math lessons - 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

$X^2=\sum\frac{(\mathrm{observed}-\mathrm{expected})^2}{\mathrm{expected}},$

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

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