Effect size for ANOVAs

Calculates eta-squared and partial eta-squared effect sizes for an analysis of variance.

Usage

etaSquared(x, type = 2, anova = FALSE)

Arguments

x

An aov object, as returned by aov.

type

Which type of sums of squares to use: 1 for Type I, 2 for Type II (the default), or 3 for Type III. Type II is recommended for most unbalanced designs.

anova

Set to TRUE to include the full ANOVA table alongside the effect sizes. Defaults to FALSE.

Value

A matrix with one row per term in the ANOVA model and columns for eta-squared (eta.sq) and partial eta-squared (eta.sq.part). If anova = TRUE, additional columns show the sums of squares, mean squares, degrees of freedom, F-statistics, and p-values.

Details

Calculates eta-squared and partial eta-squared, two commonly used measures of effect size in analysis of variance. The input x should be an ANOVA fitted with aov.

For unbalanced designs, Type II sums of squares (type = 2) are recommended and are the default, consistent with the Anova function in the car package. Type I (type = 1) matches the output of anova but tests hypotheses that are often not of interest in unbalanced designs. Type III (type = 3) is also available.

See also

aov, summary.aov

Examples

outcome <- c(1.4, 2.1, 3.0, 2.1, 3.2, 4.7, 3.5, 4.5, 5.4)
treatment1 <- factor(c(1, 1, 1, 2, 2, 2, 3, 3, 3))

# one-way ANOVA
anova1 <- aov(outcome ~ treatment1)
summary(anova1)
#>             Df Sum Sq Mean Sq F value Pr(>F)  
#> treatment1   2  7.936   3.968   3.663 0.0913 .
#> Residuals    6  6.500   1.083                 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
etaSquared(anova1)
#>               eta.sq eta.sq.part
#> treatment1 0.5497229   0.5497229

# include the full ANOVA table
etaSquared(anova1, anova = TRUE)
#>               eta.sq eta.sq.part       SS df       MS        F          p
#> treatment1 0.5497229   0.5497229 7.935556  2 3.967778 3.662564 0.09129344
#> Residuals  0.4502771          NA 6.500000  6 1.083333       NA         NA

# two-way ANOVA
treatment2 <- factor(c(1, 2, 3, 1, 2, 3, 1, 2, 3))
anova2 <- aov(outcome ~ treatment1 + treatment2)
etaSquared(anova2)
#>               eta.sq eta.sq.part
#> treatment1 0.5497229   0.9653961
#> treatment2 0.4305727   0.9562393