Applied MANOVA and Discriminant Analysis - Carl J. Huberty and Stephen Olejnik

«A statistical assessment of whether or not actual classification results obtained are better than those obtained by “chance” was discussed above. Suppose one concludes that the total-group results obtained are statistically better than chance [...] It seems natural now to ask: How much better than chance can we predict group membership? The answer to this question may be addressed by using the index:

where H_0 is the observed hit rate, and H_e is the hit rate expected by chance. [...] The index may thus be viewed as a proportional reduction in error or "improvement over chance descriptive statistic"»

H_0 = accuracy

H_e = majority class frequency = max(class i count / nrow ∀ i ∈ classes)