On 12 Oct 2001 11:14:54 -0700, [EMAIL PROTECTED] (Lise DeShea) wrote: > Re robustness of the between-subjects ANOVA, I obtained permission from Dr. > Rand Wilcox to copy three pages from his book, "New Statistical Procedures > for the Social Sciences," and place them on a webpage for my students. He > cites research showing that with four groups of 50 observations each and > population standard deviations of 4, 1, 1, and 1, the empirical Type I > error rate was .088, which is beyond Bradley's liberal limits on sampling > variability [.025 to .075]. You can read this excerpt at
Well, I suggest that a variance difference of 16 to 1 practically washes out the usual interest in the means. Isn't that beyond the pale of the usual illustrations of what is robust? I may remember wrong, but it seems to me that Tukey used Monte Carlo with "10% contamination" of a sample, where the contaminant had excessive variances: 10-fold for the variances? What can you say about an example like that? Will a Box-Cox transformation equalize the variances? (no?) Is there a huge outlier or two? If not -- if the scores are well scattered -- all the extreme scores in *both* directions will be in that one group. And a "mean difference" will implicitly be determined by the scaling: That is, if you spread out the low scores (say), then the group with big variance will have the lower mean. > www.uky.edu/~ldesh2/stats.htm -- look for the link to "Handout on ANOVA, > Sept. 19-20, 2001." Error rates are much worse when sample sizes are > unequal and the smaller groups are paired with the larger sigma -- up to an > empirical alpha of .309 when six groups, ranging in size from 6 to 25, have > sigmas of 4, 1, 1, 1, 1, 1. > > The independent-samples t-test has an inoculation against unequal variances > -- make sure you have equal n's of at least 15 per group, and it doesn't > matter much what your variances are (Ramsey, 1980, I think). But the ANOVA > doesn't have an inoculation. > > I tell my students that the ANOVA is not robust to violation of the equal > variances assumption, but that it's a stupid statistic anyway. All it can > say is either, "These means are equal," or "There's a difference somewhere > among these means, but I can't tell you where it is." I tell them to move > along to a good MCP and don't worry about the ANOVA. Most MCP's don't > require a significant F anyway. And if you have unequal n's, use > Games-Howell's MCP to find where the differences are. Some of us don't like MCPs. We think that the overall test is not (or at least, not always) a bad way to start, if a person *really* can't be more particular about what they want to test. And if you have unequal Ns, you are stuck with one approximation or another, which has to be ugly when the Ns are too unequal; or else you are stuck with inconsistent statements, where the smaller difference in means is 'significant' but the larger one is not. (I am unfamiliar with Games-Howell's MCP.) Just another opinion. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
