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-test | 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-test | 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-test | 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, t-tests are often valid even when the assumption of normality is violated, but only if the distribution is not highly skewed. This property makes them one of the most useful procedures for making inferences about population means.

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