# Confidence interval for $\eta^{2}$ for MANOVA in R

I have to report the Confidence Intervals for the $\eta^{2}$ obtained in a MANOVA in R.

I use the function etasq of the package heplots to obtain the $\eta^{2}$.

library(heplots)
fit2 <- manova(cbind(data$V247d,data$V248d,data$V249d,data$V250d,data$V251d,data$V252d,data$V253d,data$V254d,data$V255d,data$V256d,data$V257d) ~ data$cond)
summary(fit2)
etasq(fit2) # eta^2 = 0.03


cond is a binary variable (yes/no) that decides whether people are in group 1 or group 2.

How do I obtain to the CI for eta squared here?

Thank you

• What kind of variable is data$cond, factor or quantitative variable? If it's a factor, how many levels does it have, and what confidence interval are you specifically looking for such a factor? Sep 17, 2014 at 16:00 • cond is binary, yes/no. the journal asks me to report effect size and confidence intervals for every statistic reported. i thought eta squared would work well for manova, but any other effect size measure (as long as standardized) is also ok. Sep 17, 2014 at 18:20 ## 2 Answers Alternatively, you can bootstrap$\eta^2\$ to compute its sampling distribution.

## using mtcars as an example dataset
f <- function(d){
temp <- d[sample(nrow(d), replace = TRUE), ]
return(as.numeric(etasq(manova(with(temp, cbind(mpg, wt) ~ am)))))
}
r_etasq <- replicate(999, f(mtcars))
(ci95_etasq <- quantile(r_etasq, c(0.025, 0.975)))
2.5%     97.5%
0.3194276 0.6869550
hist(r_etasq)


I found the answer. Here the steps to build the CI of eta-squared:

1. Transform eta-squared into r (squareroot)
2. Use fisher transformation and sample N to transform r into z; that gives you CI of z
3. Transform CI of z back into CI of r
4. Square CI of r to obtain CI of eta-squared.