If one variable is dichotomous and the other is interval or ratio, which correlation measure is appropriate?

If one variable is dichotomous and the other is interval or ratio, which correlation measure is appropriate?

• A. Phi-Coefficient
• B. Point-Biserial Correlation
• C. Spearman Correlation
• D. Pearson Correlation

Answer: (B)

When one variable is dichotomous and the other is interval or ratio, the relationship is best described by the point-biserial correlation. This measure is a special case of Pearson correlation where the dichotomous variable is coded as 0 and 1, so the coefficient reflects how the continuous variable differs between the two groups. In practice, you can think of it as comparing the mean of the continuous variable in each group relative to the overall dispersion, giving a sense of how strongly group membership associates with the continuous measure. The phi coefficient is for two binary variables, which isn’t the situation here. Spearman correlation handles ordinal data or nonparametric monotonic relationships and isn’t tailored to a binary-vs-continuous pairing. Pearson correlation could be used if both variables are truly continuous, but the standard term and interpretation for a binary-versus-continuous pairing is point-biserial. The sign and magnitude tell you which group tends to have higher values on the continuous variable and how strong that association is.

When one variable is dichotomous and the other is interval or ratio, the relationship is best described by the point-biserial correlation. This measure is a special case of Pearson correlation where the dichotomous variable is coded as 0 and 1, so the coefficient reflects how the continuous variable differs between the two groups. In practice, you can think of it as comparing the mean of the continuous variable in each group relative to the overall dispersion, giving a sense of how strongly group membership associates with the continuous measure.

The phi coefficient is for two binary variables, which isn’t the situation here. Spearman correlation handles ordinal data or nonparametric monotonic relationships and isn’t tailored to a binary-vs-continuous pairing. Pearson correlation could be used if both variables are truly continuous, but the standard term and interpretation for a binary-versus-continuous pairing is point-biserial. The sign and magnitude tell you which group tends to have higher values on the continuous variable and how strong that association is.