Rellevant information:
-I'm specifically looking for a robust alternative (also parametric) to One-Way ANOVA that I can conduct with SPSS software.
-I've disregarded non parametric tests (K-W).
-No transformations of participants' response make sense (conceptually speaking)
-I've already removed outliers and trimmed the mean.
-The factor has three levels; there's only one continuous dependent variable.
-Normality is achieved.
-"Small sample" means < 20 for each group
-"Unbalanced sample" means two groups with 19 subjects, the third group with 10 (don't reflecting the variance of the population)
-The variance for the group 1 (n=19) is more than five times the variance for the group 2 (n=19) and nearly four times the variance for the group 3 (n=10).
I greatly appreciate your help!
* I'm facing the same problem with a mixed design ANOVA (SPANOVA), but I guess it should be a major challenge.
Many thanks in advance!
I would recommend the robust test of equal means Brown-Forsythe, it is preferable to the F statistic when the equality of variances are not supposed.
References:
- Brown, M. B., & Forsythe, A. B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16(1), 129-132.
- Clinch, J. J., & Keselman, H. J. (1982). Parametric alternatives to the analysis of variance. Journal of educational and behavioral statistics, 7(3), 207-214.
- Mehrotra, D. V. (1997). Improving the Brown-Forsythe solution to the generalized Behrens-Fisher problem. Communications in Statistics-Simulation and Computation, 26(3), 1139-1145.
Your difference in variance sounds pretty small, and if sample sizes are nearly equal would cause little concern.
Welch-type adjustments* for degrees of freedom exist for ANOVA just as with two-sample t-tests; and just as with their use in two sample t-tests, there's little reason not to use them as a matter of course.
Welch, B.L. (1951) On the comparison of several mean values: an alternative approach.Biometrika, 38, 330–336
You can also use any from the following in SPSS:
Tamahane's T2, Dunnet's T3, Dunnet's C and also Games-Howell
Thank you very much, Enrique anb Robert.
I'm aware about both Welch-type adjustments and the Brown-Forsythe test. But I was not sure they were the best choices. To my knowledge, most of authors prefer Welch adjustment to Brown-Forsythe. Do you agree?
Very kind of you!
Jaume
Well, It depends. Maybe you'd like to have a look at
http://www.psych.nyu.edu/cohen/eps12dr1.pdf
which discusses both of them in comparison
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