F-ratio



Analysis of variance (ANOVA)
•Application of the F-test principle
•Allows comparisons of multiple mean values
•H0: means of all groups are identical
•Decomposes the total Sum of Squares (= numerator in the variance formula) into
•Systematic component (Sum of squares effect) – can be scaled by corresponding DFeffect (=number of
groups – 1) to get Mean Square (MSeffect)
•Residual variability (Error Sum of Sq.) – can be scaled by DFerror (= number of obs. – 1 –
DFeffect  ) to obtain the MSerror
•F = MSeff/MSerror to be compared with the F distribution with corresponding DFs
•R2 (proportion of explained variability) = SSeffect/ SStotal
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ANOVA assumptions
•Homogeneity of variances (variances in all groups are equal)
•Normal distribution of residuals (= of values within individual groups)
•ANOVA may be unbalanced (= unequal sample size within groups)
•Formal tests exist to check the assumptions
•Difficult to interpret
•Graphical inspection of residuals using plot(anova.object) is a better option
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Post-hoc comparisons
•Rejecting H0 in ANOVA means that all group means are not identical, i.e. at least one is different
•We wonder, which mean is significantly different from which
•Post-hoc pairwise comparisons are used for that
•Tukey HSD test and others
•Various control levels of type-I error in multiple comparisons
•Results are best displayed on graphs (groups with different letters are significantly different)