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t-statistic

SnPM: Statistical nonParametric Mapping A Permutation Test for PET & Second Level fMRI Thomas Nichols, University of Michigan Andrew Holmes, University of Glasgow. B. B. B. B. B. B. A. A. A. A. A. A. B. B. B. B. B. B. A. A. A. A. A. A. B. B. B. B. B. B. A. A. A. A.

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t-statistic

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  1. SnPM:Statistical nonParametric MappingA Permutation Test for PET &Second Level fMRIThomas Nichols, University of MichiganAndrew Holmes, University of Glasgow

  2. B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B A A A A A A B B B B B B 1 2 3 4 5 6 i difference V5 PET activation experiment… 6 BA… randomise 7 8 9 6AB… 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: minimal assumptions 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 SnPM

  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. SnPM (standard t) • 12 scans • 212 permutations • All 2048/2 computed • p=1/2048 • a = 0.05 critical threshold:ua = 7.9248 • Bonferoni critical threshold: ua = 9.0717 • 30 min on Sparc Ultra 10

  9. SnPM (pseudo t) • 12 scans • 212 permutations • All 2048/2 computed • p = 1/2048 • a = 0.05 critical threshold:ua = 5.120 • 40 min on a Sparc Ultra10

  10. SnPM vs Parametric RF Permutation Corrected Significance of Threshold RT Theory

  11. 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 Metabolism16:7-22 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 (2002)“Nonparametric permutation tests for functional neuroimaging experiments: A primer with examples” Human Brain Mapping15:1-25 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” (ENAR Conference Proceedings) Marchini JL, Ripley BD (2000)“A new statistical approach to detecting significant activation in functional MRI” NeuroImage

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