There's a similar discussion thread which may help to answer your question:

https://www.researchgate.net/post/Can_I_do_a_meta-analysis_of_means_standard_deviations_and_confidence_intervals

Does anybody know that it is OK if we use mean and SD of z-scores instead of raw mean and SD for calculating effect size for systematic review?

Thanks,

Mahdi

I'm not sure whether I understand this question correctly. Effect sizes such as Cohen's d (standardized mean differences) are used to produce standardized effects. Since d = [mean(x1) - mean(x2)] / SD[pooled], using z-scores for x1 and x2 would always result in d=0. Moreover, what would be the benefit of using z-scores. I presume your effects are all measured on the same scale. Right?

Hi Thomas,

Thank you for your answer!

I have studies that reported mean of BMD and Mean of BMD Z-scores. However, some of them just reported mean of BMD Z-scores or Mean of BMD. So, is it ok if I use these means of BMD Z-scores to calculate effect sizes? Since my d=[mean of BMD Z-scores (x1)- mean of BMD Z-scores (x2)/SD of BMD Z-scores[pooled].

BMD=Bone Mineral Density

Hi Mahdi,

The scale of the BMD measures is of no relevance as long as you end up with a standardized effect size. Here's a bit of R code that demonstrates that you will end up with the same effect size (Cohen's d), no matter whether you use the unstandardized BMD (g/cm2) or the respective standardized z-scores:

# reference group BMD mean and standard deviation

bmd.mu

Hi Thomas,

Great!

Thank you so much for your complete and practical answer.

Hello there,

I am experiencing a similar issue in a meta-analysis I am running using cognitive performance scores across different measures. When using a mixture (or really one or two) studies with both raw/un-corrected and standardised scores (either z-scores between 0 and 1, or corrected to unavailable normative values) it reduces the overall effect size and cranks up the heterogeneity??

Would this logic still apply? Thomas Volken