12. t-Tests

A t-test is used when we want to evaluate a research question about a mean or a difference between means. Unlike the chi-square tests in ?sec-chi-square, which analyze frequencies or counts, t-tests analyze continuous variables.

There are three main types of t-tests covered in this chapter. The appropriate test depends on what the sample mean is being compared to: a known or hypothesized value, another independent group, or a paired measurement from the same participants or matched cases.

Test	Variables and Design	Research Question
One-sample t-test	One continuous variable compared with a known or hypothesized value	Is the sample mean different from a comparison value?
Independent-samples t-test	One continuous outcome and one categorical grouping variable with two independent groups	Do two independent groups differ in their means?
Dependent/paired-samples t-test	One continuous outcome measured twice for the same participants or matched cases	Do two related means differ?

Each t-test follows the same four-step hypothesis-testing process introduced earlier in the book: look at the data, check assumptions, perform the test, and interpret the results. What changes across the three tests is the structure of the data and the comparison being made.

The most important decision is whether the observations being compared are independent or paired. If the two means come from different people or different cases, use an independent-samples t-test. If the two means come from the same people measured twice or from matched pairs, use a dependent/paired-samples t-test.