Chi-square test

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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
• Yates' chi-square test also known as Yates' correction for continuity
• Mantel-Haenszel chi-square test
• linear-by-linear association chi-square test
• Chi-square goodness-of-fit test

The most common form of the test statistic is:

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

where the word "expected" often does not denote an expected value, but an observable estimate of an expected value. However, likelihood ratio tests do not have this form.

The chi-square test is a statistical tool to separate real effects from random variation. It can be used on data that is:

1. randomly drawn from the population
2. reported in raw counts of frequency (not percentages or rates)
3. measured variables must be independent
4. values on independent and dependent variables must be mutually exclusive
5. observed frequencies cannot be too small

The chi-square test determines the probability of obtaining the observed results by chance, under a specific hypothesis. It tests independence as well as goodness of fit for a set of data.

See also

• General likelihood-ratio tests, which are approximately chi-square tests.
• McNemar's test, related to a chi-square test
• The Wald test, which can be evaluated against a chi-square distribution

de:Chi-Quadrat-Test fr:Test du χ² lv:Hī kvadrāta kritērijs nl:Chi-kwadraattoets su:Tes chi-kuadrat vi:Kiểm định chi-bình phương