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How do i check that two random variables satisfy the requirements for computing correlation via Pearson or Spearman? If the data is non-linear/ non-Monotonic, are there other tests i could use to compute a correlation coefficient?

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Once the variables are random, there is nothing like linear and non-linear. Only thing you need is adequate/ minimum sample size to cope with population. – subhash c. davar Sep 12 '14 at 15:30
the tests are not needed. What is needed is to examine data-type. – subhash c. davar Sep 12 '14 at 15:35

Distance correlation takes also nonlinear correlations into account.

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The link in your answer is not hyperlinking correctly. Please try putting triangle braces (< >) around it or putting space between the parenthesis and link. – Evan Teitelman Feb 23 '13 at 12:33

If one has an interval data on each of two variables, Pearson correlation can be calculated. Spearman correlation requires the rank data.

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