Posted by B. Douglas Ward on February 19, 2002 at 15:32:42:
In Reply to: Re: 3dttest input posted by Steve Roys on February 19, 2002 at 10:45:27:
Hello Steve:
" ... And please be gentle with me, I'm not a Statistician...yet."
Sorry, I can't be gentle. The life of a Statistician is nasty, brutish,
and short. So, get used to it.
Okay, seriously ...
There are several caveats:
1) Never concatenate time series data from different subjects.
2) Be very careful when concatenating time series data from a single subject.
I think it is very dangerous to do a t-test (paired or unpaired) across
different time series datasets (runs). Even if the mean and linear trend have
been removed, how does one avoid accidental confounding of the effect that
is of interest with a "run" effect? That is, if the t-test finds a significant
difference, is this due to the different test conditions, or are the datasets
simply different (irrespective of the test conditions)?
A paired t-test might make sense in the context of comparing different test
conditions within a run (or randomly intermixed across several concatenated
runs), if, for example, one is concerned about variation in the common
response over time. In this case, pairing the data points may yield increased
statistical power, by subtracting out this common variation.
It would probably be best to detrend the time series datasets first (see
program 3dTcat). Then use program 3dcalc to calculate the differences at
the paired time points:
3dcalc \
-a "myData+orig[5,13,27,36,42,55,67,...]" \
-b "myData+orig[8,15,22,33,46,57,64,...]" \
-expr "b-a" -fscale \
-prefix myDiff
The individual time points must be listed in the order corresponding to
their pairing. Now, use 3dDeconvolve to determine if the mean difference is
significantly different from zero:
3dDeconvolve \
-input myDiff+orig \
-polort 0 \
-tout -bucket myPairedTtest
The output bucket dataset, myPairedTtest+orig, will have 2 sub-bricks.
The contents of the sub-bricks are:
Sub-brick #0 -- Mean of paired differences
Sub-brick #1 -- t-stat for paired differences
Doug Ward