When should the Spearman correlation coefficient be preferred over the Pearson correlation coefficient?

The Spearman correlation coefficient should be preferred over the Pearson correlation coefficient primarily when the data does not meet the assumptions required for Pearson's correlation. Specifically, this includes situations where one or both variables are not normally distributed, or when the data contains outliers that may disproportionately influence the results of the Pearson correlation.

The Spearman correlation does not assume a normal distribution and is a non-parametric measure that assesses the strength and direction of the association between two ranked variables. It is especially useful when the relationship between the variables is not linear, which is a requirement for Pearson's correlation.

In cases where neither variable adheres to a normal distribution, Spearman’s method allows for a robust evaluation of correlation, while Pearson's would yield potentially misleading results due to its sensitivity to outliers and linearity assumptions. The correct option acknowledges that the situation where both variables are normally distributed is not the specific criterion for choosing Spearman over Pearson; rather, it is the violations of the assumptions that warrant using Spearman.

Thus, the preference for the Spearman correlation coefficient arises when the data characteristics suggest that the assumptions underlying the Pearson correlation are not satisfactorily met, making it a more appropriate choice for analyzing relationships between variables in such contexts.