1. A Nonparametric approach…

2. randomise V5 PET activation experiment… i B A 1 2 3 4 5 6 7 8
difference i B A 1 2 3 4 5 6
6 BA…
randomise 7 8 9
6 AB…
10
11
12
12 subjects
mean difference
variance
t-statistic =

3. …example H0: scan would have been same whatever the condition
labelling as active or baseline arbitrary
re-label scans  equally likely statistic image
consider all possible relabellings (exchangability)
permutation distribution
of each voxel statistic ?
of maximal voxel statistic

4. mean difference
mean difference
variance
smoothed variance
“pseudo” t-statistic
t-statistic

5. SnPM with “pseudo” t-statistic
permutation distribution
SPM with standard t-statisic
SnPM with standard t-statisic? – similar!

6. SnPM SnPM: minimal assumptions intuitive, flexible, powerful
guaranteed valid
intuitive, flexible, powerful
any statistic: voxel / summary
any summary statistic
maximum pseudo t – restricted volume – cluster size / height / mass – omnibus tests
computational burden
need sufficient relabellings
Uses
low df
dodgy parametric
no parametric results

7. Non-parametric tests in fNI…
weak distributional assumptions
don’t assume normality
replace data by ranks
lose information
exchangeability
independence – fMRI 
Classic tests
Wilcoxon rank sum test
Kolmogorov-Smirnov test
Permutation tests
Holmes, Arndt (PET)
Bullmore, Locascio (fMRI) noise whitening, permutation
Nichols & Holmes (fMRI) label (re)-randomisation
minimal assumptions
exchangeability
valid often exact
multiple comparisons
via maximal statistics
flexible
computational burden
sufficient permutations
additional power at low d.f.
via “pseudo” t-statistics

8. Nonparametric approaches…
Holmes AP, Blair RC, Watson JDG, Ford I (1996) “Non-Parametric Analysis of Statistic Images from Functional Mapping Experiments” Journal of Cerebral Blood Flow and Metabolism 16:7-22
Arndt S, Cizadlo T, Andreasen NC, Heckel D, Gold S, O'Leary DS (1996) “Tests for comparing images based on randomization and permutation methods” Journal of Cerebral Blood Flow and Metabolism 16:
Nichols TE, Holmes AP (2000) “Nonparametric permutation tests for functional neuroimaging experiments: A primer with examples” Human Brain Mapping (accepted)
Bullmore ET, Brammer M, Williams SCR, Rabe-Hesketh S, Janot N, David A, Mellers J, Howard R, Sham P (1995) “Statistical Methods of Estimation and Inference for Functional MR Image Analysis” Magnetic Resonance in Medicine 35:
Locascio JJ, Jennings PJ, Moore CI, Corkin S (1997) “Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging” Human Brain Mapping 5:
Raz J, Zheng H, Turetsky B (1999) “Statistical Tests for fMRI based on experimental randomisation” (in preparation)
Marchini JL, Ripley BD (2000) “A new statistical approach to detecting significant activation in functional MRI” (in preparation)