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t-statistic

SnPM offers a non-parametric approach for statistical mapping in PET and fMRI experiments, allowing flexible, powerful analyses without strict assumptions. It uses permutation testing to provide valid and intuitive results for various statistics.

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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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