User Guide

Chapter

Bivariate Co

rrelations

The Bivariate Correlations procedure computes Pearson’s correlation coefficient,

Spearman’s

rho, and Kendall’s tau-b with their significance levels. Correlations

measure how variables or rank orders are related. Before calculating a correlation

coefficient, screen your data for outliers (which can cause misleading results) and

evidence o

f a linear relationship. Pearson’s correlation coefficient is a measure of

linear association. Two variables can be perfectly related, but if the relationship is not

linear, Pearson’s correlation coefficient is not an appropriate statistic for measuring

their ass

ociation.

Example. Is the number of games won by a basketball team correlated with the

average number of points scored per game? A scatterplot indicates that there is

alinearr

elationship. Analyzing data from the 1994–1995 NBA season yields that

Pearson’s correlation coefficient (0.581) is significant at the 0.01 level. You might

suspect that the more games won per season, the fewer points the opponents scored.

These va

riables are negatively correlated (–0.401), and the correlation is significant

at the 0.05 level.

Statistics. For each variable: number of cases with nonmissing values, mean, and

standa

rd deviation. For each pair of variables: Pearson’s correlation coefficient,

Spearman’s rho, Kendall’s tau-b, cross-product of deviations, and covariance.

Data. Use symmetric quantitative variables for Pearson’s correlation coefficient and

quanti

tative variables or variables with ordered categories for Spearman’s rho and

Kendall’s tau-b.

Assumptions. Pearson’s correlation coefficient assumes that each pair of variables is

bivari

ate normal.

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