# R in addition to om Field Theory Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data

## R in addition to om Field Theory Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data

Fu, Joseph, Health & Medicine Reporter has reference to this Academic Journal, PHwiki organized this Journal R in addition to om Field Theory Will Penny SPM short course, London, May 2005 realignment & motion correction smoothing normalisation General Linear Model model fitting statistic image corrected p-values image data parameter estimates design matrix anatomical reference kernel Statistical Parametric Map R in addition to om Field Theory

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Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data 4. Cluster level inference SPM Results FDR Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data 4. Cluster level inference SPM Results FDR Inference at a single voxel a = p(t>uH) NULL hypothesis, H: activation is zero u=2 t-distribution p-value: probability of getting a value of t at least as extreme as u. If a is small we reject the null hypothesis. u=(effect size)/std(effect size)

Sensitivity in addition to Specificity Sensitivity in addition to Specificity Eg. t-scores from regions that truly do in addition to do not activate o o o o o o o x x x o o x x x o x x x x u1 Sensitivity in addition to Specificity Eg. t-scores from regions that truly do in addition to do not activate o o o o o o o x x x o o x x x o x x x x u2

Inference at a single voxel a = p(t>uH) NULL hypothesis, H: activation is zero u=2 t-distribution We can choose u to ensure a voxel-wise significance level of a. This is called an uncorrected p-value, as long as reasons well see later. We can then plot a map of above threshold voxels. Inference as long as Images Signal+Noise Noise Using an uncorrected p-value of 0.1 will lead us to conclude on average that 10% of voxels are active when they are not. This is clearly undesirable. To correct as long as this we can define a null hypothesis as long as images of statistics.

Family-wise Null Hypothesis Family-Wise Error (FWE) rate = corrected p-value Use of uncorrected p-value, a=0.1 FWE Use of corrected p-value, a=0.1 The Bonferroni correction The Family-Wise Error rate (FWE), a, as long as a family of N independent voxels is = Nv where v is the voxel-wise error rate. There as long as e, to ensure a particular FWE set v = / N BUT

The Bonferroni correction Independent Voxels Spatially Correlated Voxels Bonferroni is too conservative as long as brain images Overview 1. Terminology 2. R in addition to om Field Theory 3. Imaging Data 4. Cluster level inference SPM Results FDR R in addition to om Field Theory Consider a statistic image as a discretisation of a continuous underlying r in addition to om field Use results from continuous r in addition to om field theory Discretisation

Euler Characteristic (EC) Topological measure threshold an image at u EC = blobs at high u: Prob blob = avg (EC) So FWE, a = avg (EC) Example  2D Gaussian images = R (4 ln 2) (2) -3/2 u exp (-u2/2) Voxel-wise threshold, u Number of Resolution Elements (RESELS), R N=100×100 voxels, Smoothness FWHM=10, gives R=10×10=100 Example  2D Gaussian images = R (4 ln 2) (2) -3/2 u exp (-u2/2) For R=100 in addition to =0.05 RFT gives u=3.8

Resel Counts as long as Brain Structures FWHM=20mm (1) Threshold depends on Search Volume (2) Surface area makes a large contribution Overview 1. Terminology 2. Theory 3. Imaging Data 4. Levels of Inference 5. SPM Results Functional Imaging Data The R in addition to om Fields are the component fields, Y = Xw +E, e=E/ We can only estimate the component fields, using estimates of w in addition to To apply RFT we need the RESEL count which requires smoothness estimates

Estimated component fields data matrix design matrix parameters errors + = voxels scans estimate residuals estimated component fields parameter estimates estimated variance = Each row is an estimated component field Applied Smoothing Smoothness smoothness » voxel size practically FWHM 3 VoxDim Typical applied smoothing: Single Subj fMRI: 6mm PET: 12mm Multi Subj fMRI: 8-12mm PET: 16mm Overview 1. Terminology 2. Theory 3. Imaging Data 4. Levels of Inference 5. SPM Results

Cluster Level Inference We can increase sensitivity by trading off anatomical specificity Given a voxel level threshold u, we can compute the likelihood (under the null hypothesis) of getting a cluster containing at least n voxels CLUSTER-LEVEL INFERENCE Similarly, we can compute the likelihood of getting c clusters each having at least n voxels SET-LEVEL INFERENCE Levels of inference set-level P(c 3 n 12, u 3.09) = 0.019 cluster-level P(c 1 n 82, t 3.09) = 0.029 (corrected) voxel-level P(c 1 n > 0, t 4.37) = 0.048 (corrected) At least one cluster with unspecified number of voxels above threshold At least one cluster with at least 82 voxels above threshold At least 3 clusters above threshold Overview 1. Terminology 2. Theory 3. Imaging Data 4. Levels of Inference 5. SPM Results

False Discovery Rate Signal+Noise Noise Summary We should not use uncorrected p-values We can use R in addition to om Field Theory (RFT) to correct p-values RFT requires FWHM > 3 voxels We only need to correct as long as the volume of interest Cluster-level inference False Discovery Rate is a viable alternative

## Fu, Joseph Health & Medicine Reporter

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