On Wed, 24 Nov 1999, Rich Ulrich wrote:
> On 23 Nov 1999 13:40:34 -0800, [EMAIL PROTECTED] (dennis roberts) wrote:
>
> My Newsreader invoked HTML-reading to show Dennis's post to me, but
> it saved me the problem of deleting it all, by dropping it.
>
> 1) Dennis, please don't post in HTML.
> 2) Why did you write out all the data, when illustrating the problem
> only uses the 2x3 set of means?
Thanks, Rich; I cannot read HTML at all, and could only
decipher the first sentence of Dennis' post.
> 3) ... data are supposed Disordinal if plotted one way "Ordinal" if
> the other. Well, I hardly ever use the terms,
I consider them unhelpful at best, myself.
>From the perspective of one sort of purist, I suppose it could be argued
that plots of the kind being discussed are not really "interaction plots"
at all, in the sense of "plots displaying the interaction effect".
What they are, are plots of observed cell means when interaction is
present, and they can be "ordinal" (or, as Karl points out, "monotonic")
only in two-way designs and only when (1) at least one main effect is
also present and (2) the two main effects are different (that is, one's
bigger than the other).
If one were ever in the business of displaying the interaction effect
itself (that is, what one has left after removing the main effects from
the cell means), the plot would necessarily be "disordinal" (etc.) from
any point of view -- that is, from any choice of axes.
[One might even coin a truism:
in the absence of main effects, all interactions are disordinal.
Doesn't fall quite so trippingly off the tongue as
"In the dark, all cats are grey", but one can't have everything ...]
Of course, it is nearly always easier to _interpret_ the results of an
analysis (when interaction is present) using plots of the observed means
-- the "pure interaction" is, so to speak, one step removed from reality
(or from what most people can see), and is often not really what the
investigator (nor his audience) find useful to converse about.
I might be more impressed with the idea of "ordinal" and "disordinal" if
either I could see a useful application of them in interpreting two-way
data (I cannot see reporting to a client that in his data the interaction
is ordinal (or dis-); he'd just ask what the %#& I meant by that, and
I'd have to describe the shape of the interaction-cum-main-effects in
_useful_ terms), particularly in two-way data of designs larger than
2x2; OR if anyone could describe (with illustrative, if possibly
fictional, data) the use of those terms in a three-way (or higher)
context of any kind.
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
