CHAPTER 69 – Smoothness Variance Estimate and Its Effects on Probability Values in Statistical Parametric Maps

Correction for the number of pixels tested in statistical parametric maps requires a measure of the spatial dependency of pixel values. This measure is more often than not, done through the measure of the smoothness parameter. This method implies that the parameter is random, therefore casting some uncertainty on the p-values computed in the statistical analysis of the data. This chapter derives and validates a first-order approximation of the smoothness variance and presents the effect on the assessment of significant changes in statistical parametric maps using the spatial extent of the activated region and its peak intensity value or height. It has been confirmed that estimating the smoothness on the data is a reasonable way to proceed and it is found that the p-values, “confidence intervals,” due to the assessment of this parameter are of the order of 20%. This should be taken into account when reporting results and should moderate the role associated with a “knife-edged” 5% α-risk threshold.