):
length as $size
| (sort_index | if $dir == "UP" then reverse else . end) as $order
| ([range(0;$size) as $i | $mult[$i] * .[$order[$i]] ]
| ratchet($dir)) as $pa
| ($order | sort_index) as $order2
| [ range(0; $size) as $i | $pa[$order2[$i]]] ;
 
# $type should be one of `types`
def adjust($type):
length as $size
| if $size == 0 then "The array of p-values cannot be empty." | error end
| if $type == "Benjamini-Hochberg"
then
[range(0;$size) as $i | $size / ($size - $i)] as $mult
| schwartzian($mult; "UP")
elif $type == "Benjamini-Yekutieli"
then (reduce range(1; 1+$size) as $i (0; . + (1/$i))) as $q
| [range(0; $size) as $i | $q * $size / ($size - $i)] as $mult
| schwartzian($mult; "UP")
 
elif $type == "Bonferroni"
then map( [(. * $size), 1] | min)
 
elif $type == "Hochberg"
then
[range(0;$size) as $i | $i + 1] as $mult
| schwartzian($mult; "UP")
 
elif $type == "Holm"
then
[range(0; $size) as $i | $size - $i] as $mult
| schwartzian($mult; "DOWN")
 
elif $type == "Hommel"
then
sort_index as $order
| [range(0; $size) as $i | .[$order[$i]]] as $s
| [range(0; $size) as $i | $s[$i] * $size / ($i + 1)] as $m
| ($m | min) as $min
| { q: ($min | array($size)),
pa: ($min | array($size)) }
| reduce range($size-1; 1; -1) as $j (.;
.lower = (0 | array($size - $j + 1)) # lower indices
| reduce range(0; .lower|length) as $i (.; .lower[$i] = $i)
| .upper = (0|array($j - 1))
| reduce range(0; .upper|length) as $i (.; .upper[$i] = $size - $j + 1 + $i)
| .qmin = ($j * $s[.upper[0]] / 2)
| reduce range(1; .upper|length) as $i (.;
($s[.upper[$i]] * $j / (2 + $i)) as $temp
| if $temp < .qmin then .qmin = $temp end )
| reduce range(0; .lower|length) as $i (.;
.q[.lower[$i]] = ([.qmin, ($s[.lower[$i]] * $j)] | min) )
| reduce range(0; .upper|length) as $i (.; .q[.upper[$i]] = .q[$size - $j])
| reduce range(0; $size) as $i (.; if (.pa[$i] < .q[$i]) then .pa[$i] = .q[$i] end)
)
| ($order | sort_index) as $order2
| [range(0; $size) as $i | .pa[$order2[$i] ]]
 
elif $type == "Šidák"
then map(1 - pow(1 - .; $size) )
 
else
"\nSorry, do not know how to do '\($type)' correction.\n" +
"Perhaps you want one of the following?\n" +
(types | map( " \(.)" ) | join("\n") )
end;
 
def adjusted($type):
"\n\($type)",
(check | adjust($type) | pFormat(5));
 
### Example
 
def pValues: [
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
];
 
pValues | adjusted( types[] )
</syntaxhighlight>
{{output}}
The output shown here is from a run using jq. The output using gojq
is the same except that numbers are presented without using scientific notation.
<pre>
Benjamini-Hochberg
0.6126681081 0.8521710465 0.19872052 0.1891595417 0.3217789286
0.930145 0.487037 0.930145 0.6049730556 0.6826752564
0.6482628947 0.72537225 0.5280972727 0.8769925556 0.4705703448
0.9241867391 0.6049730556 0.7856107317 0.4887525806 0.1136717045
0.4991890625 0.8769925556 0.9991834 0.3217789286 0.930145
0.2304957692 0.5832475 0.0389954722 0.8521710465 0.1476842609
0.016836375 0.0025629017 0.0351608437 0.0625018947 0.0036365888
0.0025629017 0.0294688286 0.0061660636 0.0389954722 0.0026889914
0.0004502863 1.25223e-05 0.0788155476 0.03142613 0.004846527
0.0025629017 0.004846527 0.0011017083 0.072520325 0.0220595769
 
 
Benjamini-Yekutieli
1 1 0.8940844244 0.8510676197 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 0.5114323399
1 1 1 1 1
1 1 0.1754486368 1 0.6644618149
0.0757503083 0.0115310209 0.1581958559 0.2812088585 0.0163617595
0.0115310209 0.1325863108 0.0277423864 0.1754486368 0.0120983246
0.0020259303 5.63403e-05 0.3546073326 0.1413926119 0.0218055202
0.0115310209 0.0218055202 0.004956812 0.3262838334 0.0992505663
 
 
Bonferroni
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 0.7019185 1 1
0.2020365 0.015166745 0.5625735 1 0.02909271
0.01537741 0.4125636 0.0678267 0.680348 0.01882294
0.0009005725 1.25223e-05 1 0.47139195 0.043955765
0.010889155 0.04846527 0.003305125 1 0.2867745
 
 
Hochberg
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.46326621 0.9991834 0.9991834
0.15758847 0.013839669 0.39380145 0.76002304 0.0250197306
0.013839669 0.305297064 0.05426136 0.46263664 0.0165641872
0.0008825611 1.25223e-05 0.9930759 0.339402204 0.0369228426
0.0102358057 0.0397415214 0.00317292 0.89925203 0.21794862
 
 
Holm
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 0.46326621 1 1
0.15758847 0.0139534054 0.39380145 0.76002304 0.0250197306
0.0139534054 0.305297064 0.05426136 0.46263664 0.0165641872
0.0008825611 1.25223e-05 0.9930759 0.339402204 0.0369228426
0.0102358057 0.0397415214 0.00317292 0.89925203 0.21794862
 
 
Hommel
0.9991834 0.9991834 0.9991834 0.99876238 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.9991834 0.9991834 0.959518
0.9991834 0.9991834 0.9991834 0.9991834 0.9991834
0.9991834 0.9991834 0.43518947 0.9991834 0.97665225
0.14142555 0.0130434007 0.3530936533 0.68877088 0.0238560222
0.0132245726 0.272291976 0.05426136 0.42181576 0.0158112696
0.0008825611 1.25223e-05 0.8743649143 0.301690848 0.035164612
0.0095824564 0.038772216 0.00317292 0.81222764 0.19500666
 
 
Šidák
1 1 0.9946598274 0.9914285749 0.9999515274
1 0.9999999688 1 1 1
1 1 0.9999999995 1 0.9999998801
1 1 1 0.9999999855 0.9231179729
0.9999999956 1 1 0.9999317605 1
0.9983109511 1 0.506825394 1 0.9703301333
0.183269244 0.0150545753 0.4320729669 0.6993672225 0.0286818157
0.0152621104 0.3391808707 0.0656206307 0.4959194266 0.0186503726
0.0009001752 1.25222e-05 0.8142104886 0.3772612062 0.0430222116
0.0108312558 0.0473319661 0.003299778 0.7705015898 0.2499384839
</pre>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using MultipleTesting, IterTools, Printf
 
p = [4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
Line 3,001 ⟶ 3,261:
println("\n", corr)
printpvalues(adjust(p, corr))
end</langsyntaxhighlight>
 
{{out}}
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''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]''.
 
<langsyntaxhighlight lang="scala">// version 1.1.51
 
import java.util.Arrays
Line 3,339 ⟶ 3,599:
println(f.format(type, types[type], error))
}
}</langsyntaxhighlight>
 
{{out}}
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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.
<langsyntaxhighlight lang="scala">// version 1.2.21
 
typealias DList = List<Double>
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types.forEach { println(adjusted(pValues, it)) }
}</langsyntaxhighlight>
 
{{out}}
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=={{header|Nim}}==
{{trans|Kotlin (Version 2)}}
<langsyntaxhighlight Nimlang="nim">import algorithm, math, sequtils, strformat, strutils, sugar
 
type
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for ctype in CorrectionType:
echo adjusted(PVals, ctype)</langsyntaxhighlight>
 
{{out}}
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{{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]''.
<langsyntaxhighlight lang="perl">#!/usr/bin/env perl
 
use strict;
Line 4,159 ⟶ 4,419:
printf("type $method has cumulative error of %g.\n", $error);
}
</syntaxhighlight>
</lang>
 
{{out}}
Line 4,178 ⟶ 4,438:
 
=={{header|Phix}}==
Translation of Kotlin (version 2), except for the Hommel part, which is translated from Go.<br>
<!--<syntaxhighlight lang="phix">(phixonline)-->
Note that sq_min(), extract(), and custom_sort() as used below require 0.8.0+
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<lang Phix>enum UP, DOWN
<span style="color: #008080;">enum</span> <span style="color: #000000;">UP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DOWN</span>
 
function ratchet(sequence p, integer direction)
<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>
atom m = p[1]
<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>
for i=1 to length(p) do
<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>
if iff(direction=UP?p[i]>m:p[i]<m) then p[i] = m end if
<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>
m = p[i]
<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>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return sq_min(p,1)
<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>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function schwartzian(sequence p, mult, integer direction)
<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>
sequence order = custom_sort(p,tagset(length(p)))
<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>
if direction=UP then order = reverse(order) end if
<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>
sequence pa = ratchet(sq_mul(mult,extract(p,order)), direction)
<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>
return extract(pa,order,invert:=true)
<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>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function adjust(sequence p, string method)
<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>
integer size = length(p)
<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>
sequence mult = tagset(size)
<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>
switch method
<span style="color: #008080;">switch</span> <span style="color: #000000;">method</span>
 
case "Benjamini-Hochberg":
<span style="color: #008080;">case</span> <span style="color: #008000;">"Benjamini-Hochberg"</span><span style="color: #0000FF;">:</span>
mult = sq_div(size,sq_sub(size+1,mult))
<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>
return schwartzian(p, mult, UP)
<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>
 
case "Benjamini-Yekutieli":
<span style="color: #008080;">case</span> <span style="color: #008000;">"Benjamini-Yekutieli"</span><span style="color: #0000FF;">:</span>
atom q = sum(sq_div(1,mult))
<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>
mult = sq_div(q*size,sq_sub(size+1,mult))
<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>
return schwartzian(p, mult, UP)
<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>
 
case "Bonferroni":
<span style="color: #008080;">case</span> <span style="color: #008000;">"Bonferroni"</span><span style="color: #0000FF;">:</span>
return sq_min(sq_mul(p,size),1)
<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>
 
case "Hochberg":
<span style="color: #008080;">case</span> <span style="color: #008000;">"Hochberg"</span><span style="color: #0000FF;">:</span>
return schwartzian(p, mult, UP)
<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>
case "Holm":
<span style="color: #008080;">case</span> <span style="color: #008000;">"Holm"</span><span style="color: #0000FF;">:</span>
mult = sq_sub(size+1,mult)
<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>
return schwartzian(p, mult, DOWN)
<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>
case "Hommel":
<span style="color: #008080;">case</span> <span style="color: #008000;">"Hommel"</span><span style="color: #0000FF;">:</span>
sequence ivdx = repeat(0,size)
<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>
for i=1 to size do ivdx[i] = {p[i],i} end for
<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>
ivdx = sort(ivdx)
<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>
sequence s = vslice(ivdx,1),
<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>
m = sq_div(sq_mul(s,size),mult),
<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>
{q,pa} @= repeat(min(m),size),
<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>
order = vslice(ivdx,2)
<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>
for j=size-1 to 2 by -1 do
<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>
sequence lwr = tagset(size-j+1),
<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>
upr = sq_add(size-j+1,tagset(j-1))
<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>
atom qmin = j*s[upr[1]]/2
<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>
for i=2 to length(upr) do
<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>
qmin = min(s[upr[i]]*j/(i+1),qmin)
<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>
end for
<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>
for i=1 to length(lwr) do
<span style="color: #008080;">end</span> q[lwr[i]]<span style="color: min(s[lwr[i]]*j, qmin)#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>
end for
<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>
for i=1 to length(upr) do
<span style="color: #008080;">end</span> q[upr[i]]<span style="color: q[size-j+1]#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>
end for
<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>
pa = sq_max(pa,q)
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<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>
return extract(pa,order,invert:=true)
<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>
case "Sidak":
for i=1 to length(p) do
<span style="color: #008080;">case</span> <span style="color: #008000;">"Sidak"</span><span style="color: #0000FF;">:</span>
p[i] = 1 - power(1-p[i],size)
<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>
end for
<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>
return p
<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>
else
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
return {} -- (unknown method)
 
<span style="color: #008080;">else</span>
end switch
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- (unknown method)</span>
return p
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
 
<span style="color: #008080;">return</span> <span style="color: #000000;">p</span>
constant {types,correct_answers} = columnize({
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
{"Benjamini-Hochberg",
{6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
<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>
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Benjamini-Hochberg"</span><span style="color: #0000FF;">,</span>
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
<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>
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
<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>
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
<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>
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
<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>
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
<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>
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
<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>
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
<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>
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02}},
<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>
{"Benjamini-Yekutieli",
<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>
{1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Benjamini-Yekutieli"</span><span style="color: #0000FF;">,</span>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
<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>
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
<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>
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
<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>
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
<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>
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02}},
<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>
{"Bonferroni",
<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>
{1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Bonferroni"</span><span style="color: #0000FF;">,</span>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
<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>
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
<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>
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
<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>
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
<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>
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01}},
<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>
{"Hochberg",
<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>
{9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Hochberg"</span><span style="color: #0000FF;">,</span>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
<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>
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
<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>
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
<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>
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
<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>
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01}},
<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>
{"Holm",
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{1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Holm"</span><span style="color: #0000FF;">,</span>
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<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>
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
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1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
<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>
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
<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>
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
<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>
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
<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>
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
<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>
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01}},
<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>
{"Hommel",
<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>
{9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Hommel"</span><span style="color: #0000FF;">,</span>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
<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>
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
<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>
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
<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>
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
<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>
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
<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>
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
<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>
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01}},
<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>
{"Sidak",
<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>
{1.0000000000, 1.0000000000, 0.9946598274, 0.9914285749, 0.9999515274,
<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>
1.0000000000, 0.9999999688, 1.0000000000, 1.0000000000, 1.0000000000,
<span style="color: #0000FF;">{</span><span style="color: #008000;">"Sidak"</span><span style="color: #0000FF;">,</span>
1.0000000000, 1.0000000000, 0.9999999995, 1.0000000000, 0.9999998801,
<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>
1.0000000000, 1.0000000000, 1.0000000000, 0.9999999855, 0.9231179729,
<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>
0.9999999956, 1.0000000000, 1.0000000000, 0.9999317605, 1.0000000000,
<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>
0.9983109511, 1.0000000000, 0.5068253940, 1.0000000000, 0.9703301333,
<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>
0.1832692440, 0.0150545753, 0.4320729669, 0.6993672225, 0.0286818157,
<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>
0.0152621104, 0.3391808707, 0.0656206307, 0.4959194266, 0.0186503726,
<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>
0.0009001752, 0.0000125222, 0.8142104886, 0.3772612062, 0.0430222116,
<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>
0.0108312558, 0.0473319661, 0.0032997780, 0.7705015898, 0.2499384839}}})
<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>
-- {"Unknown",{1}}})
<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>
constant pValues = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
<span style="color: #000080;font-style:italic;">-- {"Unknown",{1<nowiki>}}</nowiki>})</span>
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,
<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>
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
<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>
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
<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>
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
<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>
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
<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>
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
<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>
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
<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>
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03}
<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>
if length(pValues)=0 or min(pValues)<0 or max(pValues)>1 then
<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>
crash("p-values must be in range 0.0 to 1.0")
end if
<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>
for i=1 to length(types) do
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
string ti = types[i]
sequence res = adjust(pValues,ti)
<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>
if res={} then
<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>
printf(1,"\nSorry, do not know how to do %s correction.\n"&
<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>
"Perhaps you want one of these?:\n %s\n",
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span>
{ti,join(types[1..$-1],"\n ")})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nSorry, do not know how to do %s correction.\n"</span><span style="color: #0000FF;">&</span>
exit
<span style="color: #008000;">"Perhaps you want one of these?:\n %s\n"</span><span style="color: #0000FF;">,</span>
end if
<span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">types</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #008000;">"\n "</span><span style="color: #0000FF;">)})</span>
-- printf(1,"%s\n",{ti})
<span style="color: #008080;">exit</span>
-- res = correct_answers[i] -- (for easier comparison only)
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-- pp(res,{pp_FltFmt,"%13.10f",pp_IntFmt,"%13.10f",pp_Maxlen,75,pp_Pause,0})
<span style="color: #000080;font-style:italic;">-- printf(1,"%s\n",{ti})
atom error = sum(sq_abs(sq_sub(res,correct_answers[i])))
-- res = correct_answers[i] -- (for easier comparison only)
printf(1,"%s has cumulative error of %g\n", {ti,error})
-- pp(res,{pp_FltFmt,"%13.10f",pp_IntFmt,"%13.10f",pp_Maxlen,75,pp_Pause,0})</span>
end for</lang>
<span style="color: #004080;">atom</span> <span style="color: #000000;">error</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_abs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">correct_answers</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s has cumulative error of %g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">error</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
Matches Kotlin (etc) when some of those lines just above are uncommented.
Line 4,385 ⟶ 4,649:
{{trans|Perl}}
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
<langsyntaxhighlight lang="python">from __future__ import division
import sys
 
Line 4,620 ⟶ 4,884:
error += abs(q[i] - correct_answers[key][i])
print '%s error = %g' % (key.upper(), error)
</syntaxhighlight>
</lang>
 
{{out}}
Line 4,635 ⟶ 4,899:
The '''p.adjust''' function is built-in, see [https://stat.ethz.ch/R-manual/R-devel/library/stats/html/p.adjust.html R manual].
 
<langsyntaxhighlight Rlang="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,
Line 4,663 ⟶ 4,927:
 
p.adjust(p, method = 'hommel')
writeLines("Hommel\n")</langsyntaxhighlight>
 
{{out}}
Line 4,735 ⟶ 4,999:
{{works with|Rakudo|2019.03.1}}
 
<syntaxhighlight lang="raku" perl6line>########################### Helper subs ###########################
 
sub adjusted (@p, $type) { "\n$type\n" ~ format adjust( check(@p), $type ) }
Line 4,828 ⟶ 5,092:
{
say adjusted @p-values, $_
}</langsyntaxhighlight>
 
{{out}}
Line 4,917 ⟶ 5,181:
=={{header|Ruby}}==
{{trans|Perl}}
<langsyntaxhighlight lang="ruby">def pmin(array)
x = 1
pmin_array = []
Line 5,181 ⟶ 5,445:
puts "total error for #{method} = #{error}"
end
</syntaxhighlight>
</lang>
{{out}}
<pre>Benjamini-Yekutieli
Line 5,195 ⟶ 5,459:
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}}==
 
<langsyntaxhighlight lang="sas">data pvalues;
input raw_p @@;
cards;
Line 5,216 ⟶ 5,802:
 
proc multtest pdata=pvalues bon sid hom hoc holm;
run;</langsyntaxhighlight>
 
'''output'''
Line 5,293 ⟶ 5,879:
First, install the package with:
 
<syntaxhighlight lang ="stata">ssc install qqvalue</langsyntaxhighlight>
 
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:
 
<langsyntaxhighlight lang="stata">clear
 
#delimit ;
Line 5,319 ⟶ 5,905:
}
 
list</langsyntaxhighlight>
 
'''output'''
Line 5,386 ⟶ 5,972:
50. | .00573549 .2867745 .24993848 .21794862 .19633763 .21794862 .02205958 .09925057 |
+-----------------------------------------------------------------------------------------------+</pre>
 
=={{header|Wren}}==
{{trans|Kotlin (version 2)}}
{{libheader|Wren-dynamic}}
{{libheader|Wren-fmt}}
{{libheader|Wren-seq}}
{{libheader|Wren-math}}
{{libheader|Wren-sort}}
<syntaxhighlight lang="wren">import "./dynamic" for Enum
import "./fmt" for Fmt
import "./seq" for Lst
import "./math" for Nums
import "./sort" for Sort
 
var Direction = Enum.create("Direction", ["UP", "DOWN"])
 
// test also for 'Unknown' correction type
var types = [
"Benjamini-Hochberg", "Benjamini-Yekutieli", "Bonferroni", "Hochberg",
"Holm", "Hommel", "Šidák", "Unknown"
]
 
var pFormat = Fn.new { |p, cols|
var i = -cols
var fmt = "$1.10f"
return Lst.chunks(p, cols).map { |chunk|
i = i + cols
return Fmt.swrite("[$2d $s", i, chunk.map { |v| Fmt.swrite(fmt, v) }.join(" "))
}.join("\n")
}
 
var check = Fn.new { |p|
if (p.count == 0 || Nums.min(p) < 0 || Nums.max(p) > 1) {
Fiber.abort("p-values must be in range 0 to 1")
}
return p
}
 
var ratchet = Fn.new { |p, dir|
var pp = p.toList
var m = pp[0]
if (dir == Direction.UP) {
for (i in 1...pp.count) {
if (pp[i] > m) pp[i] = m
m = pp[i]
}
} else {
for (i in 1...pp.count) {
if (pp[i] < m) pp[i] = m
m = pp[i]
}
}
return pp.map { |v| (v < 1) ? v : 1 }.toList
}
 
var schwartzian = Fn.new { |p, mult, dir|
var size = p.count
var pwi = List.filled(size, null)
for (i in 0...size) pwi[i] = [i, p[i]]
var cmp = (dir == Direction.UP) ? Fn.new { |a, b| (b[1] - a[1]).sign } :
Fn.new { |a, b| (a[1] - b[1]).sign }
var order = Sort.merge(pwi, cmp).map { |e| e[0] }.toList
var pa = List.filled(size, 0)
for (i in 0...size) pa[i] = mult[i] * p[order[i]]
pa = ratchet.call(pa, dir)
var owi = List.filled(order.count, null)
for (i in 0...order.count) owi[i] = [i, order[i]]
cmp = Fn.new { |a, b| (a[1] - b[1]).sign }
var order2 = Sort.merge(owi, cmp).map { |e| e[0] }.toList
var res = List.filled(size, 0)
for (i in 0...size) res[i] = pa[order2[i]]
return res
}
 
var adjust = Fn.new { |p, type|
var size = p.count
if (size == 0) Fiber.abort("List cannot be empty.")
if (type == "Benjamini-Hochberg") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = size / (size - i)
return schwartzian.call(p, mult, Direction.UP)
 
} else if (type == "Benjamini-Yekutieli") {
var q = (1..size).reduce { |acc, i| acc + 1/i }
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = q * size / (size - i)
return schwartzian.call(p, mult, Direction.UP)
 
} else if (type == "Bonferroni") {
return p.map { |v| (v * size).min(1) }.toList
 
} else if (type == "Hochberg") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = i + 1
return schwartzian.call(p, mult, Direction.UP)
 
} else if (type == "Holm") {
var mult = List.filled(size, 0)
for (i in 0...size) mult[i] = size - i
return schwartzian.call(p, mult, Direction.DOWN)
 
} else if (type == "Hommel") {
var pwi = List.filled(size, null)
for (i in 0...size) pwi[i] = [i, p[i]]
var cmp = Fn.new { |a, b| (a[1] - b[1]).sign }
var order = Sort.merge(pwi, cmp).map { |e| e[0] }.toList
var s = List.filled(size, 0)
for (i in 0...size) s[i] = p[order[i]]
var m = List.filled(size, 0)
for (i in 0...size) m[i] = s[i] * size / (i + 1)
var min = Nums.min(m)
var q = List.filled(size, min)
var pa = List.filled(size, min)
for (j in size-1..2) {
var lower = List.filled(size - j + 1, 0) // lower indices
for (i in 0...lower.count) lower[i] = i
var upper = List.filled(j - 1, 0) // upper indices
for (i in 0...upper.count) upper[i] = size - j + 1 + i
var qmin = j * s[upper[0]] / 2
for (i in 1...upper.count) {
var temp = s[upper[i]] * j / (2 + i)
if (temp < qmin) qmin = temp
}
for (i in 0...lower.count) {
q[lower[i]] = qmin.min(s[lower[i]] * j)
}
for (i in 0...upper.count) q[upper[i]] = q[size - j]
for (i in 0...size) if (pa[i] < q[i]) pa[i] = q[i]
}
var owi = List.filled(order.count, null)
for (i in 0...order.count) owi[i] = [i, order[i]]
var order2 = Sort.merge(owi, cmp).map { |e| e[0] }.toList
var res = List.filled(size, 0)
for (i in 0...size) res[i] = pa[order2[i]]
return res
 
} else if (type == "Šidák") {
return p.map { |v| 1 - (1 - v).pow(size) }.toList
 
} else {
System.print("\nSorry, do not know how to do '%(type)' correction.\n" +
"Perhaps you want one of these?:\n" +
types[0...-1].map { |t| " %(t)" }.join("\n")
)
Fiber.suspend()
}
}
 
var adjusted = Fn.new { |p, type| "\n%(type)\n%(pFormat.call(adjust.call(check.call(p), type), 5))" }
 
var pValues = [
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
]
types.each { |type| System.print(adjusted.call(pValues, type)) }</syntaxhighlight>
 
{{out}}
<pre>
Same as Kotlin (version 2) entry.
</pre>
 
=={{header|zkl}}==
Line 5,391 ⟶ 6,145:
''This work is based on R source code covered by the '''GPL''' license. It is thus a modified version, also covered by the GPL. See the [https://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic FAQ about GNU licenses]''.
 
<langsyntaxhighlight 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 5,455 ⟶ 6,209:
}
psz.pump(List,'wrap(n){ pa[ro[n]] }); // Hommel q-values
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">pvalues:=T(
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
Line 5,481 ⟶ 6,235:
}
println();
}</langsyntaxhighlight>
{{out}}
<pre style="height:45ex">
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