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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.
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.
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
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.
In statistics, the Jonckheere trend test [1] (sometimes called the Jonckheere–Terpstra [2] test) is a test for an ordered alternative hypothesis within an independent samples (between-participants) design. It is similar to the Kruskal-Wallis test in that the null hypothesis is that several independent samples are from the same population ...
where T is the sample size, is the residual and is the row of the design matrix, and is the Bartlett kernel [8] and can be thought of as a weight that decreases with increasing separation between samples. Disturbances that are farther apart from each other are given lower weight, while those with equal subscripts are given a weight of 1.
Conversely, a “large" R 2 (scaled by the sample size so that it follows the chi-squared distribution) counts against the hypothesis of homoskedasticity. An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a ...
In statistics, the Goldfeld–Quandt test checks for heteroscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups, and hence the test is sometimes called a two-group test. The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt. Both a parametric ...