The other day Rik Henson posted this RE testing 1 patient versus a group
(1-sample t-test at the second level):
post:
http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0704&L=SPM&P=R7490&I=-3
See:
http://www.mrc-cbu.cam.ac.uk/~rh01/singlepatient.pdf
Hope that helps to solve (part of?) your problem.
Most articles describing between-group studies with unequal sample sizes
seem to use permutation tests at higher levels. Might be worth a try...
best
Alle Meije
James Rowe wrote:
> Your reviewer wonders whether SPM2 can compare 2 vs 16. Clearly it can
> do so, since you have done it. The question is whether it is optimal to
> do so. There are alternative models, for example:
>
> 1. one 2 vs 16 2-sample t-test as you have done.
> 2. two separate 1 vs 16 2-sample t-test, treating the patients as a case
> and replication, with each patient group having n=1. (note that this is
> not the same as a one-sample t-test of the differences between your
> patient and each control: this should be avoided)
> 3. a 1x3 anova, with groups 'controls n=16' vs 'patient n=1' vs 'other
> patient n=1', enabling you to look at individual or averaged
> differences between patients and controls.
>
> The choice depends on the inferences you wish to make, the flexibility,
> and the assumptions you are prepared to make. For your model, you
> should be able to state that the first level models for patients were
> similar to controls, in terms of number of scans, covariates and
> residual variance, since large differences in the first level (e.g. due
> to many more patient errors or worse patient movement) would undermine
> the assumptions behind the two-step random effects approach used in
> SPM2 (since it is not a true mixed effects model). With your 2 vs 16
> model in SPM 2 you are assuming that the {expected} error variance of
> you patients is not different from the control group. This might be
> contributing to your reviewer's unease. If you want to avoid many of
> these assumptions, you could have a look at SnPM3. Or to allow for
> unequal variances you could look at SPM5.
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