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How should I measure correlation between, for example, population size or crossover probability and time ?

Pearson coefficient seems like an obvious choice. However my data do not follow normal distribution.

From what I remember Pearson should only be used when X and Y form bivariate normal distribution. Which is obviously not a case when X denominates mutation probability or population size.

Is there other way to measure correlation between variables or should I just use Pearson?

Furthermore how should I judge the strength of correlation? The tests I know about all rely on normal distribution in some way. Are there any others or should I just use rule of thumb?

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    $\begingroup$ Correlation coefficients measure correlation, regardless of the distributions. In your title do you mean "non-Normal" rather than "non-bivariate"? $\endgroup$
    – whuber ♦
    Commented Sep 17, 2017 at 15:01
  • $\begingroup$ Pearson correlations describe pairwise linear dependence only. If the bivariate association is anything other than that, the Pearson is not the right choice. Another metric for monotonic dependence is the Spearman correlation which plugs ordinal rankings into the Pearson calculation. Some have suggested that this also makes them equivalent--this is wrong as they evaluate different types of association. There are many other measures of dependence, see this thread ... stats.stackexchange.com/questions/179511/… $\endgroup$
    – user78229
    Commented Sep 17, 2017 at 15:29
  • $\begingroup$ Yeah that's what I meant, sorry my statistics education was extremely limited. Anyway the problem is that my data do not follow normal distribution and even if I could measure correlation with them how would I determine its strength. $\endgroup$
    – user1561358
    Commented Sep 17, 2017 at 16:00
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    $\begingroup$ Normality is not the mot central issue. Are you trying to measure linear correlation or monotonic association or something else? $\endgroup$
    – Glen_b
    Commented Sep 17, 2017 at 19:33
  • $\begingroup$ At present, this question is not clear enough to be answerable. But, I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 19, 2017 at 15:32

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