Comparing Group Means: T-tests and One-way ANOVA Using Stata, SAS, R, and SPSS

Abstract

T-tests and analysis of variance (ANOVA) are widely used statistical methods to compare group means. For example, the independent sample t-test enables you to compare annual personal income between rural and urban areas and examine the difference in the grade point average (GPA) between male and female students. Using the paired t-test, you can also compare the change in outcomes before and after a treatment is applied.

For a t-test, the mean of a variable to be compared should be substantively interpretable. Technically, the left-hand side (LHS) variable to be tested should be interval or ratio scaled (continuous), whereas the right-hand side (RHS) variable should be binary (categorical). The ttest can also compare the proportions of binary variables. The mean of a binary variable is the proportion or percentage of success of the variable. When sample size is large, t-tests and z-test for comparing proportions produce almost the same answer.