Pearson's r and Spread: A Classroom Demonstration

Abstract

For many students, the connection between spread and Pearson's r is elusive. Confusion arises because different factors that increase score variability do not have the same effect on r. To help students understand that increases in a may lead to an increase or a decrease in r or to no change whatsoever, we devised a simple and enjoyable classroom exercise. Using standard decks of playing cards, students generate hypothetical data on two well-known variables (IQ and GPA). Once analyzed, the data make clear the point that changes in score variability influence r in different ways—or not at all—depending on the reason why σ_x (or σ_y) increases or decreases.