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How important is the normality assumption for the Pearson correlation test?

  • Does it just has a lower validity or the result is actually invalid?

I have a data set and i did all three correlation tests (pearson vs spearman vs kendall) with this data. The normality assumption is not meet and the results are as follow:

  • pearson = 0.73 kendall = 0.46 spearman = 0.65

the results are "diverse". So how can i interpret these result?

*the data is simply y~x with 1 variable.

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The main difference between pearson and kendall/spearman is that pearson identifies linear relationships while kendall/spearman identify any monotonic relationship (including linear). Further, you don't need the normality assumption for spearman and hence, your spearman/kendall results imply a semi-strong monotonic relationship. Also, as your pearson result is not drastically apart from your spearman result, the conclusion of semi-strong monotonic correlation is reasonable. Keep in mind that kendall's tau is only an indicator for co-movements and shouldn't really be relied on when it comes to the real strength of the relationship.

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