The Gardner and Eberhart Analyses II and III
for Diallel Crosses of Non-Inbred Populations: 
What's Going On?

Leigh Murray

New Mexico State University

      Gardner and Eberhart (1966) proposed three analyses for data
taken from diallel cross experiments when there are a fixed set of
random-mating varieties or homogeneous lines as parents.  Analyses II and
III have traditionally been recommended when parents constitute
non-inbred populations (such as in alfalfa).  As with many analyses written
before the advent of easy computing, the Gardner and Eberhart paper
provides a "cook-book" method of sequentially fitting models to obtain
sums of squares and F-tests, without also providing a clear,
parameter-based explanation of what the various quantities estimate and
test.  This lack of clarity is exacerbated by the use of non-full rank effects
models.

      This talk discusses estimates and tests of hypotheses obtained from
the two analyses from the standpoint of the full-rank cell-means model.