Introduction: Significance Tests versus Measures of Association

A bivariate relationship involves the relationship between two variables. For example, if you conduct an investigation in which you study the relationship between GRE verbal test scores and college grade point average (GPA), you are studying a bivariate relationship.

There are numerous statistical procedures that you can use to examine bivariate relationships. These procedures can provide a test of statistical significance, a measure of association, or both. A test of statistical significance allows you to test hypotheses about the relationship between variables in the population. For example, the Pearson product moment correlation coefficient allows you to test the null hypothesis that the correlation between two interval- or ratio-level variables is zero in the population. In a study, you might draw a sample of 200 participants and determine that the Pearson correlation coefficient between the GRE verbal test and GPA is .35 for this sample. You can then use this finding to test the null hypothesis that the correlation between GRE verbal and GPA is zero in the population. The resulting test might prove to be significant at p < .01(depending on the sample size). This p value suggests that there is less than 1 chance in 100 of obtaining a sample correlation of r = .35 or larger from the overall population if the null hypothesis were true. You therefore reject the null hypothesis and conclude that the degree of relationship between variables does not occur due to chance alone.

In addition to serving as a test of statistical significance, a Pearson correlation coefficient can also serve as a measure of association. A measure of association reflects the strength of the relationship between variables (regardless of the statistical significance of the relationship). For example, the absolute value of a Pearson correlation coefficient reveals how strongly the two variables are related. A Pearson correlation can range from –1.00 through 0.00 through +1.00, with larger absolute values indicative of stronger relationships. For example, a correlation of 0.00 indicates no relationship between variables, a correlation of .20 (or –.20) indicates a weak relationship, and a correlation of .90 (or –.90) indicates a strong relationship. (A later section provides more detailed guidelines for interpreting Pearson correlations.)