Dear Joseph,
At 10:01 25/01/99 -0500, Joseph Tracy wrote:
| I have SPM z score volumes on 5 individuals, each z score volume
| resulted from the identical contrast following the same experimental fMRI
| run. Each individual's z score volume has also been rethresholded. I
| want to create a group volume.
|
| Is it valid to just average across individuals and create a mean z score
| volume?
|
| Other methods such as summing the z volumes and dividing by
| square root of k have been suggested to me (k represents the number
| of z score maps, which in this case would be 5).
Just to clarify Eric, Tim & Cathy's answers to this question (answers
repeated below): Both are right! There's no confusion, just that Tim and
Eric are answering different questions: In combining the evidence from a
small group of subjects by combining their SPM{Z}'s, you're looking at the
average significance of an effect *for these subjects*. What Eric is noting
is that this doesn't account for having sampled those subjects from a wider
population, so inferences cannot be extended to the population.
Unfortunately, numerous subjects are required to deduce a population mean
effect. Even if there is an overall effect (either for the group or the
population) this doesn't mean that every individual subject will show an
effect. The conjunctions approach Cathy outlines looks for areas where all
subjects in the current group have an effect. If interest lies in whether
or not an individual exhibits the effect (at a given threshold), rather
than the average population effect, then this conjunction approach can be
used to estimate the proportion of the population showing the effect (paper
in submission).
Some of this has been discussed before on the list, in more detail, and I
encourage you to re-read the thread:
http://www.mailbase.ac.uk/lists/spm/1998-07/0026.html (Russell Poldrack)
http://www.mailbase.ac.uk/lists/spm/1998-07/0027.html (Russell Poldrack)
http://www.mailbase.ac.uk/lists/spm/1998-07/0028.html (Jonathan Raz)
http://www.mailbase.ac.uk/lists/spm/1998-07/0032.html (Jonathan Raz)
http://www.mailbase.ac.uk/lists/spm/1998-07/0034.html (Andrew Holmes)
(The possibility of "performing a t-test on z-scores" that Eric mentioned
is also discussed here. It's subtly different to the random effects
approach, in that it assesses population average significance rather than
population average effect size.)
Incidentally, both your methods are the same: Averaging (independent)
standard normal N(0,1) observations gives a normal variate with mean zero
and variance 1/k. Summing them and dividing by sqrt(k) (as opposed to k as
with the mean approach) gives standard normal variate. (The multi-subject
correlation module in SPMclassic used this approach.) Further, this
approach will be the same as the sum of square z approach using a
chi-squared distribution.
Lastly, I should point out that the SPM{Z} from SPM is not a "Z-score" map.
Whilst the voxel values do have a standard normal distribution under the
null hypothesis, they are derived from t-statistics using a probability
integral transform. Z-scores are normalised observations.
Hope this helps,
-andrew
At 11:42 25/01/99 -0500, Timothy M. Ellmore wrote:
| A method for combining several individual Z-score maps to create
| a group statistical map is described in:
|
| Clark VP, Maisog JM, Haxby JV. fMRI Study of Face
| Perception and Memory Using Random
| Stimulus Sequences. J. Neurophysiology
| 79:3257-3265, 1998
|
| The authors make use of fact that the sum of squared Z score values
| has been shown to have a chi-square distribution. For more information
| on that derivation see:
|
| Hugill, MJ. Advanced Statistics. London: Bell and Hyman, 1985.
At 12:03 25/01/99 -0500, ERIC ZARAHN wrote:
| This z^2 method is not valid for testing population means
| as it in no way takes into account between subject variability
| (or sign of the effect). What it would seem to test is the null hypothesis
| that the null is true in each and every subject. Note that
| this is not the same as testing the hypothesis that the population
| mean activation is different from zero (which is implemented in
| the 'SPM Random Effects Kit' by Andrew Holmes).
| The other method suggested (of performing a t-test on the
| z-scores) would be an appropriate way to test the hypothesis about the
| population mean (if the z-scores are iid Gaussian random variables).
| This is similar to the method used in Andrew's algorithm.
At 13:33 26/01/99 +0000, Cathy Price wrote:
| To create an SPM which represents what is common to a group of individuals,
| we find conjunction analyses with masking very useful. To use conjunction
| analyses all subjects are entered into the same statistical model but the
| parameters for each subject are estimated independently in a subject
| seperable design matrix. You then enter your contrasts seperately for each
| subject.
|
| To identify areas where there are consistent effects for each subject, you
| do a conjunction of the 5 contrasts (one for each subject). This will sum
| over the effects and eliminate any significant interactions. To ensure that
| the individual effects are significant for each subject, you can also mask
| the conjunction with each of the 5 contrasts. The resulting SPM will
| display only those voxels that are significant for each subject.
| If you had more subjects an alternative approach would be to use a random
| effects analysis. This allows you to make generalisations to the
| population but does not determine the consistency of your activations.
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