EtaSq: Effect size calculations for ANOVAs

Description

Calculates eta-squared and partial eta-squared

Usage

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

Arguments

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

Value

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.

Details

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 EtaSq 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.

Examples

Run this code

#### 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
EtaSq( 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
EtaSq(anova2)                                    # effect size


# define other contrasts
dfMD  <- data.frame(IV1=factor(rep(1:3, c(3+5+7, 5+6+4, 5+4+6))),
                    IV2=factor(rep(rep(1:3, 3), c(3,5,7, 5,6,4, 5,4,6))),
                    DV=c(c(41, 43, 50), c(51, 43, 53, 54, 46), c(45, 55, 56, 60, 58, 62, 62),
                         c(56, 47, 45, 46, 49), c(58, 54, 49, 61, 52, 62), c(59, 55, 68, 63),
                         c(43, 56, 48, 46, 47), c(59, 46, 58, 54), c(55, 69, 63, 56, 62, 67)))

dfMD$IV1s <- C(dfMD$IV1, "contr.sum")
dfMD$IV2s <- C(dfMD$IV2, "contr.sum")
dfMD$IV1t <- C(dfMD$IV1, "contr.treatment")
dfMD$IV2t <- C(dfMD$IV2, "contr.treatment")

op    <- options(contrasts=c("contr.treatment", "contr.poly"))
fitT  <- aov(DV ~ IV1*IV2, data=dfMD)
fitTs <- aov(DV ~ IV1s*IV2s, data=dfMD)

options(contrasts=c("contr.sum", "contr.poly"))
fitS  <- aov(DV ~ IV1*IV2, data=dfMD)
fitSt <- aov(DV ~ IV1t*IV2t, data=dfMD)

options(op)

dfBal <- data.frame(IV1=factor(rep(1:2, times=8*3)),
                    IV2=factor(rep(1:3,  each=8*2)),
                    DV=rnorm(8*2*3, 0, 1))

fitB <- aov(DV ~ IV1*IV2, data=dfBal)

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