Question

what is the difference between Cohen’s d and eta^2? In one way ANOVA, two way ANOVA, and repeated measures ANOVA is cohen’s d only used for one way ANOVA and repeated measures ANOVA?

Answer 1

Since you are able to calculate Cohen's d, I presume you are comparing two groups. For that purpose, you might as well use

Pearson's r as eta-squared. (Well, I guess technically it would be a point-biserial correlation, but the calculations work out the

same way.) Each represents a proportion of the variance.You probably know that it is pretty easy to convert r to d. For

example, r is equal to the square root of the quantity [(d-squared) divided by (4 plus d-squared)].

If the two groups are roughly the same size, the corresponding value of d will usually work out to a bit more than twice that of

r - relatively greater with smaller samples. So the two statistics will tend to yield similar interpretations.Since you seem to be

obtaining discrepant results from the two techniques, I think you may have very different sample sizes. If one group is much

larger than the other, then there is less variance in the dichotomous variable.Since correlation depends on variability, this will

constrain your correlation coefficient. But because d considers only the sample means, it will not be affected by such a

disparity.