A chi-squared test, also referred to as chi-square test or xw2 test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi- squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough.
Some examples of chi-squared tests where the chi-squared distribution is only approximately valid: Pearson’s chi-squared test, also known as the chi-squared goodness-of-fit test or chi-squared test for independence. When the chi-squared test is mentioned without any modifiers or without other precluding context, this test is usually meant (for an exact test used in place of r, see Fisher’s exact test). Yates’s correction for continuity, also known as Yates’ chi-squared test.
Cochran-Mantel-Haenszel chi- squared test. McNemar’s test, used in certain 2 x 2 tables with pairing Tukey’s test of additivity The portmanteau test in time-series analysis, testing for the presence of utocorrelation 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-squared 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.