Calculates eta-squared and partial eta-squared
etaSquared(x, type = 2, anova = FALSE)An analysis of variance (aov) object.
What type of sum of squares to calculate?
Should the full ANOVA table be printed out in addition to the effect sizes?
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.
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.
# 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
#> 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 ) # effect size
#> eta.sq eta.sq.part
#> treatment1 0.5497229 0.5497229
# 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
#> Df Sum Sq Mean Sq F value Pr(>F)
#> treatment1 2 7.936 3.968 55.8 0.00120 **
#> treatment2 2 6.216 3.108 43.7 0.00191 **
#> Residuals 4 0.284 0.071
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
etaSquared( anova2 ) # effect size
#> eta.sq eta.sq.part
#> treatment1 0.5497229 0.9653961
#> treatment2 0.4305727 0.9562393