The subject is *disordinal* interactions.
Among other things, Don quoted me, quoting him -
On 28 Jan 2001 15:16:27 -0800, [EMAIL PROTECTED] (Donald Burrill)
wrote:
> On Fri, 26 Jan 2001, Rich Ulrich quoted me:
< ... >
> > DB: > Then: a disordinal display -- of what plot? (As remarked in a
> > > thread a year or two ago, an interaction (displayed as a plot of cell
> > > means or of regression lines) may appear ordinal from one direction
> > > and disordinal from the other.)
< snip, comment about a year ago; request for example>
DB: >
> As requested. Consider the two-way table of cell means below:
>
> B1 B2
> A1 10 20
> A2 40 30
>
> 40 - 1 40 - 2
> - -
> 30 - 2 30 - 2
> - -
> 20 - 2 20 - 1
> - -
> 10 - 1 10 - 1
> - -
> 0 ---+------+--- ---+------+---
> A1 A2 B1 B2
>
> Plotting Y-bar vs. A, we have the left-hand diagram (plotting symbols
> are levels of B); plotting Y-bar vs. B, we have the right-hand diagram
> above (symbols are levels of A). The left-hand plot is disordinal
> (B2 > B1 at A1, but B1 > B2 at A2), the right-hand plot is ordinal
> (A1 > A2 at both levels of B).
For 4 independent groups, both left- and right-hand plots are
*disordinal*, by my standards. Here is a criterion I offered a year
ago (Nov 30, 1999, on sci.stat.edu): "IS it, the observed interaction,
an artifact of the strong main effect, combined with bad scaling?"
Neither one above is that sort of artifact.
I used Deja's "power search"
on Disordinal,
in *.stat.*,
before July, 2000,
and that found me the earlier thread. Dennis had provided a plot in
HTML, which I can't read today from Deja, but I assume it might have
been like the above. My comment, back then, was that both plots
showed variables as disordinal. (And I do consider the term to be a
choice, in particular, for 2x2 tables, and not necessarily for larger
ones.)
Now, just lately, we have been talking about Repeated Measures, and
regression to the mean. This calls for some caution in language.
Suppose the design has been grossly improper: it split
the groups on the Pre variable, as in the second plot.
In that case, I would say, "The first suspicion one *must* have is
that the pattern of means demonstrates Regression to the
mean -- and not a single thing more. After that, you can't even look
at the first plot.
The pattern of these means is disordinal, but R-to-the-M is a
*standard* hazard; a new effect (interaction) cannot satisfy Ockham's
razor nearly so well. I am saying: you might have to describe the
means as disordinal, but you could never, fairly, claim that there "is
a disordinal interaction between the variables" until you had ruled
out the argument of R-to-the-M.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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