Statistics-Test-WilcoxonRankSum version 0.0.1
Performs the Wilcoxon (aka Mann-Whitney) rank sum test on two sets of numeric data.
In statistics, the Mann-Whitney U test (also called the
Mann-Whitney-Wilcoxon (MWW), Wilcoxon rank-sum test, or
Wilcoxon-Mann-Whitney test) is a non-parametric test for assessing
whether two samples of observations come from the same
distribution. The null hypothesis is that the two samples are drawn
from a single population, and therefore that their probability
distributions are equal. See the Wikipedia entry
http://en.wikipedia.org/wiki/Mann-Whitney_U (for eg.) or statistic
textbooks for further details.
When the sample sizes are small the probability can be computed
directly. For larger samples usually a normal approximation is used.
Input to the test are two sets (lists) of numbers. The values of both
lists are ranked from the smallest to the largest, while remembering
which set the items come from. When the values are the same, they get
an average rank. For each of the sample sets, we compute the rank
sum. Under the assumption that the two samples come from the same
population, the rank sum of the first set should be close to the value
B, where n1 and n2 are the sample sizes. The
test computes the (exact, resp. approximated) probability of the
actual rank sum against the expected value (which is the one given
above). So, when the computed probability is below 0.05, we can
reject the null hypothesis at level 0.05 and conclude that the two
samples are significantly different.
The implementation follows the mechanics described above. The exact
probability is computed for sample sizes less than 20, but this
threshold can be set with `new'. For larger samples the probability is
computed by normal approximation.
INSTALLATION
To install this module, run the following commands:
perl Makefile.PL
make
make test
make install
Alternatively, to install with Module::Build, you can use the following commands:
perl Build.PL
./Build
./Build test
./Build install
DEPENDENCIES
uses the following:
Carp
Carp::Assert
Class::Std
Contextual::Return
Set::Partition
List::Util qw(sum)
Math::BigFloat
Math::Counting
Statistics::Distributions
COPYRIGHT AND LICENCE
Copyright (C) 2008, Ingrid Falk
This library is free software; you can redistribute it and/or modify
it under the same terms as Perl itself.