 Chisquared test

 "Chisquare test" is often shorthand for Pearson's chisquare test.
A chisquare test, also referred to as chisquared test or χ^{2} test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chisquare distribution when the null hypothesis is true, or any in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chisquare distribution as closely as desired by making the sample size large enough.
Some examples of chisquare tests where the chisquare distribution is only approximately valid:
 Pearson's chisquare test, also known as the chisquare goodnessoffit test or chisquare test for independence. When mentioned without any modifiers or without other precluding context, this test is usually understood (for an exact test used in place of χ^{2}, see Fisher's exact test).
 Yates's correction for continuity, also known as Yates' chisquare test.
 Cochran–Mantel–Haenszel chisquare test.
 Linearbylinear association chisquare test.
 The portmanteau test in timeseries analysis, testing for the presence of autocorrelation
 Likelihoodratio 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 chisquare distribution is the test that the variance of a normallydistributed 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.
Contents
Chisquare test for variance in a normal population
If a sample of size n is taken from a population having a normal distribution, then there is a wellknown result (see distribution of the sample variance) which allows a test to be made of whether the variance of the population has a predetermined value. For example, a manufacturing process might have been in stable condition for a long period, allowing a value for the variance to be determined essentially without error. Suppose that a variant of the process is being tested, giving rise to a small sample of product items whose variation is to be tested. The test statistic T in this instance could be set to be the sum of squares about the sample mean, divided by the nominal value for the variance (i.e. the value to be tested as holding). Then T has a chisquare distribution with n – 1 degrees of freedom. For example if the sample size is 21, the acceptance region for T for a significance level of 5% is the interval 9.59 to 34.17.
See also
 Pearson's chisquare test for a more detailed explanation
 Chisquare distribution
 Chisquare test nomogram
 Gtest
 Likelihoodratio tests are approximately chisquare tests
 McNemar's test, related to a chisquared test
 t test
 The Wald test can be evaluated against a chisquare distribution
References
 Weisstein, Eric W., "ChiSquared Test" from MathWorld.
 Corder, G.W., Foreman, D.I. (2009). Nonparametric Statistics for NonStatisticians: A StepbyStep Approach Wiley, ISBN 9780470454619
 Greenwood, P.E., Nikulin, M.S. (1996) A guide to chisquared testing. Wiley, New York. ISBN 047155779X
 Nikulin, M.S. (1973). "Chisquared test for normality". In: Proceedings of the International Vilnius Conference on Probability Theory and Mathematical Statistics, v.2, pp. 119–122.
External links
 Penn State's Chi Squared Explanation and example
 ChiSquared Calculator from GraphPad
 ChiSquared Test in QtiPlot
 Vassar College's 2×2 ChiSquared with Expected Values
Categories: Statistical tests
 Nonparametric statistics
 Categorical data
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