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I have read that the variables must be approximately normally distributed to apply Pearson correlation; enter image description here

However, I came across this answer here that they dont need to be, so I am confused about that. Can i have a clarification about that ?

user101
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1 Answers1

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As Rob's answer in the post you link to would suggest, you certainly don't need it to calculate a Pearson correlation.

The need for normality would notionally apply if you used a test or interval that assumed normality in its calculations.

However, you can construct tests and intervals that avoid that assumption, if it's important to. For example, one could easily conduct a permutation test (a nonparametric test) of a Pearson correlation.

You should probably approach some of the advice you're getting at that site with some caution (e.g. see Harvey's answer at Is normality testing 'essentially useless'?)

Glen_b
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  • my data isn't either normal or follow a linear relashionship, so can i apply pearson in that case? – user101 Jan 16 '18 at 10:55
  • You *can* (you type the commands to calculate a Pearson correlation, *et voilà*, you will have a Pearson correlation). The issue is whether it tells you what you want to know. The Pearson won't capture how strongly related they are in whatever form the relationship is, it will capture the portion of the relationship that's linear (i.e. it will be high if the relationship is nearly linear and less high if it's strongly monotonic but nonlinear, and it may be near zero if it's a non-monotonic relationship). So the question is *what are you trying to achieve*? (We have questions relating to this) – Glen_b Jan 16 '18 at 23:04
  • If you want to capture the strength of a monotonic relationship, you might use Kendall's tau or Spearman's rho (among numerous other possibilities). See, for example, the answers by mbq and Gravitas at https://stats.stackexchange.com/questions/8071/how-to-choose-between-pearson-and-spearman-correlation for some relevant issues. If you want to measure how strong a relationship is in some non-monotonic sense, you need some more general measure of relationship/association. What may be suitable will depend on what kind of data you have and what you want to do with the measure (among other things) – Glen_b Jan 16 '18 at 23:11
  • This is a much more involved question than the original thing you posted. – Glen_b Jan 16 '18 at 23:16
  • now its clear to me. Can you provide me an example of a general measure of relationship/association to measure non monotonic/linear relation? – user101 Jan 17 '18 at 12:41
  • See the section on *Other measures of dependence among random vairiables* in the wikipedia page on [Correlation and dependence](https://en.wikipedia.org/wiki/Correlation_and_dependence#Other_measures_of_dependence_among_random_variables) for example. – Glen_b Jan 18 '18 at 00:00