t-test for Independent Samples - Introductory Overview

The t-test is the most commonly used method to evaluate the differences in means between two groups. For example, the t-test can be used to test for a difference in test scores between a group of patients who were given a drug and a control group who received a placebo. 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 normally distributed within each group and the variation of scores in the two groups is not reliably different (see also Elementary concepts). As mentioned before, the normality assumption can be evaluated by looking at the distribution of the data (via histograms) or by performing a normality test (via the descriptive statistics option). The equality of variances assumption can be verified with the F-test (which is included in the t-test output), or you can use the more robust Levene test option (as well as the Brown-Forsythe modification of this test). If these conditions are not met, then you can evaluate the differences in means between two groups using one of the nonparametric alternatives to the t-test (see Nonparametric Statistics).

The p-value reported with a t-test represents the probability of error involved in accepting our research hypothesis about the existence of a difference. Technically speaking, this is the probability of error associated with rejecting the hypothesis of no difference between the two categories of observations (corresponding to the groups) in the population when, in fact, the hypothesis is true. Some researchers suggest that if the difference is in the predicted direction, you can consider only one half (one "tail") of the probability distribution and thus divide the standard p-value reported with a t-test (a "two-tailed" probability) by two. Others, however, suggest that you should always report the standard, two-tailed t-test probability.

For additional overview topics on Independent t-tests, see:

Arrangement of data