8.3 Identifying a moderator

Here are 3 scenarios demonstrating how a third variable can modify the relationship between the original two variables.

Scenario 1 - Significant relationship at bivariate level (saying expect the effect to exist in the entire population) then when test for moderation the third variable is a moderator if the strength (i.e., p-value is Non-Significant) of the relationship changes. Could just change strength for one level of third variable, not necessarily all levels of the third variable.

Scenario 2 - Non-significant relationship at bivariate level (saying do not expect the effect to exist in the entire population) then when test for moderation the third variable is a moderator if the relationship becomes significant (saying expect to see it in at least one of the sub-groups or levels of third variable, but not in entire population because was not significant before tested for moderation). Could just become significant in one level of the third variable, not necessarily all levels of the third variable.

Scenario 3 - Significant relationship at bivariate level (saying expect the effect to exist in the entire population) then when test for moderation the third variable is a moderator if the direction (i.e., means change order/direction) of the relationship changes. Could just change direction for one level of third variable, not necessarily all levels of the third variable.

8.3.1 What to look for in each type of analysis

• ANOVA - look at the \(p\)-value, \(r\)-squared, means, and the graph of the ANOVA and compare to those values in the Moderation (i.e., each level of third variable) output to determine if third variable is moderator or not.
• Chi-Square - look at the \(p\)-value, the percents for the columns in the crosstab table, and the graph for the Chi-Square and compare to those values in the Moderation (i.e., each level of third variable) output to determine if third variable is a moderator or not.
• Correlation and Linear Regression - look at the correlation coefficient (\(r\)), \(p\)-value, regression coefficients, \(r\)-squared, and the scatterplot. Compare to those values in the Moderation (i.e., each level of third variable) output to determine if third variable is a moderator or not.