Which statement describes a limitation of Pearson's r?

Which statement describes a limitation of Pearson's r?

• A. It can be distorted by outliers
• B. It proves causation
• C. It applies to categorical data
• D. It assesses nonlinear relationships

Answer: (A)

Pearson's r is a measure of the linear association between two continuous variables, but it is not robust to extreme values. Outliers can pull the covariance and the standard deviations in different directions, causing the r value to be pulled toward or away from the rest of the data. In practice, a single far-out observation can inflate or deflate the correlation, giving a misleading sense of how strongly the variables are related for the main pattern of data. For example, if most points show no clear linear pattern, adding one extreme point with high values for both variables can create a noticeable, but misleading, positive correlation. This limitation is separate from the fact that correlation does not imply causation, that Pearson's r requires continuous data rather than categorical data, and that it primarily detects linear rather than nonlinear relationships.

Pearson's r is a measure of the linear association between two continuous variables, but it is not robust to extreme values. Outliers can pull the covariance and the standard deviations in different directions, causing the r value to be pulled toward or away from the rest of the data. In practice, a single far-out observation can inflate or deflate the correlation, giving a misleading sense of how strongly the variables are related for the main pattern of data. For example, if most points show no clear linear pattern, adding one extreme point with high values for both variables can create a noticeable, but misleading, positive correlation.

This limitation is separate from the fact that correlation does not imply causation, that Pearson's r requires continuous data rather than categorical data, and that it primarily detects linear rather than nonlinear relationships.