In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r is reported as .40. Which of the following would be a correct interpretation?
A) Mobility explains 16% of the variation in number of friends.
B) There is a strong positive relationship between number of friends and mobility.
C) As mobility increases, number of friends decreases.
D) Mobility explains 40% of the variation in number of friends.

Question

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r is reported as .40. Which of the following would be a correct interpretation?
A) Mobility explains 16% of the variation in number of friends.
B) There is a strong positive relationship between number of friends and mobility.
C) As mobility increases, number of friends decreases.
D) Mobility explains 40% of the variation in number of friends.

Quizplus · Accepted Answer

Pearson's r is a measure of correlation that ranges from -1 to 1. A value of .40 indicates a moderate positive relationship between geographical mobility and number of friends. According to Cohen's guidelines, a correlation coefficient of .40 can be interpreted as a "moderate" effect size. Additionally, Pearson's r squared (r^2) indicates the amount of variance in one variable that can be explained by the other variable. In this case, r^2 = .16, which means that 16% of the variation in number of friends can be explained by geographical mobility. Therefore, D is the correct interpretation. A is incorrect because it misrepresents the amount of variance explained. B is incorrect because the relationship is only moderate, not strong. C is incorrect because the correlation coefficient indicates a positive relationship, not a negative one.

In a Study of the Relationship Between Geographical Mobility (Number