NAME

Statistics::Multtest - Control false discovery rate in multiple test problem

SYNOPSIS

use Statistics::Multtest qw(bonferroni holm hommel hochberg BH BY);
use Statistics::Multtest qw(:all);
use strict;

my $p;
# p-values can be stored in an array by reference
$p = [0.01, 0.02, 0.05,0.41,0.16,0.51];
# @$res has the same order as @$p
my $res = BH($p);
print join "\n", @$res;

# p-values can also be stored in a hash by reference
$p = {"a" => 0.01,
      "b" => 0.02,
      "c" => 0.05,
      "d" => 0.41,
      "e" => 0.16,
      "f" => 0.51 };
# $res is also a hash reference which is the same as $p
$res = holm($p);
foreach (sort {$res->{a} <=> $res->{$b}} keys %$res) {
    print "$_ => $res->{$_}\n";
}

DESCRIPTION

For statistical test, p-value is the probability of false positives. While there are many hypothesis for testing simultaneously, the probability of getting at least one false positive would be large. Therefore the origin p-values should be adjusted to decrease the false discovery rate.

Six procedures to controlling false positive rates is provided. The names of the methods are derived from p.adjust in stat package in R. Code is translated directly from R to Perl using List::Vectorize module.

All six subroutines receive one argument which can either be an array reference or a hash reference, and return the adjusted p-values in corresponding data structure. The order of items in the array does not change after the adjustment.

Subroutines

bonferroni($pvalue)

Bonferroni single-step process.

hommel($pvalue)

Hommel singlewise process.

Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75, 383¨C386.

holm($pvalue)

Holm step-down process.

Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6, 65¨C70.

hochberg($pvalue)

Hochberg step-up process.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75, 800¨C803.

BH($pvalue)

Benjamini and Hochberg, controlling the FDR.

Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57, 289¨C300.

BY($pvalue)

Use Benjamini and Yekutieli.

Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29, 1165¨C1188.

AUTHOR

Zuguang Gu <jokergoo@gmail.com>

COPYRIGHT AND LICENSE

Copyright 2012 by Zuguang Gu

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.12.1 or, at your option, any later version of Perl 5 you may have available.

SEE ALSO

List::Vectorize