Re: Are parametric assumptions importat ?

[Lise DeShea]

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 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.

Cheers.
Lise
~~~
Lise DeShea, Ph.D.
Assistant Professor
Educational and Counseling Psychology Department
University of Kentucky
245 Dickey Hall
Lexington KY 40506
Email:  [EMAIL PROTECTED]
Phone:  (859) 257-9884
Website for students:  www.uky.edu/~ldesh2/stats.htm