Chi-square test

A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution if the null hypothesis is true. These include:

• Pearson's chi-square test
• Some likelihood-ratio tests are approximately chi-square tests when the sample-size is large. They are widely used in logistic regression. Other likelihood-ratio tests cannot be regarded as even approximately chi-square tests; e.g., F-tests in the analysis of variance and t-tests are likelihood-ratio tests, but the test statistic does not have a chi-square distribution under the null hypothesis.
• Yates' chi-square test, or Yates' correction for continuity
• Mantel-Haenszel chi-square test
• linear-by-linear association chi-square test

All such tests involve a statistic of the form

where the word "expected" often does not denote an expected value, but an observable estimate of an expected value.