I have a data set from an experiment where several genotypes of a plant were
subjected to a factorial combination of environmental treatments. Analysing
the data with GLM required log-transformation of the data. Now I am
interested in whether one of the environmental factors affects the relative
amount of variation found among genotypes. That means: does it affect the
Coefficient of variation (CV) of genotype (=group) means?
SOLUTION 1: Use raw data to calculate genotypic means, and their CV at each
factor level.
However, the experiment had other environmental factors, a significant block
effect, unequal mortality during the experiment  may all not be 100%
orthogonal any more. Fitting the GLM and using the LS means will correct for
these other influences, right?
Therefore,
SOLUTION 2: Extract LS means of the factor by genotype interaction,
back-transform to original scale, and calculate CV at each factor level.
If I do this, I get pretty different results than with the other solution. Why?
Log-transformation is homogenizing the variance, but shouldn’t the group
means be similar again after back-transformation, and therefore also their CV?
I do not think that this has got to do with confounding of different
experimental factors, because if I do the same GLMs with untransformed data,
then the extracted LS means are extremely similar to the simple group means
from the raw data.
So it must be the log transformation that is somehow changing the variation
in the data, even after their back-transformation.
I would be grateful for any suggestion as to what is going on there.
Regards, Oliver
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