[R-meta] effect size question

[Viechtbauer, Wolfgang (NP)]

Dear Huang,

I don't think you have received an answer to your question so far.

Cohen's omega (assuming chi^2 was computed without a continuity correction) is equal to sqrt(chi^2 / N). Here is an example for a 3x3 table demonstrating this

tab <- matrix(c(8, 5, 10, 2, 6, 18, 9, 11, 15), nrow=3, byrow=TRUE)
tab

# carry out chi^2 test
res <- chisq.test(tab, correct=FALSE)
res

# sqrt(chi^2 / N)
sqrt(res$statistic[[1]] / sum(tab))

# compute Cohen's omega
obs <- tab / sum(tab)
exp <- outer(rowSums(tab), colSums(tab), "*") / sum(tab)^2
sqrt(sum((obs - exp)^2 / exp))

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of H W via R-sig-meta-analysis
> Sent: Saturday, November 9, 2024 00:33
> To: R meta <r-sig-meta-analysis using r-project.org>
> Cc: H W <wuhuang0421 using gmail.com>
> Subject: [R-meta] effect size question
>
> Hi all, I have a question regarding Cohen's *w*.
>
> A textbook I have been using describes the effect size Cohen's *w* =
> chi-square/ (N(J-1)) for a goodness of fit test. N is the total sample size
> and J is the number of categories.
>
> However, other material shows the formula for Cohen's *w* was the square
> root of (chi-square/n).
>
> These two seem to be different, but I don't have enough familiarity to
> immediately tell which one is correct, or if both are correct under certain
> circumstances. Thank you for your help.
>
> Best regards,
> Huang