ANOVA+Assumptions

ANOVA Assumptions (Analysis of Variance) (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

One-Way ANOVA | 2K Factorial


 * "the errors are independently, identically, and normally distributed for fixed effects models" - ([|Wikipedia])

From Lattin's Regression Analysis Chapter, "The error (term) "is independently and identically distributed with mean 0 and variance sigma squared." - Lattin. Is this the same as above?
 * "Independence of cases – this is a requirement of the design.
 * "Normality – the distributions of the residuals are normal.
 * "Equality (or "homogeneity") of variances, called homoscedasticity — the variance of data in groups should be the same.

"Levene's test for homogeneity of variances is typically used to examine the plausibility of homoscedasticity. The Kolmogorov–Smirnov or the Shapiro–Wilk test may be used to examine normality.

"When used to test the equality of the variances of two populations, the F-test is unreliable if there are deviations from normality (Lindman, 1974). On the other hand, when used in the analysis of variance to test the hypothesis that all treatments have exactly the same effect, the F-test is robust (Ferguson & Takane, 2005, pp. 261–2).

The Kruskal–Wallis test is a nonparametric alternative which does not rely on an assumption of normality." - [|Wikipedia]

Bartlett's Test for Equal Variances may be used instead of Levene's. Minittab shows both for. - EMSE 271, Fall 2009


 * Sources:**
 * Analysis of variance. (2009, November 24). In //Wikipedia, The Free Encyclopedia//. Retrieved 16:30, December 2, 2009, from []
 * Analyzing Multivariate Data, by James Lattin, Douglas Carroll and Green, (c) 2003 ([|Amazon]), page 44
 * EMSE 271, Fall 2009