The t test is used when the DV of interest is continuous (interval or ratio) and the IV is categorical with two classes (such as gender measured as male or female). The t test is a test for differences between two means. In the officer-to-resident ratio example, a t test would be the analysis we select to determine whether or not to reject the null hypothesis (since we had two types of police agencies and the ratio variable is continuous). The third type of test is the analysis of variance (ANOVA). The ANOVA is an extension of the t test and is used when the DV is continuous and the IV is categorical with three or more classes. If we added state police agencies to our ratio analysis, we would use an ANOVA instead of a t test. The rationale behind this is that conducting multiple t tests is time consuming and cumbersome, and creates statistical problems. The ANOVA streamlines the process by using a single analysis across all classes of the IV.
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