Dear Francesca,
> we're attempting to conduct a parametric analysis.
> We have two condition A(experimental condition) B(control condition); in the
> experimental condition the parameter assumes 3 different values.
> 1) Which is the difference between choosing a polynomial or a linear
> relationship in the model?
A linear model is simply a polynomial model with 0th and 1st order
terms. Any curvilinear relationship between evoked responses and
the parameter of interest would require 2nd or higher order terms
to be modeled.
> 2) In the results session how can we specify the contrast for the AB
> difference? and for the parameter effect on the experimental condition?
Simply test for the [polynomial] coefficients one by one. The 0th
order term (e.g. [1 0 0]) models the mean difference between A and B
averaged over the three levels. The 1st order coefficient (e.g. [0 1
0]) reflects the linear dependency on the parameter and the 2nd (e.g.
[0 0 1]) or higher reflect the nonlinear components. The 0th order
term is the conventional box-car or condotion-specific effect modeled
in simple, non-paramteric analyses. Note that because you only have 3
levels in condition A a 2nd order model is the highest you would
consider (- a parabola can join three points together).
I hope this helps - Karl
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