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My survey collected data from 384 respondents, and I have an overall score for each of them on each variable. Therefore, I'm working with 3 composite variables at the scale/ratio level. I want to know what the relationship between these 3 variables is. Unfortunately, my data violates many of the Pearson's and Linear Regression assumptions: non-normal distribution, non-linear or monotonic relationship, outliers. I can't seem to find an appropriate test. Any suggestions? (FYI, not a stats pro so layman's language appreciated).

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Spearman's correlation can be used to correlate your variables. It is invented for situations where the assumptions of Pearson's do not hold.

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  • $\begingroup$ Thank you Tim. From what I've read, Spearman's also assume a monotonic relationship, which my variables don't have. The scatterplots are all over the place. Any other suggestions? $\endgroup$ – Mich Feb 28 '17 at 21:48
  • $\begingroup$ Hi @Mich. Having a scatterplot "all over the place" is not a problem. The requirement for a monotonic relationship that you refer to is probably only that, as the values of one variable increase then, on average, so do the values of the other. Or, as one increases, the other decreases. That you have a lot of noise on your scatterplots means that the correlation will be low, which is separate to the question of the monotonicity of the underlying relationship. If you do not expect a monotonically increasing/decreasing relationship, you should not be computing correlations at all. $\endgroup$ – Tim Mar 1 '17 at 3:17
  • $\begingroup$ Awesome! Thanks very much. I'll go ahead with the Spearman's then. Much appreciated. $\endgroup$ – Mich Mar 1 '17 at 4:34

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