Which test is a non-parametric method for assessing the relationship between two continuous variables (correlation)?

Which test is a non-parametric method for assessing the relationship between two continuous variables (correlation)?

• A. Spearman
• B. Pearson
• C. Kendall tau
• D. Chi-square

Answer: (A)

When you want to see if two continuous variables are related without assuming a specific form of the relationship or normal distributions, you look at a non-parametric correlation that uses ranks. Spearman correlation works by ranking the data for each variable and then measuring how well those ranks align. It detects monotonic relationships: if one variable rises as the other tends to rise (or fall), their ranks tend to move together. Because it relies on ranks, it doesn’t require the variables to be normally distributed and it’s more robust to outliers than methods that assume linearity. Pearson correlation, in contrast, is parametric and assumes a linear relationship with bivariate normal distributions. Kendall tau is another non-parametric rank-based measure of association, similar in purpose but computed differently. Chi-square is used for relationships between categorical variables, not continuous ones. Thus, for a non-parametric assessment of the relationship between two continuous variables, the Spearman correlation is the appropriate choice.

When you want to see if two continuous variables are related without assuming a specific form of the relationship or normal distributions, you look at a non-parametric correlation that uses ranks. Spearman correlation works by ranking the data for each variable and then measuring how well those ranks align. It detects monotonic relationships: if one variable rises as the other tends to rise (or fall), their ranks tend to move together. Because it relies on ranks, it doesn’t require the variables to be normally distributed and it’s more robust to outliers than methods that assume linearity.

Pearson correlation, in contrast, is parametric and assumes a linear relationship with bivariate normal distributions. Kendall tau is another non-parametric rank-based measure of association, similar in purpose but computed differently. Chi-square is used for relationships between categorical variables, not continuous ones.

Thus, for a non-parametric assessment of the relationship between two continuous variables, the Spearman correlation is the appropriate choice.