t-test (for Independent and Dependent Samples)

The t-test is the most commonly used method to evaluate the differences in means between two groups. The groups can be independent (e.g., blood pressure of patients who were given a drug vs. a control group who received a placebo) or dependent (e.g., blood pressure of patients "before" vs. "after" they received a drug, see below). Theoretically, the t-test can be used even if the sample sizes are very small (e.g., as small as 10; some researchers claim that even smaller n's are possible), as long as the variables are approximately normally distributed and the variation of scores in the two groups is not reliably different (see also Elementary Concepts).

Dependent samples test. The t-test for dependent samples can be used to analyze designs in which the within-group variation (normally contributing to the error of the measurement) can be easily identified and excluded from the analysis. Specifically, if the two groups of measurements (that are to be compared) are based on the same sample of observation units (e.g., subjects) that were tested twice (e.g., before and after a treatment), then a considerable part of the within-group variation in both groups of scores can be attributed to the initial individual differences between the observations and thus accounted for (i.e., subtracted from the error). This, in turn, increases the sensitivity of the design.

One-sample test. In the so-called one-sample t-test, the observed mean (from a single sample) is compared to an expected (or reference) mean of the population (e.g., some theoretical mean), and the variation in the population is estimated based on the variation in the observed sample.

See Hays, 1988. See also the Basic Statistics Introductory Overviews: t-test for Independent Samples - Introductory Overview, t-test for Dependent Samples - Introductory Overview, and t-test for Single Means - Introductory Overview.