Define Pearson product-moment correlation coefficient.

• A. A measure of central tendency
• B. A measure of the strength and direction of linear association between two nominal variables
• C. A measure of the strength and direction of linear association between two interval-level variables
• D. The square of the covariance

Answer: (C)

The Pearson product-moment correlation coefficient measures the strength and direction of the linear relationship between two interval-level (continuous) variables. It yields a value between -1 and +1: +1 indicates a perfect positive linear relationship, -1 a perfect negative linear relationship, and 0 means no linear relationship. The value is obtained by standardizing the covariance of the two variables by the product of their standard deviations, so the measure is unitless and comparable across datasets.

Because it focuses on linear association, the coefficient can be low even when a nonlinear relationship exists. It relies on both variables being measured on an interval or ratio scale, and it can be distorted by outliers. It does not tell you about central tendency, and it isn’t appropriate for nominal data (where other methods, like chi-square, are used) or for ordinal data (where Spearman’s rho might be more suitable). Also, the correlation is not simply the square of the covariance; you must divide the covariance by the standard deviations. The square of the correlation, r^2, is often interpreted as the proportion of variance in one variable explained by the other in simple linear regression.