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I would like to test the correlation between a quantitative continuous variable normally distributed (body mass index) and a quantitative continuous variable positively skewed (kurtosis=5, skewness=2)(see picture). As recommended, I log10 transform my data to get a normal distribution but it is not really convincing.

What is your recommendations to test the correlation between the two variables?

PS: would you have a good recommendation for statistic book that explain how to handle "non common" distributions tests and choose the best statistical test depending on your situation, I am also interested.

I am using R as statistical software. enter image description here

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François-Xavier Chalet
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  • Why do you transform your skewed variable? – Dave Mar 03 '20 at 17:53
  • As I am learning stat, in the literature is often mention the possibility of transforming positively skewed variable to get closer to a normal shape and then being able to do a normal correlation test (for example). In my case, the transformation seems not to be an option as the distribution is highly skewed on the right (I just mention it as part of my thinking process). What I want most of all, is to be able to test the correlation between BMI (normally distributed) and glyhb (not normally distributed). – François-Xavier Chalet Mar 03 '20 at 18:01
  • Who is saying that, and in what context? – Dave Mar 03 '20 at 18:07
  • https://stats.stackexchange.com/questions/107610/what-is-the-reason-the-log-transformation-is-used-with-right-skewed-distribution – François-Xavier Chalet Mar 03 '20 at 18:09
  • To come back to my initial question, are non-parametric correlation tests (such as Kendall's tau or Spearman' rho) an option to my problematic? – François-Xavier Chalet Mar 03 '20 at 18:11
  • Please post a scatter plot of the data without the transformation. – Dave Mar 03 '20 at 18:22
  • I had the scatter plot in the initial post. Some glyhb values are extremes. I don't really know how to interpret the correlation if there is one. – François-Xavier Chalet Mar 03 '20 at 18:30
  • Yes, Spearman's $\rho$ and Kendall's $\tau$ are correlation coefficients that do not rely on distributional assumptions and should thus serve your needs. – Bernhard Mar 03 '20 at 19:24

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