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Residuals can be tested for homoscedasticity using the Breusch–Pagan test, [20] which performs an auxiliary regression of the squared residuals on the independent variables. From this auxiliary regression, the explained sum of squares is retained, divided by two, and then becomes the test statistic for a chi-squared distribution with the ...
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.
It tests the null hypothesis that the population variances are equal (called homogeneity of variance or homoscedasticity). If the resulting p -value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with ...
“Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”. [ 1 ] [ 2 ] [ 3 ] Assuming a variable is homoscedastic when in reality it is heteroscedastic ( / ˌ h ɛ t ər oʊ s k ə ˈ d æ s t ɪ k / ) results in unbiased but inefficient point estimates and in biased estimates of standard errors , and may ...
This is the basis of the Breusch–Pagan test. It is a chi-squared test: the test statistic is distributed nχ 2 with k degrees of freedom. If the test statistic has a p-value below an appropriate threshold (e.g. p < 0.05) then the null hypothesis of homoskedasticity is rejected and heteroskedasticity assumed.
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 modification of one of the tests, they can be found to be algebraically equivalent. [4]
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Herbert Glejser, in his 1969 paper outlining the Glejser test, provides a small sampling experiment to test the power and sensitivity of the Goldfeld–Quandt test. His results show limited success for the Goldfeld–Quandt test except under cases of "pure heteroskedasticity"—where variance can be described as a function of only the underlying explanatory variable.