Hypothesis testing, power and sample size determination for health science data

Health science datasets often have small sample sizes due to time and cost associated in obtaining the samples. In addition, there are very few statistical procedures in the literature that deal with the problems encountered in analyses of these datasets. In this dissertation I consider three different problems related to hypothesis testing, power and sample size determination for small datasets. The first part of this thesis covers new testing procedures for the shape, scale and mean of the gamma distribution based on small samples. All proposed testing procedures maintain nominal Type I error rates for small samples and retain pre-specified statistical power. The second part of this thesis deals with a sample size determination problem for two-level logistic mixed-effects regression models for binary data in longitudinal designs. The third part of the thesis entails a large-sample based test for between group comparisons for fMRI datasets and control of False Discovery Rate (FDR) using the procedure proposed by Benjamini and Hochberg, 1995. I have also determined the necessary sample size in order to obtain a target power via simulation under various alternatives for a given pre-specified significance level using the proposed testing procedure.