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:

 A: 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.
A: Generally, Pearson correlation coefficient is the first choice. I found three possible reasons to choose Spearman instead:


*

*One or both variables are measured on ordinal level. (not this case)

*There are outliers in your data. (also probably not this case)

*The relationship between your variables is monotonous but not linear. (you should check)


Draw a scatterplot and decide if the data are contaminated with outliers or if the relationship resembles more a curve than line.
