Dear Jérôme,


Sorry I didn't see your earlier message - have been having major Outlook trouble.

Just to add to the pointers you've already received, you are in a fortunate and privileged position because you (should) have a large control group (39 when I left?). This will enable you to empirically test what the 2-sample t-test does with your data - if you compare each control against the remaining ones, you will get a proportion of false positives; if it is around 5% my interpretation would be that your assumptions about data distribution normality hold.

The procedure also gives you a good feel for what the resulting SPMs normally look like (remember not to use any extent thresholds); to detect any possible remaining artefacts in your control group; and my experience has certainly been that patients are often unequivocally different from controls...

Good luck and see you soon,

Alexander



-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Roberto Viviani
Sent: 29 February 2008 14:41
To: [log in to unmask]
Subject: Re: [SPM] patient vs group of normal subjects

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
>
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