Hello,
I've read several posts from the archives related to the statement on
the FSL website that in a design with three levels of stimulation, the
contrast "[-1 1 0] shows where the response to level 2 is greater than
that for level 1" and "[-1 0 1] shows the general linear increase across
all three levels."
i.e.,
https://www.jiscmail.ac.uk/cgi-bin/webadmin?
A2=ind0901&L=FSL&D=0&1=FSL&9=A&I=-3&J=on&d=No+Match%3BMatch%
3BMatches&z=4&P=214931
and
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind06&L=FSL&D=0&P=1810746
Perhaps it is a matter of what is meant by a "linear" trend, but after
reading these posts, I'm still confused about the interpretation of
these contrasts in the case of 3 levels. (A related question came up on
the SPM list recently, so I'm trying to understand the previous FSL
posts on this matter).
First, how is it that the contrast [-1 1 0] is simply checking for lev 2
greater than lev 1 (and not saying anything about lev 3), whereas [-1 0
1] somehow checks for a "linear increase across all three levels"? That
seems to be an inconsistency in interpretation that doesn't make sense,
given that all you are doing is moving the position of the "0" in the
contrast.
Second, in the example that was provided, it was stated that if you plot
x=[1 2 3] vs. y1 = [1 4 3] and y2 = [1 -4 3] that "you would still draw
exactly the same regression line". While that statement is true in the
sense that the regression line of x vs. y1 and x vs. y2 will both have
positive slope, the r-squared of the best (least squares) fit is
certainly dependent on the value of all elements of the y vector, and
thus, at least in the sense that I think of a "linear trend" it is not
the case that the "second point carries no information about the
presence or absence of a linear trend".
Any elaboration on these previous posts (or this issue in general) would
be very helpful!
thanks,
-Mike H.
--
Michael Harms, Ph.D.
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Conte Center for the Neuroscience of Mental Disorders
Washington University School of Medicine
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