When there are two categorical variables, you can use a specific type of frequency distribution table called a contingency table to show the number of observations in each combination of groups. A frequency distribution table shows the number of observations in each group. A frequency distribution describes how observations are distributed between different groups.įrequency distributions are often displayed using frequency distribution tables. There are two types of Pearson’s chi-square tests, but they both test whether the observed frequency distribution of a categorical variable is significantly different from its expected frequency distribution. Test hypotheses about frequency distributions Note: Parametric tests can’t test hypotheses about the distribution of a categorical variable, but they can involve a categorical variable as an independent variable (e.g., ANOVAs). Because they can only have a few specific values, they can’t have a normal distribution. Categorical variables can be nominal or ordinal and represent groupings such as species or nationalities. If you want to test a hypothesis about the distribution of a categorical variable you’ll need to use a chi-square test or another nonparametric test. Nonparametric tests are used for data that don’t follow the assumptions of parametric tests, especially the assumption of a normal distribution. Pearson’s chi-square (Χ 2) tests, often referred to simply as chi-square tests, are among the most common nonparametric tests. Frequently asked questions about chi-square tests.
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