A Nonparametric approach…

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 =

…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

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

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

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

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

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 16:1271-1279 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 35:261-277 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 5:168-193 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)