Re: repeated measures custom contrasts for linear trends

Posted by Richard Ristow on Feb 07, 2007; 9:43pm
URL: http://spssx-discussion.165.s1.nabble.com/repeated-measures-custom-contrasts-for-linear-trends-tp1073671p1073675.html

I realized this has been tickling at the back of my skull since you
posted it.

At 08:27 AM 2/5/2007, Paul Mcgeoghan wrote:

>The Tests of Within-Subjects effects Greenhouse-Geisser is significant
>.040 and Huynh-Feldt is significant .027 for the MOVES*IAC interaction.
>
>The Tests of Within Subjects Contrasts indicates a significant cubic
>effect (.039) for MOVES*IAC.

That *may* mean what it says it means, but I recommend caution  in
interpreting higher-order polynomial effects, unless you have a lot of
data with good resolution.

On a quick glance through your postings, I don't see your sample size;
but for this, it should be *BIG*. (How many degrees of freedom in your
model? I'm being sloppy here, but isn't it about 30?)

If I understand what you're seeing, it's that, having found the
best-fitting polynomial with the 10-level interval variable MOVES
within each of the three levels of IAC, the cubic terms of these
polynomials differ significantly between levels.

It takes a lot of discriminatory power to even 'see' a cubic term.
Think like this:

. The linear term is what we all know and love: an effect that plots Y
vs. X as (surprise) a straight line.

. The quadratic term may measure a U-shaped effect: Y is high at the
extreme values of X, low at the intermediate values. (Look for this if
the linear term is small.) Or, it may mean an accelerating or
decelerating effect: the effect of the same change in X is considerably
larger at one end of the scale, than at the other. (This will usually
go with a significant linear term.)

. The cubic term is acceleration or deceleration at the scale
*extremes*: the effect of changes of X on Y is higher (or lower) near
both extremes of the scale, than near the middle.

(All this assumes that if any polynomial term is in the model, all
lower terms are as well. That is standard practice, and strongly
recommended.)

If I saw what you're seeing, I'd inspect very carefully: for each level
of IAC, plot your independent (MOVES) vs. the polynomial in variable
'trial' (WS factor, move number 1-10). Since it looks like you have an
ANOVA-like problem, i.e. multiple observations per cell, you'd want the
mean value of MOVE with a standard-deviation error bar, at each point.

I'd watch, specifically, for very large values ('outliers') in data for
the higher or lower move numbers. Following current statistical wisdom,
'outliers' are not to be rejected out of hand. But they're to be
inspected carefully, lest they be simply wrong - blunders in
measurement or data entry.

Real 'outlier' values are, well, real, and must be accounted for in
analysis. But there's always question whether they're a atypical from
the influence of some important unobserved effect.

At best, a small fraction of vary large values raises Cain with the
estimation robustness of any linear model.

-Cheers, and good luck,
  Richard