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

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

**Correct Answer:** .

**Core Concept:** Correlation is a statistical measure that quantifies the strength and direction of the relationship between two variables. It helps determine whether two variables tend to change together or not. In the case of continuous variables, three commonly used correlation coefficients are Pearson's, Spearman's, and Kendall's rank correlation coefficients.

**Why the Correct Answer is Right:** Pearson's correlation coefficient (R) is suitable when the data is normally distributed and there is a linear relationship between the two continuous variables. This coefficient measures the strength and direction of the linear relationship between the variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

**Why Each Wrong Option is Incorrect:**

A. Spearman's rank correlation coefficient (rs) is used when the data is non-parametric (skewed) and does not assume a linear relationship between the variables. It measures the strength and direction of the monotonic relationship between the variables. The range of rs is from -1 to +1, similar to Pearson's coefficient. However, it is not applicable when the data is normally distributed and linear relationship exists between the variables.

B. Kendall's rank correlation coefficient (τ) is another non-parametric test used when the data is ordinal or non-numeric. It measures the strength and direction of the monotonic relationship between the variables. The range of τ is from -1 to +1, similar to Pearson's and Spearman's coefficients. However, it is not applicable when the data is normally distributed and a linear relationship exists between the variables.

C. Point-biserial correlation coefficient (rpb) is used when one variable is continuous and the other is binary (dichotomous). It measures the correlation between a continuous variable and a binary variable. This coefficient is primarily used when the data is categorical and not suitable for continuous data.

**Clinical Pearl:** When dealing with continuous data and assuming a linear relationship between the variables, Pearson's correlation coefficient should be used. Spearman's rank correlation coefficient and Kendall's rank correlation coefficient are suitable when dealing with ordinal or non-numeric data and monotonic relationship between variables. However, these coefficients are not appropriate for continuous data with a linear relationship. The point-biserial correlation coefficient is used when one variable is continuous and the other is binary, but it is not suitable for continuous data with a linear relationship.