etaSquared: Effect size calculations for ANOVAs
In lsr: Companion to "Learning Statistics with R"

Description Usage Arguments Details Value Examples

Calculates eta-squared and partial eta-squared

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

`x`	An analysis of variance (aov) object.
`type`	What type of sum of squares to calculate?
`anova`	Should the full ANOVA table be printed out in addition to the effect sizes?

Calculates the eta-squared and partial eta-squared measures of effect size that are commonly used in analysis of variance. The input x should be the analysis of variance object itself.

For unbalanced designs, the default in etaSquared is to compute Type II sums of squares (type=2), in keeping with the Anova function in the car package. It is possible to revert to the Type I SS values (type=1) to be consistent with anova, but this rarely tests hypotheses of interest. Type III SS values (type=3) can also be computed.

If anova=FALSE, the output is an M x 2 matrix. Each of the M rows corresponds to one of the terms in the ANOVA (e.g., main effect 1, main effect 2, interaction, etc), and each of the columns corresponds to a different measure of effect size. Column 1 contains the eta-squared values, and column 2 contains partial eta-squared values. If anova=TRUE, the output contains additional columns containing the sums of squares, mean squares, degrees of freedom, F-statistics and p-values.

# Example 1: one-way ANOVA

outcome <- c( 1.4,2.1,3.0,2.1,3.2,4.7,3.5,4.5,5.4 )  # data
treatment1 <- factor( c( 1,1,1,2,2,2,3,3,3 ))        # grouping variable
anova1 <- aov( outcome ~ treatment1 )                # run the ANOVA
summary( anova1 )                                    # print the ANOVA table
etaSquared( anova1 )                                 # effect size

# Example 2: two-way ANOVA

treatment2 <- factor( c( 1,2,3,1,2,3,1,2,3 ))      # second grouping variable
anova2 <- aov( outcome ~ treatment1 + treatment2 ) # run the ANOVA
summary( anova2 )                                  # print the ANOVA table
etaSquared( anova2 )                               # effect size