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# NAME

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

# 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 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).

``    \$es->r_squared_adj(ss_b => NUM, ss_w => NUM, df_b => NUM, df_w => NUM);``

## 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, count => NUM);``

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

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

(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 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 ( MSbMSw ) / ( dfb . MSb + ( Ndfb ) MSw )

(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 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 provided by D. Lakens.

## 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 ...

`croak`ed if the sufficient statistics have not been provided.

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 t-tests and ANOVAs. Frontiers in Psychology, 4, 863. doi:10.3389/fpsyg.2013.00863

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-0.02 at rt.cpan.org`, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Statistics-ANOVA-EffectSize-0.02. 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: