A t-test is a hypothesis test of the mean of one or two normally distributed populations. Several types of t-tests exist for different situations, but they all use a test statistic that follows a t-distribution under the null hypothesis:

Test | Purpose | Example |
---|---|---|

1-Sample t | Tests whether the mean of a single population is equal to a target value | Is the mean height of female college students greater than 5.5 feet? |

2-Sample t | Tests whether the difference between the means of two independent populations is equal to a target value | Does the mean height of female college students significantly differ from the mean height of male college students? |

Paired t | Tests whether the mean of the differences between dependent or paired observations is equal to a target value | If you measure the weight of male college students before and after each subject takes a weight-loss pill, is the mean weight loss significant enough to conclude that the pill works? |

t-test in regression output | Tests whether the values of coefficients in the regression equation differ significantly from zero | Are high school SAT test scores significant predictors of college GPA? |

An important property of the t-test is its robustness against assumptions of population normality. In other words, with large samples t-tests are often valid even when the assumption of normality is violated. This property makes them one of the most useful procedures for making inferences about population means.

However, with a small sample size and nonnormal and highly skewed distributions, it might be more appropriate to use nonparametric tests.