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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.
Levene's test assesses this assumption. 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 ...
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. In meta-analysis , which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity ).
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.
[citation needed] The BG test is considered to be more general than the Ljung-Box test because the latter requires the assumption of strict exogeneity, but the BG test does not. However, the BG test requires the assumptions of stronger forms of predeterminedness and conditional homoscedasticity.
Step 4: Perform a t-test on the equation selected from step 3 on γ 1. If γ 1 is statistically significant, reject the null hypothesis of homoscedasticity.
The test has been discussed in econometrics textbooks. [2] [3] Stephen Goldfeld and Richard E. Quandt raise concerns about the assumed structure, cautioning that the v i may be heteroscedastic and otherwise violate assumptions of ordinary least squares regression. [4]
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. If the Breusch–Pagan test shows that there is conditional heteroskedasticity, one could either use weighted least squares (if the source of heteroskedasticity is known) or ...