With Respect
Below are the two responsive replies I received.
The trouble with the contingency table idea is that I don't have a simple count for each cell but a set of ratio responses. I am interested not in the distribution of cases over cells but in the impact being in a particular cell had.
I have looked at Brunner et al.'s book , particularly the section on the "ANOVA -like statistic"(71-73). I don't understand much but I do note that they keep saying "for the range of interest (.90, .99) which doesn't sound likely to fit my data.
Log-transforming the ratio variable would produce a distribution closer to the normal but somewhat left-skewed and would not addresss the unequal numbers in cells.
I suspect I was aiming at sophistication and precision beyond my statistical resources and sample size and should use the crude measures I have already for indicators of where future work should look.
Yours Sincerely,
Alan E. Dunne
from Gilbert McKenzie
"Looks to me like you may have a multidimensional contingency table with
> an ordered (categorical) response variable - there is lots of
> literature on
> this see the books by McCullagh & Nelder for the GLM background and
> Cox & Snell
> the analysis of binary data and Agresti's book.
>
> The analysis of multi-dimensional tables goes back to Lancaster, Birch,
> Bishop, Goodman
> Feinberg, Haberman and even further to Stephan & Demings IPF algorithnm
> in c1947.
> if I remember correctly."
from Stephen Senn
"Have a look at
> Nonparametric Analysis of Longitudinal Data in Factorial Experiments
> (Hardcover)
> by Edgar Brunner (Author), Sebastian Domhof (Author), Frank Langer (Author)
> , Wiley
>
> However, you could always log-transform the ratio data."
>
>
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