/ 
Statistics-ANOVA-0.11
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/ Statistics::ANOVA::EffectSize

NAME

Statistics::ANOVA::EffectSize - Calculate effect-sizes from ANOVAs incl. eta-squared and omega-squared

VERSION

This is documentation for Version 0.01 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 effect-sizes from ANOVAs.

For eta-squared, 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 omega-squared, 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 sums-of-squares, needed to calculate the effect-sizes.

eta_sq_partial_by_ss, r_squared

$es->eta_sq_partial_by_ss(ss_b => NUM, ss_w => NUM);

Returns partial eta-squared given between- and within-group sums-of-squares (SS):

  η2P = SSb / ( SSb + SSw )

This is also what is commonly designated as R-squared (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 R-squared.

eta_sq_partial_by_f

$es->eta_sq_partial_by_f(f_value => NUM , df_b => NUM, df_w => NUM);

Returns partial eta-squared given F-value and its between- and within-groups degrees-of-freedom (df):

  η2P = ( dfb . F ) / ( dfb . F + dfw )

omega_sq_partial_by_ss

$es->omega_sq_partial_by_ss(df_b => NUM, df_w => NUM, ss_b => NUM, ss_w => NUM);

Returns partial omega-squared given the between- and within-groups sums-of-squares and degrees-of-freedom.

Essentially as given by Maxwell & Delaney (1990), Eq. 92:

  ω2P = ( ssb — (dfb . SSw / dfb) ) / (( SSb + SSw ) + SSw / dfw )

omega_sq_partial_by_ms

$es->omega_sq_partial_by_ms(df_b => NUM, ms_b => NUM, ms_w => NUM, count => NUM);

Returns partial omega-squared given between- and within-group mean sums-of-squares (MS). Also needs between-groups degrees-of-freedom and sample-size (here labelled "count") N:

  ω2P = dfb ( MSb – MSw ) / ( dfb . MSb + ( N – dfb ) MSw )

omega_sq_partial_by_f

$es->omega_sq_partial_by_ms(f_value => NUM, df_b => NUM, df_w => NUM);

Returns partial omega-squared given F-value and its between- and within-group degrees-of-freedom (df):

  ω2P(est.) = ( F - 1 ) / ( F + ( dfw + 1 ) / dfb )

This is an estimate formulated by D. Lakens that will not ordinarily agree with the method by (mean) sum-of-squares.

eta_to_omega

$es->eta_to_omega(df_b => NUM, df_w => NUM, eta_sq => NUM);

Returns omega-squared based on eta-squared and the between- and within-groups degrees-of-freedom.

  ω2P = ( η2P(dfb + dfw) – dfb ) / ( η2P(dfb + dfw) – dfb ) + ( (dfw + 1)(1 – η2P) ) )

DEPENDENCIES

List::AllUtils : any method

Statistics::Data : used as base.

DIAGNOSTICS

Could not obtain values to calculate ...

croaked 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. (2015). Why you should use omega-squared instead of eta-squared, 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, 434-447. doi: 10.1037/1082-989X.8.4.434.

AUTHOR

Roderick Garton, <rgarton at cpan.org>

BUGS

Please report any bugs or feature requests to bug-statistics-anova-effectsize-0.01 at rt.cpan.org, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Statistics-ANOVA-EffectSize-0.01. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

NOTES

For independent variables only, omega-square (raw):

w2 = (SSeffect - (dfeffect)(MSerror)) / MSerror + SStotal

SUPPORT

You can find documentation for this module with the perldoc command.

perldoc Statistics::ANOVA::EffectSize

You can also look for information at:

LICENSE AND COPYRIGHT

Copyright 2015 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.