Optimizing Smoothness Kernel Size for the Smoothed Variance T-Test

• Activity Number: 402
• Type: Contributed
• Date/Time: Wednesday, August 6, 2008 : 10:30 AM to 12:20 PM
• Sponsor: General Methodology
• Author(s): Hui Zhang*+ and Timothy D. Johnson and Thomas E. Nichols+
• Companies: The University of Michigan and The University of Michigan and GlaxoSmithKline Clinical Imaging Centre
• Keywords: smoothness parameter ; smoothed variance image ; Bias ; MSE ; effective degrees of freedom ; Chisquare random field

Abstract

For small group studies with fewer subjects, the smoothed variance t-test has been found to be a powerful alternative to the usual t-test. The power is greater because smoothing the variance effectively increase the error degrees of freedom (DF). However, the unsmoothed sample variance image is unbiased and so any smoothing will induce some bias, the severity of which depends on the smoothness of the true variance image. In this work we develop a theoretical framework to obtain bias, mean square error (MSE) and effective DF (EDF) of the smoothed variance image, as a function of data smoothness, true variance image smoothness and applied variance smoothing. One novel aspect is our use of Chi-square random fields to model the true variance. We use simulation to evaluate this method. We also use splits a 150 subject data set to find equivalent empirical results.