>If we can move away from the more petty aspects of this discussion
>(i.e., an attempt to score points for/against one's favorite
>statistical package), I think we might discover an interesting
>substantive issue here.
[numerical examples and discussion of contrasts deleted]
>However, modern statistical packages like Statistica, which provides
>very extensive, user-friendly capabilities for examining assumptions
>in the analysis of variance, are moving away from the notion that
>every situation has a fixed "only fair" remedy, that should be fed to
>the user without comment.
>Certainly Bill Gould, in his erudite earlier posting, did not slam the
>door on the "full data hypothesis" contrast.
>Gould wrote:
>>What do YOU mean by a main effect?
>>
>>The language of ANOVA, once we move from simple cases, is insufficiently
>>precise. It leaves room for honest statisticians to disagree as to
>>what the linear hypothesis ought to be corresponding to the vague words.
>>
>>Stata, SAS, and the rest have one definition.
>>
>>Statistica has another.
A historical note might be in order for this discussion. Fisher
hated ANOVA and frequently warned of its dangers. He wrote that
ANOVA was nothing more than a convenient way of arranging the
arithmetic. If Fisher and his colleagues had access to modern
computing, specifically something that could do, say, a QR
decomposion, ANOVA wouldn't have ever happened. We would all be
specifying our contrasts and testing them in the context of the
general linear model instead of running some canned ANOVA
program. The dangers, which Fisher foresaw, are that concepts
like "main effects" and "interaction" (as Gould has clearly noted
in this discussion) are slippery outside the context of balanced
designs with no empty cells. I'm amazed that we continue to
confuse ourselves with these slippery concepts. I think we would
be better off if all packages got rid of their anova programs.
Now that we have computers we no longer need the convenient way
of arranging the arithmetic.
Gary.McClelland@Colorado.edu
Psycholgy, Univ of Colorado