On 21-Oct-03 Bill Shipley wrote: > 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.
It's not obvious from your description. However, one possibility (which I very strongly suspect) is apparent heterogeneity of variance, coupled with paucity of data. To wit: The denominator in F is the residual sum of squares (divided by its degrees of freedom -- 15 in your first case, 3 in your second). If the data in groups 5 and 6 are very close to their group means, the group means themselves being more widely separated, then you can indeed get a large F. The very moderate F that you get from the full set of groups is quite compatible with the extreme result from the two-group analysis if the data happen to be more widely spread about their group means than they happen to be in G5+G6. This is the "heterogeneity of variance" side of it. Your denominator df = 3 for the two-group case indicates that you only have 5 data values altogether in these two groups. Your df = 15 for the six-group case indicates that you have only 21 data all told. At an average of 3.5 data per group you have a very thin data set. Your 2.5 data per group in G5+G6 is even thinner. I would be very cautious about interpreting the results in such a case. Perhaps if you told us more about your data we could give a more focussed diagnosis. Best wishes, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 167 1972 Date: 21-Oct-03 Time: 17:56:53 ------------------------------ XFMail ------------------------------ ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help