Chisquare test
From Wikipedia, the free encyclopedia
 "Chisquare test" is often shorthand for Pearson's chisquare test.
A chisquare test (also chisquared or χ^{2} test) is any statistical hypothesis test in which the test statistic has a chisquare 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 chisquare distribution as closely as desired by making the sample size large enough.
Some examples of chisquared 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.
 Yates' chisquare test, also known as Yates' correction for continuity.
 MantelHaenszel 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.
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[edit] 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 (ie. 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.
[edit] See also
 Pearson's chisquare test for a more detailed explanation
 General likelihoodratio tests, which are approximately chisquare tests
 McNemar's test, related to a chisquare test
 The Wald test, which can be evaluated against a chisquare distribution
[edit] External links
[edit] References
 Greenwood, P.E., Nikulin, M.S. (1996) A guide to chisquared testing. Wiley, New York. ISBN 047155779X
