# Re: [R] Looking for transformation to overcome heterogeneity of variances

Date: Fri 04 Aug 2006 - 05:11:26 EST

Paul: It is too bad that most peoples statistical thought processes lead them to thinking heterogeneity is something to overcome so that a simple test of differences in means with ANOVA can be made. If you have that much heterogeneity among 96 groups (hard for me to imagine otherwise), perhaps the distributional heterogeneity rather than simple shifts in means is the more important effect. You might try using omnibus tests of distributional differences (eg., MRPP, coverage tests, etc.) or compare multiple quantiles (e.g., with quantile regression) since you've already admitted that the group distributions differ by more than just a shift in means. Heterogeneous variances among groups immediately implies that there is not a single parameter describing changes in distributions among groups. Focusing on just a comparison of means, while traditional and analytically expedient, is unlikely to be very enlightening. You could of course, weight each group inversely by its variance to achieve a weighted comparison of means. But doing this just makes it so that you've made a valid test on only one of the parameters characterizing distributional differences. A better analysis but still not as enlightening as possible.

My 2 pence.

Brian

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO 80526-8818

tel: 970 226-9326

"Paul Smith" <phhs80@gmail.com>
Sent by: r-help-bounces@stat.math.ethz.ch 08/03/2006 07:33 AM

To
r-help@stat.math.ethz.ch
cc

Subject
[R] Looking for transformation to overcome heterogeneity of variances

Dear All

My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at

Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity?

Paul

R-help@stat.math.ethz.ch mailing list