[R] What is Mandel's (Fitting) Test?

[Mike Lawrence]

Hello everyone,

A little background first:
I have collected psychophysical data from 12 participants, and each
participant's data is represented as a scatter plot (Percieved roughness versus
Physical roughness). I would like to know whether, on average, this data is
best fit by a linear function or by a quadratic function. (we have a priori
reasons to expect a quadratic)

Some of my colleagues have suggested the following methods of testing this:
1. For each participant, calculate the r-square values for linear and quadratic
fits, z-transform the resulting values. Collect these z-transformed scores and
then perform a dependent t-test across participants. If significant, then a
quadratic fits better.
2. For each participant, calculate the amount of variance left over from the
linear fit that is accounted for by the quadratic fit. Perform a one-sample
t-test to see if this population of scores differs from zero
3. Same as #2, but z-transform before performing the t-test.

However, I'm sure that these tests fail to take into account the fact that a
quadratic function will generally have an advantage over a linear function
simply by dint of having more terms to play with. So I've been looking for a
test that takes this advantage into account and I came across something called
the Mandel Test. It is available in the quantchem package, but the manual
contains a very meagre description of it's details (assumptions, etc).
Furthermore, besides biology/chemistry papers that reference it in passing,
I've been able to find only one reference online that addresses it's use
(http://www.econ.kuleuven.be/public/ndbae06/PDF-FILES/vanloco.doc), but even
then it lacks specificity.

So the question is, what is the Mandel Test? What are the assumptions and
limitations of the test? Does it sound appropriate for my purposes (if not, how
about the other tests suggested above)? How does it differ from the Lack-of-Fit
test?

Any help would be greatly appreciated.

Cheers,

Mike

-- 

Mike Lawrence, BA(Hons)
Research Assistant to Dr. Gail Eskes
Dalhousie University & QEII Health Sciences Centre (Psychiatry)

Mike.Lawrence at Dal.Ca

"The road to Wisdom? Well, it's plain and simple to express:
Err and err and err again, but less and less and less."
- Piet Hein