Solved – How to know whether Pearson’s or Spearman’s correlation is better to use

I have this question that is really confusing. I already know that Pearson is used for normal distribution and Spearman for the opposite, but how do we apply this to the question? As you can see, question "b" asks for that:

look at b

To me, Spearman's $rho$ is the first choice because

  • it doesn't assume linearity
  • it is resistant to outliers
  • its statistical test is more powerful than the linear correlation test if you average over the distributions you're likely to see in practice
  • it handles ordinal data that are not interval-scaled

Looking at the data to drive which statistic you use will change the operating characteristics including invalidating confidence interval coverage.

So to me the big question is what would shake me off the default position of using $rho$? The only answer I can think of is when you need to think about variation explained on the original data scale. $r^{2} = R^{2}$ in the $p=1$ case, and is the fraction of variance in $Y$ explained by $X$. We don't have a similar interpretation for $r$. But there are other natural interpretations of $rho$ related to concordance probabilities, and in some ways such probabilities are also natural.

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