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I work with wind data. In order to estimate the strength of the correlation between two anenometers, in my department they usually calculate the pearson R.

As far as I know the pearson R should be used under 2 assumptions: -Linear relationship between the variables (yes) -The data follows a normal distribution (no, as wind data has a weibull distribution)

Should we use then a non parametric coefficient like spearman to calculate the correlation?

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Pearson correlation does not assume that the data are normally distributed but the Pearson and Spearman correlations ask different questions. Pearson lets outliers have a lot of influence, Spearman does not. Which you want is up to you.

Exact results will depend on the shape parameter, but Weibull has long tails, so it has outliers.

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