The t-test is a statistical test that compares the means of two groups of observations. The observations should be randomly assigned to the two groups, so that any difference in response is due to the treatment and not to other factors. For instance in a medical study patients with high blood pressure are randomly assigned to a placebo group and a treatment group. The patients in the placebo group receive an inactive pill and the patients in the treatment group receive a new drug that is expected to lower blood pressure. After treating the subjects, the t test is used to compare the average blood pressures level for the placebo group and the treatment group.
Consider the following fictitious data:
Group bloodpressure treatment 88 treatment 83 treatment 82 treatment 101 treatment 99 treatment 85 treatment 87 treatment 89 treatment 88 placebo 88 placebo 82 placebo 101 placebo 106 placebo 96 placebo 92 placebo 112 placebo 120 placebo 97
There are two groups, treatment and placebo. The null hypothesis in the t-test is that mean of the treatment is equal to the mean of the placebo group.
| Group | N | Mean | |
| placebo | 9.0 | 99.33333 | |
| treatment | 9.0 | 89.11111 |
| Test Statistic | df | p-value |
| 2.25094 | 16.0 | 0.0388 |