[R-sig-eco] nested Kruskal Wallis

[Philip Dixon]

Jude,

Fundamentally, the concept of analyzing ranks of observations (leading to the 
KW test) can not be extended, except in very special circumstances, to a 
general linear model.  Blocks, where you can rank within blocks, is one of 
those special circumstances.  The concept of additive field and sample effects 
simply does not apply to ranks.  Back in the 70's, a few folks tried to 
popularize a 'rank transform' but that has faded because it didn't work.
For example, it is easy to construct a data set with a 2way factorial 
treatment structure where the means have no interaction, but the mean ranks 
have an interaction.

I am a real fan of Paul Murtaugh's 'simplicity and complexity' paper in 
Ecology (Jan 07).  Applying that idea suggests that you:
calculate the sample average, probably before transformation, for each field
use KW (or some other appropriate test), treating fields within crop type as 
replicates.

This approach ignores the unequal contributions to the variance when you 
average 2 observations, compared to an average of 10 observations.  Your 
comment about unequal variances suggests there are other, larger, 
contributions to unequal variance among fields, so I would be comfortable 
ignoring the unequal # samples per field.  Others might not want to do this.

Best wishes,
Philip Dixon