Which analysis is used to determine whether mean scores on two or more variables differ significantly?

The selection of factorial analysis of variance is appropriate for situations where you want to examine the differences in mean scores across two or more variables, especially when there are multiple independent variables. Factorial ANOVA allows researchers to analyze the effects of two or more categorical independent variables on a continuous dependent variable simultaneously. This method not only tests for overall differences but also evaluates interaction effects between the independent variables to understand how they jointly affect the dependent variable.

In contrast, a simple analysis of variance is designed specifically for scenarios with a single independent variable and multiple groups. A t-test is suitable for comparing the means of two groups only. Regression analysis focuses on the relationship between one dependent variable and one or more independent variables, primarily used for prediction rather than comparison of means. Thus, factorial analysis of variance is the correct approach when comparing mean scores across multiple independent variables.