R help - Aug 2006 - 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

http://phhs80.googlepages.com/hist1.png

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

Thanks in advance,

Paul

"Paul Smith" <phhs80 at gmail.com> writes:
> 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
> 
> http://phhs80.googlepages.com/hist1.png
> 
> Is someone able to suggest to me a transformation to overcome the
> problem of heterocedasticity?
Not based on that information. Try the following instead:

fit <- lm(y~g)
par(mfrow=c(2,2)); plot(fit)

-- 
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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

Brian S. Cade

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

email:  brian_cade@usgs.gov
tel:  970 226-9326



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

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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

http://phhs80.googlepages.com/hist1.png

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

Thanks in advance,

Paul

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Thanks to all contributors for the fruitfulness of this discussion. I
am speculating about a simpler solution: to use a non-parametric
approach. To avoid the requirement of having normal residuals, Frank
Harrell has suggested here the following non-parametric procedure:

library(Design)  # also requires library(Hmisc)
f <- lrm(y ~ a*b*c*d)
f
anova(f)

Could someone please tell me whether that also works when there is no
homoscedasticity? What are the assumptions of that method?

Paul