# Effect size for goodness of fit test

What effect size measure can be used for a goodness of fit test (given data and theoretical proportions)?

I read about the Cohen's w (https://en.wikipedia.org/wiki/Effect_size#Cohen's_w) but I also read (for example here https://rcompanion.org/handbook/H_03.html) that Cohen's w can be used only where the theoretical proportions are equally distributed among categories. Is it true, is it a strict bond or am I missing something? What other measure can be used?

Thanks

• The goodness of fit of what are you measuring, and how? The term "effect size" comes from a context different from goodness of fit testing, and not all tests are associated to effect sizes, certainly not in a standard manner. That said, certain goodness of fit tests may involve something that can be interpreted as effect size. – Lewian Oct 26 at 10:47
• The goodness of fit of a set of given frequencies, eg. c(25,34,73), with a set of theoretical relative frequencies, eg. (0.19,0.27,0.54). I'm using the chi-squard test. – Luke Oct 26 at 11:08
• "but I also read (for example here (...)) that Cohen's w can be used only where the theoretical proportions are equally distributed among categories" - this is not what is written there. Cohen's w can be interpreted as effect size, alright, although I wouldn't necessarily trust any fixed "small/medium/large" categorisation for any effect size. This is always context dependent. – Lewian Oct 26 at 11:34
• So the equality of proportions only affects the categorization? – Luke Oct 26 at 11:47
• This is a hard question because I don't know what "effect size" means for you. Cohen's w does what it does. It involves a standardisation by the assumed proportions $p_{0i}$ whatever these are, but I can't know what exactly you think you have learnt when you call this "effect size". If the $p_{0i}$ are different, smaller $p_{0i}$-values have a stronger influence on Cohen's w, which may or may not be a problem. – Lewian Oct 26 at 11:54