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I am trying to compare some results in different experiments by using meta-analysis. Each study involved has a different number of subgroups. Since only mean and standard deviation is available for each subgroup, then an option to deal with is to combine the known parameters in each study (e.g. mean, standard deviation). In some books appear how to do it for two groups but my questions is How to combine three or more standard deviations. Thanks in advance.

Aligomez
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    You need the sample size as well to combine these. There is a good answer here https://math.stackexchange.com/questions/2971315/how-do-i-combine-standard-deviations-of-two-groups for two sets of samples, it looks quite easy to extend that to three groups. – Suzu Hirose Jul 29 '22 at 01:58
  • You probably have to prove if the samples are independent. – callculus42 Jul 29 '22 at 04:41
  • @Suzu Hirose I read the answer for two sets of samples but I have trouble with the equation after "Upon simplification, we find". Would you give me some suggestion? – Aligomez Jul 29 '22 at 13:38
  • This might help : https://math.stackexchange.com/a/4567292/1221434 and the link from the link https://arxiv.org/ftp/arxiv/papers/1007/1007.1012.pdf – IntroductionToProbability Sep 16 '23 at 15:09

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