Σ is the summation operator (it means “take the sum of”).The chi-square formulaīoth of Pearson’s chi-square tests use the same formula to calculate the test statistic, chi-square (Χ 2): Example: Handedness and nationality Contingency table of the handedness of a sample of Americans and CanadiansĪ chi-square test (a test of independence) can test whether these observed frequencies are significantly different from the frequencies expected if handedness is unrelated to nationality.
Example: Bird species at a bird feeder Frequency of visits by bird species at a bird feeder during a 24-hour period Bird speciesĪ chi-square test (a chi-square goodness of fit test) can test whether these observed frequencies are significantly different from what was expected, such as equal frequencies. 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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