- Definition from Wikipedia
Chi-squared test
A chi-squared test (also chi-square or χ2 test) is any statistical hypothesis test in which the test statistic has a chi-square distribution when the null hypothesis is true, or any in which the probability distribution of the test statistic (assuming the null hypothesis is true) can be made to approximate a chi-square distribution as closely as desired by making the sample size large enough.
The chi-squared null hypothesis states that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution.
Some examples of chi-squared tests where the chi-square distribution is only approximately valid:
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- Pearson`s chi-square test, also known as the chi-square goodness-of-fit test or chi-square test for independence. When mentioned without any modifiers or without other precluding context, this test is usually understood.
- Yates` chi-square test, also known as Yates` correction for continuity.
- Mantel-Haenszel chi-square test.
- Linear-by-linear association chi-square test.
- The portmanteau test in time-series analysis, testing for the presence of autocorrelation
- Likelihood-ratio tests in general statistical modelling, for testing whether there is evidence of the need to move from a simple model to a more complicated one (where the simple model is nested within the complicated one).
One case where the distribution of the test statistic is an exact chi-square distribution is the test that the variance of a normally-distributed population has a given value based on a sample variance. Such a test is uncommon in practice because values of variances to test against are seldom known exactly.
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