T-tests and ANOVAs: Special Application of Linear Regressions

T-tests and ANOVAs: Simple Tools for Comparing Groups

Both t-tests and ANOVAs are methods used to compare the means (averages) of different groups, and they are special cases of linear regression.

• T-tests: We use these when comparing the means of two groups. For example, if we want to see if two groups (like men and women) have different average heights, a t-test helps us determine if the difference is statistically significant.
• ANOVAs (Analysis of Variance): ANOVAs are like t-tests but for three or more groups. For instance, if we want to compare the average exam scores of students in three different classes, ANOVA tells us if there’s a significant difference between them.

How They Relate to Linear Regression:

• Both t-tests and ANOVAs can be thought of as simple forms of linear regression where the focus is on understanding whether group membership (a categorical variable) explains the differences in a continuous outcome (like height or exam scores).

In short, use a t-test when comparing two groups and ANOVA when comparing three or more, and both are rooted in the principles of linear regression.

The remainder of the session will be about learning how to use and interpret them.