### 7.3. Testing for The Difference Between The Means of Two Independent Groups

Many studies are designed to compare two independent populations where the response of interest is a measurement on a continuous variable. Two different tests of hypotheses for the difference between the means are usually used: a pooled-variance t test in which the variances in the two populations are assumed to be equal and a separate-variance t test in which the variances in the two populations are not assumed to be equal.

#### Pooled-Variance t Test for the Difference in Two Means

The pooled-variance t test requires that the two sample variances be combined, or pooled, into one estimate of the variance common in the two groups, assuming that the population variances in ...