This rather noddy two-pager might also help:
http://www.mrc-cbu.cam.ac.uk/~rh01/singlepatient.pdf
Rik
Roberto Viviani wrote:
> Hallo Jerome,
>
>> Is "2-sample t-test" valid as the variance for the single patient is
>> not estimable?
> yes.
>
> If y is your patient piece of data, and x the data from the control
> sample, then under the null hypothesis and standard modelling
> assumptions, y ~ N(m, sigma_square), x ~ N(m, sigma_square), and
> average_x ~ N(m, sigma_square/n), where m is the mean under the null,
> n the size of the control sample (16 in your case), and N is the
> normal distribution. Under the null hypothesis, the variate y -
> average_x ~ N(m - m,sigma_square + sigma_square/n) = N(0, sigma_square
> * (n + 1) / n), and if you replace sigma_square with the variance
> estimate from x you have Student's t instead of N with n - 1 df (one
> df goes into estimating the mean of the x).
>
> If you put your data (x,y,n etc.) into the formula for the 2-sample
> t-test you see that you get a formula algebraically equivalent to the
> one above, t(0, sigma_square * (t + 1) / n), after some simple
> manipulation.
>
> Beware that this test is extremely unbalanced because one of the two
> groups has size 1. You'll have heard that unbalancedness leads to
> skewness being retained in the estimate etc. This is because you can't
> rely much on the central theorem to get closer to normality
> assumptions, since the distribution of y - average_x is dominated by
> the distribution of y (I mean, in terms of skewness and kurtosis). y
> is, so to speak, an outlier with high leverage. Hence, your test is
> rather vulnerable to departures from normality assumptions.
>
> All the best,
> Roberto Viviani
> Dept. of Psychiatry III
> University of Ulm
>
>
> Quoting Jérôme Redouté <[log in to unmask]>:
>
>> Dear SPMers,
>> We would like to compare FDG-PET scan from 1 patient to a group of
>> normal subjects (N=16)
>> Which model should we use (with SPM5) to do such a comparison?
>> Is "2-sample t-test" valid as the variance for the single patient is
>> not estimable?
>> Thanks for your help
>> Jerome
>>
>> --
>> ===============================================================
>> Jérôme Redouté
>> CERMEP - Imagerie du vivant
>> Centre d'étude et de recherche multimodal et pluridisciplinaire
>> 59 Bd Pinel
>> 69667 Bron - FRANCE
>> tel : 33 (0)4 72 68 86 13 (bureau)
>> tel : 33 (0)4 72 68 86 00 (standard)
>> fax : 33 (0)4 72 68 86 10
>> ===============================================================
--
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Dr Richard Henson
MRC Cognition & Brain Sciences Unit
15 Chaucer Road
Cambridge
CB2 7EF, UK
Tel: +44 (0)1223 355 294 x522
Fax: +44 (0)1223 359 062
http://www.mrc-cbu.cam.ac.uk/~rik.henson
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