Cohen d and Z scores


New Member
Hi everyone,

I should start by saying that I posted the same question that I will expose here on the psychological research forum. However, as I did not receive any answer, I wonder whether I misplaced my post. I apologize if this kind of repetition contravenes any of the rules of Talk Stats.

My problem is that I am trying to calculate the size of the difference between the means of two groups in a psychological test. However, I am not using my own data but those published in an article and authors do report test performance in Z scores. Therefore, I am wondering whether or not I can just apply the regular formula of Cohen's d to calculate the size of the observed difference.

Thanks in advance for any possible help


Omega Contributor
css, some times the initial posts of new contributors get stuck and marked as spam. Don't worry about it, sorry for the hassle.


New Member
First of all, thank you hlsmith for your clarification on the posts...

Thanks also for the link, but the webpage you referred to relates to Z tests, no to Z scores.

What I am trying to calculate is the effect size of a difference between males and females in cognitive performance from a published article. Unfortunately, authors did not report the means and SD of raw scores but only mean and SEM from Z scores (and, separately, the N of the groups). The authors also explain how these z scores were calculated "Raw scores were standardized (z-transformed) based on the means and SDs of the entire sample. For ease of presentation, higher z-scores always reflect better performance; z-scores where higher numbers reflected poorer performance (i.e. response time) were multiplied by −1."

Therefore, my question is whether I should use these z scores as "raw scores" for calculating the effect size of the between groups difference. Or should I just calculate the difference between the groups' "z means"? Or none of the previous?


New Member
Hi again,

First of all, thank you for your interest in helping me out. I do not have direct data to work with. In this case, I am extracting data from figures just to have an impression on the effect size of the reported differences. However, my question is also "general", because I am observing that quite a few articles follow the same strategy of reporting z scores...