In addition to inferential methods for hypothesis tests for population parameters, such as the mean, \(\mu\), and the standard deviation, \(\sigma\), there are statistical methods to make inferences about the distribution of a variable. These inferential procedures rely on the chi-square (\(\chi^2\)) distribution, and thus are called \(\chi^2\)-tests.

In the following section we discuss the chi-square goodness-of-fit test, a hypothesis test that is applied to make inferences about the distribution of a variable and the chi-square independence test, a hypothesis test that is applied to decide whether an association exists between two variables of a population.


\(\chi^2\)-Distribution

Basic Properties of \(\chi^2\)-Curves (Weiss 2010)