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In statistics, Bartlett's test, named after Maurice Stevenson Bartlett, [1] is used to test homoscedasticity, that is, if multiple samples are from populations with equal variances. [2] Some statistical tests, such as the analysis of variance , assume that variances are equal across groups or samples, which can be checked with Bartlett's test.
Homogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter.
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
For the test of independence, also known as the test of homogeneity, a chi-squared probability of less than or equal to 0.05 (or the chi-squared statistic being at or larger than the 0.05 critical point) is commonly interpreted by applied workers as justification for rejecting the null hypothesis that the row variable is independent of the ...
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When there is homogeneity of variance, sphericity of the covariance matrix will occur, because for between-subjects independence has been maintained. [5] [page needed] For the within-subject effects, it is important to ensure normality and homogeneity of variance are not being violated. [5] [page needed]
The Cochran's Q test is an extension of the McNemar's test for more than two "treatments". The Liddell's exact test is an exact alternative to McNemar's test. [10] [11] The Stuart–Maxwell test is different generalization of the McNemar test, used for testing marginal homogeneity in a square table with more than two rows/columns. [12] [13] [14]
The value q s is the sample's test statistic. (The notation | x | means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution.