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This question already has an answer here:

I want to conduct a correlation analysis between two continuous variables. The first variable is age and second one is number of relapses. The age is non normally distributed, whereas the number of relapse is normally distributed.

Should I conduct a non parametric correlation or parametric correlation?

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marked as duplicate by mdewey, Nick Cox, chl Dec 19 '16 at 20:01

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It isn't normality that matters here. The only distributional requirement is finite variance and a covariance matrix. You should use Pearson if they are linearly associated and Spearman's if they are monotonically associated. edit Added covariance matrix requirement per Michael Chernick, he is correct.

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  • $\begingroup$ Do look at the duplicate that @smdpln referenced. It is a protected post because it contains several good answers and give you a deeper understanding of the issue. To user25459 the assumption of existence of the covariance matrix is also needed. $\endgroup$ – Michael Chernick Dec 19 '16 at 19:45
  • $\begingroup$ @MichaelChernick thanks, actually I should have thought to put that as I derived the distribution of returns for all asset classes and proved that they cannot covary. In raw form it is a transformation of the Cauchy distribution and in log-log form it is the hyperbolic secant distribution, or a transform of it. I have been arguing over Pearson's and OLS for some time now. Thank you for the correction. If anyone should have mentioned that, it should be me after all the conference battles I have been having. $\endgroup$ – Dave Harris Dec 20 '16 at 3:44

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