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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

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    $\begingroup$ 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? $\endgroup$
    – bluepole
    Sep 17 '14 at 16:00
  • $\begingroup$ 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. $\endgroup$
    – Torvon
    Sep 17 '14 at 18:20
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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)

enter image description here

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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.
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