**Question:** Correlation between two continuous variables is measured by

A. Pearson's correlation coefficient
B. Spearman's rank correlation coefficient
C. Kendall's tau
D. Point-biserial correlation coefficient

**Correct Answer:** C. Kendall's tau

**Core Concept:** Correlation between two continuous variables is a statistical measure that quantifies the strength and direction of the relationship between two variables. Pearson's correlation coefficient (A) and Spearman's rank correlation coefficient (B) are commonly used for continuous variables; however, Kendall's tau (C) is also a commonly used measure of correlation for continuous variables, particularly when the data are ordinal or when the variables are not normally distributed.

**Why the Correct Answer is Right:** Kendall's tau (C) is a non-parametric measure of correlation, which means it does not assume a normal distribution of the data. It is particularly useful when dealing with ordinal or non-normal continuous variables. Kendall's tau ranges from -1 to 1, with higher values indicating stronger correlation. It is calculated using the following formula:

τ = ∑[(xi - xj)² / (n(n+1))]

**Why Each Wrong Option is Incorrect:**

A. Pearson's correlation coefficient (A) assumes a normal distribution of the data and is suitable for continuous variables. However, it is not the best choice when dealing with ordinal or non-normal continuous variables.

B. Spearman's rank correlation coefficient (B) is also a non-parametric measure of correlation, but it is typically used when the variables are ordinal. Kendall's tau is a more comprehensive choice when dealing with non-normal continuous variables.

D. Point-biserial correlation coefficient (D) is used when one variable is continuous and the other is binary. It is not relevant for continuous variables with continuous variables, like the given question.

**Clinical Pearl:** When selecting a correlation measure, consider the nature of the data (continuous, ordinal, or binary) and whether normality assumptions are met. Choose Kendall's tau for non-normal continuous variables, Spearman's rank correlation coefficient for ordinal variables, and the point-biserial correlation coefficient for categorical variables.