Differentiate Pearson and Spearman correlations.

• A. Pearson is nonparametric and based on ranks; Spearman assumes normality
• B. Pearson assesses nonlinear associations; Spearman assesses linear associations
• C. Pearson uses categorical data; Spearman uses continuous data
• D. Pearson assesses linear association with continuous data and normality assumptions; Spearman is rank-based and nonparametric

Answer: (D)

The difference being tested is how these two correlation measures treat data and relationships. Pearson correlation measures the strength and direction of a linear relationship between two continuous variables and relies on normality assumptions for inference (the variables should be approximately normally distributed, with a roughly linear, homoscedastic relationship). It uses the actual data values, not their ranks.

Spearman correlation, on the other hand, is computed on the ranks of the data, making it nonparametric. It assesses monotonic relationships (as one variable tends to increase, the other tends to either increase or decrease, though not necessarily in a straight line). It can handle ordinal data and data that violate normality.

So, the best description is that Pearson assesses a linear association with continuous data under normality assumptions, while Spearman is rank-based and nonparametric. The other characterizations—Pearson being nonparametric or relying on ranks, or Pearson using categorical data, or Spearman strictly modeling linear relationships—do not fit.