Hi Luca,
I have used SPM8 to compare single subject FDG PET scans to a control dataset. I used a 2-sample t-test with one group comprising the single subject scan and the other group comprising the control dataset. Initially I set variance to "unequal" and MatLab returned an error. Previous posts on the listserve have said to set variance to "equal" with this kind of analysis and sure enough this works!
I am hoping the SPM gurus will answer your question because like you I never really understood how it makes sense for there to be variance when one group has only one data point. I get the feeling I am exposing my incomplete grasp of SPM methodology but I'd appreciate if somebody could help me understand this. I suspect variance has a different meaning in this context.
Cheers,
Kevin
-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Luca Presotto
Sent: Tuesday, 19 January 2016 22:02
To: [log in to unmask]
Subject: [SPM] Two groups t-test with 1 scan in one group. SPM 5 vs 8
Dear experts,
We are using SPM to compare the PET scan of a single patient against a large database of normal subjects. This has been going on for a long time, and we have been updating a batch that was originally written in SPM99. Currently we use SPM5. I'd guess that the correct statistical test to perfom in this case would be a z-test, i.e.: seeing if a subject is significantly outside of the controls' distribution.
However, for reasons that nobody here seems to know, the "routine" batch uses a two-groups t-test with the variance set to "unequal". Obviously, I can't even try to guess how you could perform an unequal-variance t-test if one group has only a single data point in it. The thing is that SPM99 and SPM5 provide a result. SPM8 instead gives error. (when you pick "results" matlab prints red lines mentioning the inability to set axes to NaNs and Infs.) As you would expect!!! What's the variance of a single data point??
So, what I did to test everything out was taking an atlas, adding a random number with mean 0 and sigma 1 to the whole area and saving 100 such random "scans". Then I generated a scan adding 5 to this atlas. I first performed a two groups t-test with equal variance in spm5 and spm8. Both versions give a design matrix which is [1 0;0 1] and the spmT image is an uniform "5". Perfectly, as expected! If I select "unequal" instead I get an undisplayable design Matrix ("image CData cannot be complex") and I cannot even define contrasts to compute the con or spmT files in SPM8. In SPM5 I get a uniform spmT with a value of 16.19, and the design Matrix is [0.99 0;0 3.30]. I've briefly looked at the database of past scans and it initially appears that all of ours design matrixes have these values.
Does anybody have a clue about how SPM5 (and 99) were computing t-values under these (admittedly weird) assumptions?
Thank you,
Luca
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