Hypothesis
The t test for independent means is used when we want to know whether there is a difference between populations. For instance, we may want to know if college men and women differ on some psychological characteristic. To assess this, we would need information gathered from a group of men and information gathered from a separate group of women. The means are considered "independent" when there is no overlap between groups; a person cannot be male and female at the same time.

The t test for independent means is used only for tests of the sample means. Thus, our hypothesis tests whether the average difference between scores (M₁ - M₂) suggests that our students come from a population where there is no difference between men and women (μ₁ - μ₂ = 0) or whether they come from different populations (e.g., college men/college women).

The statistical hypotheses for t tests for independent means take one of the following forms, depending on whether your research hypothesis is directional or nondirectional. These hypotheses are identical in form to the statistical hypotheses used for t test for dependent means.