Dear Ged,
DRC SPM wrote:
> On 23/02/06, Will Penny <[log in to unmask]> wrote:
>
>>This bug has been fixed in revision 456.
>
>
> Hi Will, thanks for taking a look at this (and for fixing the masking).
>
> I've just tried this, and while it no longer throws an error, the
> results from a paired test look very different indeed to those from a
> one-sample t-test on difference images created for the pairs.
>
> Mathematically this doesn't make much sense to me, but perhaps I'm
> missing something?
The con images (at the second level) produced by paired t and one
sample t based on difference images should be the same (check this).
This is because the regression coefficient estimates should be the same.
But, the estimation of the error variances will be different. Hence the
statistics will be different.
(Aside: you may wish to use the nonsphericity correction with the
paired t - telling SPM that the within-subject effects are
correlated and have unequal variance. In this case even the regression
coefficients will be different - because SPM will use a weighted least
squares method where the weights are based on the estimated covariances).
But how can these two approaches give different results ?
Well, they do. And each approach is equally valid.
They correspond to two different types of model
(1) partitioned error models (one-sample t based on
difference) and (2) pooled error models (paired t).
This distinction applies to ANOVAs as well as to
data with just two conditions.
Generally, I would favour the partitioned approach - as
only the data immediately relevant to the inference is used.
But others may prefer pooled error, which procedurally
is easier for eg. ANOVAs as you don't have to make a new
2nd level model for every effect you wish to make an inference
about.
For more on this see
http://www.fil.ion.ucl.ac.uk/~wpenny/publications/rik_anova.pdf
Best,
Will.
> There are a few things I'm wondering about:
>
> Contrasts -- one-sample allows only one number, so I pick 1, does this
> sound right? (I was under the impression contrasts had to sum to zero,
no they don't.
> but spm won't let me pick zero, which is the only possibility for that
> constraint here); paired, spm expects two numbers, I choose 1 -1,
> which corresponds to the order that I have subtracted to create the
> difference images.
>
> Parameter estimability -- the one-sample test shows white estimable
> params everywhere; the paired test shows grey everywhere, is this
> correct? Shouldn't the paired test be unambiguously estimable too?
>
> Incidentally, I've written my own simple code to do one-sample and
> paired t-tests on images, and the resulting t-maps are identical,
> whereas the spmTs here are very different.
>
> Yours confusedly,
>
> Ged.
>
>
--
William D. Penny
Wellcome Department of Imaging Neuroscience
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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