 NAME
 VERSION
 SYNOPSIS
 SUBROUTINES/METHODS
 DEPENDENCIES
 DIAGNOSTICS
 REFERENCES
 AUTHOR
 BUGS
 SUPPORT
 LICENSE AND COPYRIGHT
NAME
Statistics::ANOVA::EffectSize  Calculate effectsizes from ANOVAs incl. etasquared and omegasquared
VERSION
This is documentation for Version 0.02 of Statistics::ANOVA::EffectSize.
SYNOPSIS
use Statistics::ANOVA::EffectSize;
my $es = Statistics::ANOVA::EffectSize>new();
$es>load(HOA); # a hash of arefs, or other, as in Statistics::Data
my $etasq = $es>eta_squared(independent => BOOL, partial => 1); # or give data => HOA here
my $omgsq = $es>omega_squared(independent => BOOL);
# or calculate not from loaded data but directly:
DESCRIPTION
Calculates effectsizes from ANOVAs.
For etasquared, values range from 0 to 1, 0 indicating no effect, 1 indicating difference between at least two DV means. Generally indicates the proportion of variance in the DV related to an effect.
For omegasquared, size is conventionally described as small where omega_sq = .01, medium if omega_sq = .059, and strong if omega_sq = .138 (Cohen, 1969).
SUBROUTINES/METHODS
Rather than working from raw data, these methods are given the statistics, like sumsofsquares, needed to calculate the effectsizes.
eta_sq_partial_by_ss, r_squared
$es>eta_sq_partial_by_ss(ss_b => NUM, ss_w => NUM);
Returns partial etasquared given between and withingroup sumsofsquares (SS):
η^{2}_{P} = SS_{b} / ( SS_{b} + SS_{w} )
This is also what is commonly designated as Rsquared (Maxwell & Delaney, 1990, Eq. 90).
r_squared_adj
$es>r_squared_adj(ss_b => NUM, ss_w => NUM, df_b => NUM, df_w => NUM);
Returns adjusted Rsquared.
eta_sq_partial_by_f
$es>eta_sq_partial_by_f(f_value => NUM , df_b => NUM, df_w => NUM);
Returns partial etasquared given Fvalue and its between and withingroups degreesoffreedom (df):
η^{2}_{P} = ( df_{b} . F ) / ( df_{b} . F + df_{w} )
omega_sq_partial_by_ss
$es>omega_sq_partial_by_ss(df_b => NUM, df_w => NUM, ss_b => NUM, ss_w => NUM, count => NUM);
Returns partial omegasquared given the between and withingroups sumsofsquares and degreesoffreedom.
ω^{2}_{P} = ( ss_{b} — (df_{b} . SS_{w} / df_{w}) ) / ( SS_{b} + (N – df_{b} ) SS_{w} / df_{w} )
(as in, e.g., Olejnik & Algina, 2003, p. 435).
omega_sq_partial_by_ms
$es>omega_sq_partial_by_ms(df_b => NUM, ms_b => NUM, ms_w => NUM, count => NUM);
Returns partial omegasquared given between and withingroup mean sumsofsquares (MS). Also needs betweengroups degreesoffreedom and samplesize (here labelled "count") N:
ω^{2}_{P} = df_{b} ( MS_{b} – MS_{w} ) / ( df_{b} . MS_{b} + ( N – df_{b} ) MS_{w} )
(as in, e.g., Lakens, 2013, Eq. 15).
omega_sq_partial_by_f
$es>omega_sq_partial_by_ms(f_value => NUM, df_b => NUM, df_w => NUM);
Returns partial omegasquared given Fvalue and its between and withingroup degreesoffreedom (df):
ω^{2}_{P}(est.) = ( F  1 ) / ( F + ( df_{w} + 1 ) / df_{b} )
This is an estimate provided by D. Lakens.
eta_to_omega
$es>eta_to_omega(df_b => NUM, df_w => NUM, eta_sq => NUM);
Returns omegasquared based on etasquared and the between and withingroups degreesoffreedom.
ω^{2}_{P} = ( η^{2}_{P}(df_{b} + df_{w}) – df_{b} ) / ( η^{2}_{P}(df_{b} + df_{w}) – df_{b} ) + ( (df_{w} + 1)(1 – η^{2}_{P}) ) )
DEPENDENCIES
List::AllUtils : any
method
Statistics::Data : used as base.
DIAGNOSTICS
 Could not obtain values to calculate ...

croak
ed if the sufficient statistics have not been provided.
REFERENCES
Cohen, J. (1969). Statistical power analysis for the behavioral sciences. New York, US: Academic.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for ttests and ANOVAs. Frontiers in Psychology, 4, 863. doi:10.3389/fpsyg.2013.00863
Lakens, D. (2015). Why you should use omegasquared instead of etasquared, The 20% statistician [Weblog].
Maxwell, S. E., & Delaney, H. D. (1990). Designing experiments and analyzing data: A model comparison perspective. Belmont, CA, US: Wadsworth.
Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistics: Measures of effect size for some common research designs. Psychological Methods, 8, 434447. doi: 10.1037/1082989X.8.4.434.
AUTHOR
Roderick Garton, <rgarton at cpan.org>
BUGS
Please report any bugs or feature requests to bugstatisticsanovaeffectsize0.02 at rt.cpan.org
, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=StatisticsANOVAEffectSize0.02. 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::EffectSize
You can also look for information at:
RT: CPAN's request tracker (report bugs here)
http://rt.cpan.org/NoAuth/Bugs.html?Dist=StatisticsANOVAEffectSize0.02
AnnoCPAN: Annotated CPAN documentation
CPAN Ratings
http://cpanratings.perl.org/d/StatisticsANOVAEffectSize0.02
Search CPAN
http://search.cpan.org/dist/StatisticsANOVAEffectSize0.02/
LICENSE AND COPYRIGHT
Copyright 20152018 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.