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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.
Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics , a sequence of random variables is homoscedastic ( / ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k / ) if all its random variables have the same finite variance ; this is also known as homogeneity of variance.
This test, and an estimator for heteroscedasticity-consistent standard errors, were proposed by Halbert White in 1980. [1] These methods have become widely used, making this paper one of the most cited articles in economics. [2]
We reject the null hypothesis of homoscedasticity and conclude that heteroscedasticity is present. See also. Breusch–Pagan test;
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 Brown–Forsythe test uses the median instead of the mean in computing the spread within each group (¯ vs. ~, above).Although the optimal choice depends on the underlying distribution, the definition based on the median is recommended as the choice that provides good robustness against many types of non-normal data while retaining good statistical power. [3]
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