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I'm using the tool in the following website to compare correlation coefficients: http://vassarstats.net/rdiff.html The tool uses Fisher's r to z transformation to ultimately compare two correlation coefficients.

Let's say I want to compare a correlation coefficient that was calculated with Pearson's correlation and a correlation coefficient that was calculated using Spearman's correlation. Is that ok to do? Or do both need to be calculated using the same correlation procedure (i.e., both Pearson's or both Spearman's?).

Thanks.

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    $\begingroup$ In what situation would it make sense to compare a linear correlation with a correlation between ranks? $\endgroup$
    – Glen_b
    May 20 at 6:48
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    $\begingroup$ Using $z$ on both is assumingthat correlations $r$ on both methods are comparable, as it's the same transformation. It is not a way of ensuring that both are comparable. It is on all fours with having two Fahrenheit temperatures and converting them both to Celsius. By all means do that if it helps. A way forward is to realise that Spearman's method is, or should be, just Pearson's method applied to the ranks. The small print is how ranks are calculated when there are ties. $\endgroup$
    – Nick Cox
    May 20 at 8:19
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    $\begingroup$ This is an example of the X-Y problem. You should indeed care what kind of correlation between IQ and biomarker is more appropriate for the data, but looking a scatter plot and knowing how variables are measured tells you immensely more than using a transformation. But on the big question, I don't think it makes much sense to compare a rank correlation on one group with a linear correlation on another. $\endgroup$
    – Nick Cox
    May 20 at 8:22
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    $\begingroup$ Sorry, no: I didn't say that and I can't say that because I have no idea what the data look like and I don't work in that science (although my bias is to doubt that there is any interesting correlation at all). I don't follow that you are committed to anything here. Another simpler take is that if Pearson and Spearman correlations are very different you probably need something different again, e.g. a transformation of one or both variables. $\endgroup$
    – Nick Cox
    May 20 at 8:42
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    $\begingroup$ If you were actually interested in comparing linear correlations (you started with Pearson), a monotonic, non-linear correlation (Spearman) would not be how I'd do that. It might be a good idea to take one step further back still and carefully consider whether it's actually correlations you wish to compare, rather than something else. What's the underlying research question? If you do conclude that you wish to compare correlations, you need to be clear about whether it's linear or monotonic correlation that you want to compare. Then ask about a way to achieve that aim. $\endgroup$
    – Glen_b
    May 20 at 18:59

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These two coefficients don't measure the same thing, so your comparison will be more appropriate if you use the same correlation in both cases. If you're worried about model assumptions, use Spearman. However keep in mind that model assumptions are always idealisations, so it is wrong to say that for example you can only use Pearson correlation if data are normal. Even if you want a formal comparison, I'd look at plots first to see whether there is anything that makes the Pearson correlation really misleading at least in one of your cases, such as domination by an outlier.

Note also that the tool you cite is about significance testing and will give you a misleading comparison at least if sample sizes are different. Also it doesn't solve the problem that not the same thing is measured by the two correlations.

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  • $\begingroup$ I'd say the main use of the z transformation was getting confidence intervals, although significance tests clearly could be linked. $\endgroup$
    – Nick Cox
    May 20 at 11:48

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