On Fri, 26 Jan 2001, Rich Ulrich quoted me:
> DB: > What most people who use "ordinal" and "disordinal" seem to mean
> > is a plot of the cell means (or of regression lines), with no
> > adjustment for main effects: so, a display that includes the
> > interaction AND the main effects. I take it that's what you mean
> > here.
and replied:
> Yes. Just like "most people," I use the definition that has draws a
> distinction, instead of the one that does not. Why do you prefer the
> one that does not?
Mostly because that was the formal definition given in the textbooks I
learned from, donkey's years ago... and because I think it useful to be
able to distinguish between main effects and interactions (an interaction
being a systematic effect among cell means (in ANOVA) that is not
accounted for by the main effects in the design; a corresponding
definition can be written, mutatis mutandis, for regression contexts).
> 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.)
> - I remember someone claimed that. (Oui, moi. -- DB)
> I remember an example that failed to make the point. I don't
> remember a valid example, or that the point was generally accepted.
> - I hope this is not a failure of my memory. But if it's my problem,
> I hope you will reproduce the illustration, or cite it somewhere.
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).
Rich continues:
> The only effect that is never potentially artifactual is the crossover
> of the means, the Disordinal interaction (as most of us define it).
I take it you must mean, whenever an interaction plot is disordinal in
any orientation? I have some mild difficulty with this, since AFAIK the
idea of "(dis)ordinal" has not been extended beyond two-way interactions,
and more complex situations may well be of interest...
> That one that can't be explained as measurement error (such as,
> strong regression owing to poor reliability); scaling (such as,
> ceiling effects); or "regression" towards the conditional expected
> values (such as, the real-life example I just cited).
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
Department of Mathematics, Boston University [EMAIL PROTECTED]
111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
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