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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.
In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part.
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 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.
In statistics, Levene's test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. [1] This test is used because some common statistical procedures assume that variances of the populations from which different samples are drawn are equal. Levene's test assesses this assumption.
Cochran's test, [1] named after William G. Cochran, is a one-sided upper limit variance outlier statistical test .The C test is used to decide if a single estimate of a variance (or a standard deviation) is significantly larger than a group of variances (or standard deviations) with which the single estimate is supposed to be comparable.
Statistical testing for a non-zero heterogeneity variance is often done based on Cochran's Q [13] or related test procedures. This common procedure however is questionable for several reasons, namely, the low power of such tests [14] especially in the very common case of only few estimates being combined in the analysis, [15] [7] as well as the specification of homogeneity as the null ...
In an agricultural study, ANCOVA can be used to analyze the effect of different fertilizers on crop yield (), while accounting for soil quality as a covariate. Soil quality, a continuous variable, influences crop yield and may vary across plots, potentially confounding the results.