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The Student's t test is, arguably, the most used statistical procedure. Because it is, by far, the most frequently used test for comparing differences between sample means for two independent groups (e.g., a treatment group receiving a treatment vs. a control group receiving no treatment), or when comparing average performance over time (e.g., before treatment and after treatment), this entry first introduces the test in these two contexts.

Inferences about μ1–μ2 Based on Independent Samples

The null and alternative hypotheses for a two-sided test (i.e., a nondirectional test) regarding equality of population means μjs(j = 1,2) for the two groups (e.g., treatment [group 1] versus control [group 2]) are:

The directional hypotheses are:

or

To test either null hypothesis (only one set of null and alternatives hypotheses are used ...

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