Steve Fromm <[log in to unmask]> said:
> There is frequent use of the term "omnibus" (as in "omnibus
> statistic") in the SPM literature.
> Does this term have a precise definition?
My copy of Chamber's Twentieth Century Dictionary (of the english language)
includes a definition of "omnibus" as an adjective meaning 'widely
comprehensive; of miscellaneous contents'. In this case there is an omnibus
meaning of 'omnibus'!
In SPM it is used in two broad senses:
[1] The first, more classical sense, originates in the Analysis of Variance
(ANOVA) of a designed experiment, where the Ftest for the effect of a factor
A with more than 2 levels (say k) is often described as an "omnibus" Ftest. I
think the usage of this term can probably be traced back to R A Fisher in the
1930s.
The reason for this name is that the test includes all the possible contrasts
and comparisons involving the different levels of the factor A. The numerator
sumofsquares of the F statistic is the total of the sumsofsquares for any
complete set of (k1) orthogonal contrasts between the k levels of A.
More generally the term 'omnibus F test' gets applied to any situation where
the numerator degrees of freedom of the F statistic are greater than 1 (e.g.
effects of interest including conditions and covariates).
Here is an example from [log in to unmask] where it is used in this sense:
(From http://www.mailbase.ac.uk/lists/spm/199807/0118.html )
 I'm not sure about the meaning of the SPMF map page after the Design
 Matrix prompting in SPM Statistic. Does it represent the result of the
 test of significance of the equality of variances between pixels or
 something else?
It's an "extrasumofsquares" Ftest, assessing the additional
variance accounted for by the effects of interest (condition effects,
covariates of interest) after accounting for the effects of no interest
(nuisance covariates, subject block effects, global effects). As such
it's an omnibus test for all possible contrasts of the effects of
interest, answering the question "do the effects of interest model
anything?"  i.e. "is there any evidence of effects of interest".
(end of example)
The book 'Human Brain Function' (Frakowiak et al. 1997) also uses the word in
this sense in the phrase 'omnibus hypothesis' (p. 81).
[2] However the term gets used in a broader way in the SPM discussion list and
in SPMrelated publications. Here it can mean 'a statistic/test for a null
hypothesis of no effect anywhere in the whole brain vs. some effect
somewhere', by contrast with a more regionally specified null hypothesis.
This is of course the heart of the 'statistical parametric map' philosophy: to
take the voxel based statistic (F, t, Z, extra sumof squares, chisquared or
whatever) and consider the resulting 'field' (statistical parametric map).
Typically one of two things is than done. Either [2.1] seeing whether there
are any voxels for which the height of the field is significant at a level set
so the probability that there is one or more such voxels is less than a chosen
alpha (op. cit. p. 89); or [2.2] applying a more globally based appraisal of
the field (e.g. spatial extent combined with height) (pp. 8997).
I append three examples from [log in to unmask]:
(Example from http://www.mailbase.ac.uk/lists/spm/199907/0118.html)
> I believe that the setlevel analysis implemented in SPM96 is similar
> to, but not the same as, the MSOS [mean sum of squares] test described
> by Worsley. This appears to be particularly true when k=0. As I am
> using SPECT data, where f<1, this is the prefered level of k for
> setlevel inferences, if I understand Friston et al. [Neuroimage 4,
> 22335, 1996].
Yes indeed. The setlevel inference (with k = 0) is a nice omnibus test
that pertains explicitly to the set of suprathreshold clusters (that
can then be tabulated). The MSOS is an alternative omnibus test that
was motivated by the detection of diffuse (less regionallyspecific
effects). These effects cannot be described very concisely because
they are distributed throughout the brain.
(Example from http://www.mailbase.ac.uk/lists/spm/199902/0017.html)
In another study with apriori anatomical hypotheses, I have used SPM
without correction for multiple comparisons, and used permutations for
the omnibus test of significance (based on the number of suprathreshold
clusters). Region of interest tests were then used for localization. And
all was fine!
(Example from http://www.mailbase.ac.uk/lists/spm/199901/0017.html)
1) Many people reference Bailey et al (1991) in setting a height threshold
of p < .001, uncorrected, to reduce risk of false positives with an omnibus
test. Should one assume that this is adequate and that, having rejected
correction, one should use the SPM96 default extent threshold of p = 0.5?
Conclusion: 'omnibus' is used by people discussing SPM to mean 'with respect
to multiple parameters' and/or 'with respect to the whole brain'. This is
confusing. I suggest it is restricted to the former (classical) meaning as
used more widely in statistics, and that an alternative term (e.g. 'global')
is used for the latter sense. Then we can speak unambiguously of 'global tests
of contrast activation represented in a tfield' and 'global test of the
effects of interest represented in an omnibus Ffield'. Better than an
'omnibus omnibus test'!
Ian

Ian NimmoSmith
MRC Cognition and Brain Sciences Unit
15 Chaucer Road
Cambridge CB2 2EF
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