Dear Mark,
At 12:38 25/05/99 -0400, ERIC ZARAHN wrote:
| At 15:29 25/05/99 +0100, Mark Daglish wrote:
| > I entered an F-contrast with 2 covariates speficied, and got no areas
| > coming out with corrected significance. I then entered a further
| > F-contrast with just 1 of these 2 covariates specified and found a
| > significant cluster. I thought that an F-contrast with the 2
covariates
| > would pick up any contribution from either of them, in which case one
of
| > them alone being significant should mean that the combination should
| > show significance, yes?
|
| No, the p-value associated with an F test will
| not necessrily get larger as you add covariates of interest. This is
| because the (standardized) effects from these covariates get effectively
| averaged in the numerator of the F-statistic. And of course adding
| new numbers to a sample (even if all of the numbers are constrained to be
| positive) will not necessarily increase the sample average.
An additional operational thought occured to me: If you have a model with
two covariates, an F-contrast assessing whether they together explain
anything would consist of *two* contrasts:
1 0 ...
0 1 ...
(assumming the parameters associated with the two covariates are estimable)
These contrasts are saying i) is parameter 1 zero *and* ii) is parameter
two zero, so the F-test is testing for any evidence that either parameter
is significantly different from zero (positively or negatively).
Wheras [1 1 ...] merely assesses whether the average slope is significantly
different from zero (in either direction).
Clearly the two are assessing rather different hypotheses!
Not implying that you're confused! ...merely using the example for didactic
purposes! The F-contrasts are extremely flexible tools, which
Jean-Baptiste introduced into SPM. I think we'll hear a lot more about
them!
----------------
Hope this helps (someone)
-andrew
+- Dr Andrew Holmes ------------------ mailto:[log in to unmask] -+
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