My thanks to Douglas Bates and others for pointing out ANOV's limitations.
Now the question is how to put my new won knowledge into practice.
Before my eyes were opened
   if row effect and interaction were both statistically significant
   I would report the row effects separately for each column.

Now
   if row effect and interaction are both statistically significant
   i'll realize this may simply be a matter of the test statistics being
interdependant (though I might still report the column effects separately
if, say, one column was different--in a practical sense--from the rest).
   if neither row nor column nor interaction effects are significant, I'll
attribute the result to too small a sample.

(As far as higher-order interactions go, I never really had a clue as to
what they were about anyway.)

Phillip Good

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