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

From: Mike Lawrence <Mike.Lawrence_at_dal.ca>
Date: Mon 03 Oct 2005 - 09:00:54 EST

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@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

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