I guess I see the issue of the covariable a little differently. The
decision of whether a covariable is used should NOT be based on
whether there are differences in initial size among treatments.
Indeed, the covariable is supposed to account for these differences.
There can be no *effect* of the treatments on initial rhizome size.
Any differences must be the result of chance or a systematic bias in
the manner in which the rhizomes were assigned to the treatments. If
the differences are not significant, then they are likely due to
chance, and one of the purposes of the covariable is to remove this
source of variation from the treatment effect. If the differences are
statistically significant, then likely there has been systematic bias
in the treatment assignment, which violates a critical assumption of
the experimental design. The investigator should seek to identify
this inadvertent bias in the treatment assignment, remove it if
possible, or start over.
The two primary purposes of including a covariable are to account for
any variation associated with initial size that is falsely
attributed to the treatment effect and to remove variation from the
experimental error term, thereby increasing your ability to detect
treatment effects.
The decision to use a covariable should be based on its correlation
with the response variable (rgr) and whether or not it interacts with
the treatments to influence the response variable, not on whether or
not there are differences among treatments in the covariable. If it
is correlated with the response variable, it should be used. If it is
not, then you should avoid using it because doing so removes 1 df
from the error term and reduces statistical power. A significant
interaction between the covariable and the treatment violates an
assumption of ANCOVA. In that case, you should turn your attention to
this interaction and abandon the simple ANCOVA, in which the
interactions are pooled with the error term.
Steve
At 4:58 PM -0400 8/5/09, Peter Gould wrote:
The previous posters made many good points, but I see it a little
differently than Mark. It would be good to measure the weight the
rhizomes before planting and compare the means among treatments. However,
I would care less about the statistical significance of the differences
than the magnitude. You want the differences in initial weight among
treatments to be small, period. Differences among treatments may or may
not be statistically significant owing to the magnitude of the
differences, the variability among rhizomes, and the number of
observations. Your only interested in the magnitude of the differences in
this case.
Cheers,
Peter
--
Department of Biology
PO Box 1848
University of Mississippi
University, Mississippi 38677-1848
Brewer web page - http://home.olemiss.edu/~jbrewer/
FAX - 662-915-5144
Phone - 662-915-1077
