# Does the sum of correlations make sense?

For the descriptive purposes, I am looking at the (Pearson) correlation coefficients between 6 variables over 4 periods separately. Thus, I computed the correlation between 15 pairs. I am doing a cross-sectional study before I start the longitudinal analysis (i.e. over 4 periods). However, as I am currently reporting the correlation coefficients for each time point (i.e. "cross-section"), it feels weird not to say anything about how they seem to evolve over time.

Now, it is easy to miss something or give a biased / subjective view when comparing 15 coefficients with 15 coefficients for example. Hence, I thought it would probably make sense to take the sum of the correlations for each variable and plot it as a line graph over time.

Does it make sense to do this; purely for descriptive purposes? So I get a picture of each variable how its overall correlation (relative to other items at the same time point) changes over time?

• Instead of just downvoting, it'd be helpful to actually give a reason for it. Imo, the question is clear and I searched on stackexchange for similar questions but could not find an answer there. If it's unclear, I am happy to reformulate.. – Amonet May 20 '18 at 11:45
• It's not clear to me why your question attracted a downvote without a comment; while there are ways the question might be better, it's not clear what the downvoter's particular objection might have been. – Glen_b May 21 '18 at 12:12

## 1 Answer

No, I recommend against that. Correlation coefficients are not on an interval scale, so summing, say, .5+.5 will reflect something different from summing .2 + .8, much less 0+1.0.

If you want to do this, computing Fisher's z first would help it make more sense. If you want to keep it in correlation metric, you could average the zs (instead of summing) and back-translate the mean to Pearson's r.

• The Fisher's z is used in meta-analysis for this very reason. However, in this application I think summing the correlations or Fisher's z is problematic as it assumes independence of the 15 correlations (which is clearly not the case). As such, the sum has no clear interpretation. I recommend just plotting a separate line for each correlation over the 15-time points. – dbwilson May 20 '18 at 13:04
• Thanks for your suggestions. @dbwilson there are four time points, but indeed there is clear dependence over time since I measure the same variables over time. I thought of plotting a separate line for each pair over time as well, but that'd be 15 lines (as I think you meant to suggest). However, if that's the only thing that makes sense, I will do that :) – Amonet May 20 '18 at 13:10