Posted by B. Douglas Ward on March 09, 2001 at 11:21:36:
In Reply to: t-test on time series data posted by Jian on March 09, 2001 at 09:43:29:
Jian:
When doing any type of statistical analysis, it is important to understand
what question is being asked, or what hypothesis is being tested.
There are at least 3 different types of questions implied by your message:
1. Is the 'on' state different from the 'off' state for Run #i of Subject #j?
2. Is the 'on' state different from the 'off' state for Subject #j across
all runs for Subject #j?
3. Is the 'on' state different from the 'off' state across all subjects?
These different questions require different types of analyses. To answer
question #1 requires time series analysis. That is, one must take into
account the temporal nature of the data.
To answer question #3 requires (non - time series) statistical analysis.
That is, there is no temporal component to question #3. Some people try to
apply time series analysis in order to answer question #3, by concatenating
runs from different subjects. That approach is WRONG.
The answer to question #2 falls somewhere in-between time series analysis and
(non - time series) statistical analysis. One could apply time series analysis
to the individual runs, and then combine the results; or, one could concatenate
the runs (for an individual subject only!), and apply time series analysis to
the concatenated data.
The AFNI programs provide a logical and convenient division of labor between
programs for time series analysis (3dfim+, 3dNLfim, 3dDeconvolve, etc.) and
programs for statistical analysis across runs and across subjects (3dttest,
3dANOVA, 3dANOVA2, 3dANOVA3, 3dRegAna, 3dMannWhitney, 3dWilcoxon,
3dKruskalWallis, 3dFriedman, etc.). Before attempting to use any of the
above programs, please consult the documentation (see files ending in ".ps").
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Now, for your specific questions. There are several different ways that one
might perform the time series analysis. You could use 3dfim+ to calculate
the correlation coefficient for the ideal function. Or, you could use
3dDeconvolve to calculate the t-stat (or F-stat) using the same ideal function.
I strongly recommend that you use the Deconvolution plugin to plot the fit
on top of the actual time series data. This allows you to interactively change
the model parameters (NFirst, min and max time lags, etc.). Due to the nature
of the hemodynamic response, you may wish to use multiple time lags to model
the system response. When you are satisfied with the model, you can use the
same input parameters to the batch program 3dDeconvolve, to process the entire
dataset. To combine runs for an individual subject, you can use program
3dTcat to concatenate the runs, and then use the -concat option of program
3dDeconvolve. See the 3dDeconvolve.ps documentation for more details.
Now, to analyze the results across subjects, the specific output parameter(s)
of interest (from the 3dfim+ or 3dDeconvolve bucket dataset output) will
have to be converted to Tlrc coordinates first (and perhaps smoothed using
the blurring option of 3dmerge). Then you can analyze the across-subject
data using 3dttest. If you are testing against the null hypothesis that there
is no difference between the 'on' and 'off' periods, then the logical choice
would be to use -base1 0.0.
Doug Ward