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st: RE: non parametric anova equivalent for factorial experiments?


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: non parametric anova equivalent for factorial experiments?
Date   Thu, 4 Mar 2010 14:07:27 -0000

I'd translate the problem into an equivalent regression-type model. I
think practitioners vary in how seriously to take these preliminary
tests and that in practice ANOVA often works well despite mild
deviations from ideal conditions. 

The point need not be an article of faith. Guessing that the problem is
a highish outlier, I'd explore sensitivity to the outlier by 

glm ... 
glm ... , link(power 0.5) 
glm ... , link(log) 

where ... indicates the appropriate response and predictors. That would
require use of factor variables (11) or -xi- (<= 10). 

I'd then monitor how the questionable data points move around on
residual vs fitted plots and observed vs fitted plots. -modeldiag- from
SJ 4(4) contains plotting commands that work after -glm-. 

Alona will find examples of -glm-s being applied in our joint paper: 

Cox, N.J. J. Warburton, A. Armstrong and V.J. Holliday. 2008. Fitting
concentration and load rating curves with generalised linear models.
Earth Surface Processes and Landforms 33: 25-39 (doi: 10.1002/esp.1523)

A roughly equivalent but in my view inferior approach is to try
transformations of the response directly. 

Nick 
n.j.cox@durham.ac.uk 

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Armstrong,
Alona
Sent: 04 March 2010 10:01
To: statalist@hsphsun2.harvard.edu
Subject: st: non parametric anova equivalent for factorial experiments?

Hi,
I have undertaken two factorial experiments. One has 3 factors each with
2 levels and the other has two factors, one with 2 levels and the other
with 3. The data are balanced with 3 replicates. I have tested for
homogeneity of variances by Levenes and Hartleys Maximum F ratio and the
data fail. Much of this is caused by one factor producing more variable
data for one level compared with the other but there are also some
outliers (but I would prefer not to exclude them as this is
representative of what I am studying). So, I have been looking around
for some non-parametric alternatives to ANOVA that can handle a
factorial design but with limited success (I have tried a rank-anova
approach but the same problems persist and there seems to be some debate
about the validity of that approach). Does anyone have any suggestions
and know of any existing Stata code? Any thoughts, recommendations or
pointers would be greatly appreciated.
Regards,
Alona

Dr Alona Armstrong
PDRA
Lancaster Environment Centre
Lancaster University
Lancaster
LA1 4YQ





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