# meta-analysis of Spearman correlation coefficients?

I have Spearman correlation coefficients (and sample sizes) from several studies and I want to meta-analyze them. Is it OK to do this using general-purpose meta-analysis software, or is it not OK because the Spearman correlation is not normally distributed? If it is not OK, what should I do?

For the SEs of the Spearman correlations I propose to use the formula on p9 of these lecture notes.

Let's assume there is no possibility of getting the original data or any more information.

Here is what I have found so far:

Some books say the Pearson and Spearman correlations are similar for large n. And the Spearman correlation is just the Pearson correlation of the ranks. So I guess it might be approximately correct to pretend that the Spearman correlations are Pearson correlations. The Pearson correlation is the same as the slope of the linear regression model that you get if you first standardize both variables, so I think that means the Pearson correlation is approximately normal (though obviously the range is only -1 to +1).

So perhaps this all means I can just stop worrying and use standard software on the Spearman correlations.

Someone here said it was OK to just meta-analyze Spearman correlations in the usual way, but he didn't seem to have thought about it very deeply. And there are lots of papers that talk about the distribution of the two correlation coefficients in a more exact way, which suggests that very crude normal approximations are not a good idea.

Similar questions have been asked on this website before, but they are either slightly different (like this one) or closed because they were unclear.

• Before meta-analysing Pearson correlations people usually use Fisher's transformation to stabilise the variances and make them more closely approximate a normal. Your assumption that Pearson is normal is only likely to hold for very large $n$ and for $\rho$ near 0.5. I know of no evidence that Fisher's transformation works for Spearman but others may so this is just a comment not an answer.. – mdewey Nov 28 '17 at 15:43
• Thanks, Fisher's transformation sounds like a good idea. I guess what I need is some more information about how legitimate it is to pretend that Spearman correlations are Pearson correlations. Or maybe there is a transformation or minor adjustment that can be made to map between Spearman correlations and (approximate) Pearson correlations. I haven't found anything convincing yet. – toby544 Nov 29 '17 at 10:36