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| Levene- und Brown-Forsythe-Test auf Varianzgleichheit× | Welch-ANOVA× | |
|---|---|---|
| Fachgebiet | Statistik | Statistik |
| Familie≠ | Regression model | Hypothesis test |
| Entstehungsjahr≠ | 1960 | 1951 |
| Urheber≠ | Howard Levene; Morton B. Brown and Alan B. Forsythe | B. L. Welch |
| Typ≠ | Homogeneity of variance test (robust) | Parametric mean comparison (heteroscedastic) |
| Wegweisende Quelle≠ | Levene, H. (1960). Robust Tests for Equality of Variances. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press. link ↗ | Welch, B.L. (1951). On the Comparison of Several Mean Values. Biometrika, 38(3/4), 330–336. link ↗ |
| Aliasnamen≠ | Levene test, Brown-Forsythe test, homogeneity of variance test, Levene ve Brown-Forsythe Varyans Testi | Welch's F-test, heteroscedastic one-way ANOVA, Welch ANOVA — Heterojen Varyans ANOVA |
| Verwandt≠ | 5 | 3 |
| Zusammenfassung≠ | The Levene and Brown-Forsythe test checks whether two or more groups share the same variance (homogeneity of variance). Levene (1960) built the test on absolute deviations from each group mean, and Brown and Forsythe (1974) made it robust to non-normal data by centring on the group median instead. | Welch ANOVA is a parametric hypothesis test that compares the means of three or more independent groups when their variances are not equal. Introduced by B. L. Welch in 1951, it replaces classic one-way ANOVA whenever the homogeneity-of-variance assumption fails, while still requiring approximately normal data. |
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