[R-sig-ME] Standard errors of variances; negative variance

[John H Maindonald]

What I am saying is that if in a randomized  block design blocks are 
chosen to be overly heterogeneous, the within blocks component 
of variance will be exaggerated, and the between blocks component
reduced accordingly. A consequence is that the variance components
apply only to the particular layout of blocks and of plots within blocks
used for that particular experiment.  

There may in such cases be ways to use the data, together with what 
one knows of the field layout, to get a wider perspective on what the 
data may have to say. One is then moving outside of the confines of 
the analysis that gave the problematic “variances”, whether negative 
or just distorted.  These sorts of issues carry over in different ways to
different contexts.

John Maindonald
Statistics Research Associates, Wellington NZ.