DescTools (version 0.99.8.1)

EtaSq: Effect size calculations for ANOVAs

Description

Calculates eta-squared and partial eta-squared

Usage

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

Arguments

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

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.

See Also

aov, anova, Anova

Examples

#### 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)