NAME
Statistics::ANOVA::Friedman  Nonparametric repeated measures analysis of variance for dependent factorial measures (Friedman Test)
VERSION
This is documentation for version 0.02, released February 2017.
SYNOPSIS
use Statistics::ANOVA::Friedman;
my $fri = Statistics::ANOVA::Friedman>new();
my ($chi_value, $df, $count, $p_value) = $fri>chiprob_test(data => HOA);
$fri>load({1 => [2, 4, 6], 2 => [3, 3, 12], 3 => [5, 7, 11]}); # or preload with HOA
($chi_value, $df, $count, $p_value) = $fri>chiprob_test();
my ($f_value, $df_b, $df_w, $p_value2) = $fri>fprob_test();
DESCRIPTION
Performs the Friedman nonparametric analysis of variance  for dependent (correlated, matched) measures of two or more discrete (nominal) variables, such as when the measures are taken from the same source (e.g., person, plot) but under different conditions. A ranking procedure is used, but, unlike the case for independent measures, the ranks are taken at each common index of each measure, i.e., withingroups.
By default, the method accounts for and corrects for ties, but if correct_ties => 0, the teststatistic is uncorrected. The correction involves accounting for the number of tied variables at each index, as per Hollander & Wolfe (1995), Eq. 7.8, p. 274.
Correctness of output is tested on installation using example data from Hollander & Wolfe (1999, p. 274ff), Rice (1995, p. 470), Sarantakos (1993, p. 404405), and Siegal (1956, p. 167ff); tests fail if the published chivalues and degreesoffreedom are not returned by the module.
The module uses Statistics::Data as a base so that data can be preloaded and added to per that module's methods.
SUBROUTINES/METHODS
new
$fri = Statistics::ANOVA::Friedman>new();
New object for accessing methods and storing results. This "isa" Statistics::Data object.
load, add, unload
$fri>load('a' => [1, 4], 'b' => [3, 7]);
The given data can now be used by any of the following methods. This is inherited from Statistics::Data, and all its other methods are available here via the class object. Only passing of data as a hash of arrays (HOA) is supported for now. Alternatively, give each of the following methods the HOA for the optional named argument data.
chiprob_test
($chi_value, $df, $count, $p_value) = $fri>chiprob_test(data => HOA, correct_ties => 1);
Performs the ANOVA and returns the chisquare value, its degreesoffreedom, the total number of observations, and associated probability value (or only the latter if called in scalar context). Default value of optional argument correct_ties is 1.
chiprob_str
$str = $fri>chiprob_str(data => HOA, correct_ties => 1);
Performs the same test as for chiprob_test but returns not an array but a string of the conventional reporting form, e.g., chi^2(df, N = total observations) = chi_value, p = p_value.
fprob_test
($f_value, $df_b, $df_w, $p_value) = $fri>fprob_test(data => HOA);
$p_value = $fri>fprob_test(data => HOA);
Performs the same test as above but transforms the chivalue into an Fdistributed value, returning this Fequivalent value, between and within groups degreesoffreedom, and then the associated probability off the Fdistribution (or only the latter if called in scalar context). Default value of optional argument correct_ties is 1. This method has not been tested against sample data as yet.
fprob_str
$str = $fri>chiprob_str(data => HOA, correct_ties => 1);
Performs the same test as for fprob_test but returns not an array but a string of the conventional reporting form, e.g., F(df_b, df_w) = f_value, p = p_value.
DEPENDENCIES
List::AllUtils : used for summing.
Math::Cephes : used for probability functions.
Statistics::Data : used as base.
Statistics::Data::Rank : used to calculate the dependent sumsquare of ranks. See this module for retrieving the actual arrays of ranks and sumsquares.
DIAGNOSTICS
 Need to have equal numbers of observations greater than 1 per two or variables for chiprob_test

croak
ed if there are not equal numbers of numerical values in each given variable, and if there are not at least two variables. Similarly for fprob_test.
REFERENCES
Hollander, M., & Wolfe, D. A. (1999). Nonparametric statistical methods. New York, NY, US: Wiley.
Rice, J. A. (1995). Mathematical statistics and data analysis. Belmont, CA, US: Duxbury.
Sarantakos, S. (1993). Social research. Melbourne, Australia: MacMillan.
Siegal, S. (1956). Nonparametric statistics for the behavioral sciences. New York, NY, US: McGrawHill
AUTHOR
Roderick Garton, <rgarton at cpan.org>
BUGS AND LIMITATIONS
Please report any bugs or feature requests to bugstatisticsanovafriedman0.02 at rt.cpan.org
, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=StatisticsANOVAFriedman0.02. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.
SUPPORT
You can find documentation for this module with the perldoc command.
perldoc Statistics::ANOVA::Friedman
You can also look for information at:
RT: CPAN's request tracker (report bugs here)
http://rt.cpan.org/NoAuth/Bugs.html?Dist=StatisticsANOVAFriedman0.02
AnnoCPAN: Annotated CPAN documentation
CPAN Ratings
http://cpanratings.perl.org/d/StatisticsANOVAFriedman0.02
Search CPAN
LICENSE AND COPYRIGHT
Copyright 20152017 Roderick Garton.
This program is free software; you can redistribute it and/or modify it under the terms of either: the GNU General Public License as published by the Free Software Foundation; or the Artistic License.
See http://dev.perl.org/licenses/ for more information.