Spatial Smoothing & Multiple Comparisons Correction (for Dummies)

1. Spatial Smoothing &Multiple Comparisons Correction (for Dummies) Acknowledgements: Jon Simons, Alexa Morcom, Matthew Brett

2. Overview • Spatial Smoothing • What does it do? • Why do you want to do it? • How is it done? • Correction for Multiple Comparisons • Bonferroni correction • Random field theory • Uncorrected thresholds • False discovery rate • Which correction method to use?

3. Overview • Spatial Smoothing • What does it do? • Why do you want to do it? • How is it done? • Correction for Multiple Comparisons • Bonferroni correction • Random field theory • Uncorrected thresholds • False discovery rate • Which correction method to use?

4. Spatial Smoothing What does it do? • Reduces effect of high frequency variation in functional imaging data, “blurring sharp edges”

5. Spatial Smoothing

6. Spatial Smoothing

7. Spatial Smoothing Why do you want to do it? • Increases signal-to-noise ratio • Enables averaging across subjects • Allows use of Gaussian Field Theory for thresholding

8. Spatial Smoothing Why do you want to do it? • Increases signal-to-noise ratio • Depends on relative size of smoothing kernel and effects to be detected • Matched filter theorem: smoothing kernel = expected signal • Practically, rule of thumb: FWHM ≥ 3 x voxel size • May consider varying kernel size if interested in different brain regions, e.g. hippocampus vs. parietal cortex

9. Spatial Smoothing Why do you want to do it? • Enables averaging across subjects • Reduces influence of functional and/or anatomical differences between subjects • Even after realignment and normalisation, residual between-subject variability may remain • Smoothing data improves probability of identifying commonalities in activation between subjects, but trade-off with anatomical specificity

10. Spatial Smoothing Why do you want to do it? • Allows use of Gaussian Field Theory for thresholding • Assumes error terms are roughly Gaussian in form • Requires FWHM to be substantially greater than voxel size • Enables hypothesis testing and dealing with multiple comparison problem in functional imaging …

11. -5 0 5 Spatial Smoothing How is it done? • Typically in functional imaging, a Gaussian smoothing kernel is used • Shape similar to normal distribution bell curve • Width usually described using “full width at half maximum” (FWHM) measuree.g., for kernel at 10mm FWHM:

12. Spatial Smoothing How is it done? • Gaussian kernel defines shape of function used successively to calculate weighted average of each data point with respect to its neighbouring data points Raw data x Gaussian function = Smoothed data

13. Spatial Smoothing How is it done? • Gaussian kernel defines shape of function used successively to calculate weighted average of each data point with respect to its neighbouring data points Raw data x Gaussian function = Smoothed data