Andrew Holmes wrote:

> 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!

Thank you for this help, both Eric & Andrew.

I was using the F-contrast you pointed out Andrew, i.e. two contrasts ...1 0
.... & .... 0 1 ..... not ..... 1 1 ....

The actual problem is more complex in fact (isn't it always) in that there are
2 conditions and 7 covariates that may be involved in modelling the data.  I
had hoped to use the F-contrast to refine the design matrix and throw out the
covariates with little or no explanatory power.  Obviously with only 144 images
(from 12 subjects) this many covariates rather eats up the degrees of freedom
(only 34 left).  If I understand correctly, reasons for non-significant F tests
of these covariates (either singly or in groups) include i) the covariates
specified have little explanatory power for the data.  ii) with so few degrees
of freedom left the effect would have to be big to be seen so I am at risk of
throwing out covariates which are useful based on an F test with all the
covariates and conditions in the design.  If so, any suggestions for a better
way of doing this?

Much obliged.

Mark



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