Hi everyone,
Here's a judgment question.
I'd like to know whether or not it is justifiable to convert betas (from 3dDeconvolve) to z-scores? Here's what I did.
First I took each subject's set of betas, and calculated the mean and standard deviation across conditions.
3dMean -prefix ${subject}.mean.beta.blur `ls ${subject}.?.?.beta.blur+tlrc.HEAD `
3dMean -sd -prefix ${subject}.sd.beta.blur `ls ${subject}.?.?.beta.blur+tlrc.HEAD `
Then I took each beta, subtracted the mean, and divided by the standard deviation.
foreach condition (s.1 s.2 s.3 s.4 t.1 t.2 t.3 t.4)
3dcalc \
-a ${subject}.${condition}.beta.blur+tlrc \
-b ${subject}.mean.beta.blur+tlrc \
-c ${subject}.sd.beta.blur+tlrc \
-expr '(a-b)/c' \
-prefix ${subject}.${condition}.z.blur
end
Then, to see how this conversion affected the results, I performed a mixed-effects anova on both the raw values and the z-scores.
raw values
3dANOVA3 -type 4 -alevels 2 -blevels 4 -clevels 40 \
-dset 1 1 1 ${subdir}/s01/h01.s.4.beta.blur+tlrc \
-dset 1 1 2 ${subdir}/s02/s02.s.4.beta.blur+tlrc \
-dset 1 1 3 ${subdir}/s03/s03.s.4.beta.blur+tlrc \
...
-fa TvS \
-fb load \
-fab TvS_x_load \
-bucket ${resdir}/${infile}
z-scores
3dANOVA3 -type 4 -alevels 2 -blevels 4 -clevels 40 \
-dset 1 1 1 ${subdir}/s01/h01.s.4.z.blur+tlrc \
-dset 1 1 2 ${subdir}/s02/s02.s.4.z.blur+tlrc \
-dset 1 1 3 ${subdir}/s03/s03.s.4.z.blur+tlrc \
...
-fa TvS \
-fb load \
-fab TvS_x_load \
-bucket ${resdir}/${infile}
Then I (informally) compared the two.
3dcalc -a H.ANOVA.TvS.load.zscores+tlrc \
-b H.ANOVA.TvS.load.raw+tlrc \
-expr 'a-b' \
-prefix H.ANOVA.TvS.load.diff
Ok so when I do this, I get a pretty dramatic increase in the f-stats, but only in regions where there already seem to be effects.
Comparison Image
The reason why I think there is this increase in power is that I am getting rid of the variation around the grand mean, and just comparing within-cell variability to between-cell variability. I've seen this type of normalization approach used for other types of data (psychophysiology, MEG, fMRI timecourse scaling, etc.), but not really for fMRI betas. What are your thoughts? Does this seem statistically justifiable?
thanks!
-nick