Earlier, I had posted the following question to the group : > Hello. I have come across a curious result that I cannot explain.
> Hopefully, someone can explain this. I am doing a 1-way ANOVA with 6 > groups (example: summary(aov(y~A)) with A having 6 levels). I get an > F of 0.899 with 5 and 15 df (p=0.51). I then do the same analysis but > using data only corresponding to groups 5 and 6. This is, of course, > equivalent to a t-test. I now get an F of 142.3 with 1 and 3 degrees > of freedom and a null probability of 0.001. I know that multiple > comparisons changes the model-wise error rate, but even if I did all > 15 comparisons of the 6 groups, the Bonferroni correction to a 5% > alpha is 0.003, yet the Bonferroni correction gives conservative > rejection levels. > > How can such a result occur? Any clues would be helpful. Brian Ripley, Robert Balshaw, Peter Dalgaard and Ted Harding all responded. The answer was basically the same from all: If there is heterogeneity of variances between the groups, and the variances of groups 5 and 6 are smaller than the others, then my result could occur because the average within-group variance over all groups in the general ANOVA is higher than the within-group variance when looking only at groups 5 and 6. Combine this with the very small sample size and unequal group membership. A number of reference books state that ANOVA is fairly robust to moderate degrees of heterogeneity of variance but not what constitutes �moderate�! Bill Shipley Associate Editor, Ecology North American Editor, Annals of Botany D�partement de biologie, Universit� de Sherbrooke, Sherbrooke (Qu�bec) J1K 2R1 CANADA [EMAIL PROTECTED] <http://callisto.si.usherb.ca:8080/bshipley/> http://callisto.si.usherb.ca:8080/bshipley/ [[alternative HTML version deleted]] ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
