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I need to test for correlation of 4 sets of weather parameters between 2 sites. I am not interested in interactions between the parameters. Because no weather parameter is independent from other weather parameters, if I was simply trying to determine if each parameter differed between the 2 sites, I would use a MANOVA followed by multiple-comparisons t-tests, and correct for family-wise error using a Bonferroni method. But since I want to see if the parameters are correlated between the sites, I'm not sure what to do.

Is there an overarching test (like MANOVA) that should be applied prior to what amounts to multiple-comparison correlations? Or can I just do multiple Spearman's correlations and interpret from there?

EDIT: I suppose in the long run it doesn't really matter to me if the 2 parameters are statistically significantly correlated. What will matter is the strength of their correlations. That, from what I understand, is subjective (based on the field)...is this correct? In this respect, is there any multiple-comparison sort of thing I should be keeping in mind?

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In light of your edit, corrections for multiple comparisons are not relevant, because you have plainly said you are interested in correlations' strength and not in their statistical significance. So set aside the MC issue and now you get to the interesting task of deciding what degree of correlation (whether assessed via Pearson's or Spearman's method) is of practical significance in your context. You are right: assigning labels such as "strong" or "moderate" is definitely a context-specific enterprise.

Sometimes this is an excessively abstract task when dealing with correlations per se; squaring them gives you a more concrete measure, namely, the portion of the variance in one variable that can be explained by the other.

If this turns out to be still too abstract for you or your colleagues, you can use an online correlation calculator/graphing tool (or Excel or statistical software) to see just what a correlation of .3 or .5 or -.7 looks like when plotted. That often turns out to be an eye-opener. More often than not people assume that for a given level of correlation the points will line up more "neatly" than they actually do.

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  • $\begingroup$ Thank you @rolando2, good to know. I'll set aside any concerns I had about multiple comparisons. I've already plotted each correlation to view them prior to determining the Spearman's rho, and yes, despite what I thought was a fairly high rho of 0.64, the paired points are surprisingly scattered (can't figure out how to stick the graph in here). However, for Spearman's, I thought squaring wasn't 'allowed', and that that was reserved for Pearson's only? (I'm using Spearman's because most of the data do not fit parametric assumptions.) $\endgroup$
    – Mog
    Commented Apr 3, 2012 at 23:49

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