Kenneth Liao

MS thesis abstract: 

There has been a growing criticism of hypothesis testing. Neuroimaging analysis almost exclusively focuses on hypothesis testing. Recent research has developed methods to use confidence sets instead, to draw conclusions, but has only focused on particular parameters or effect sizes that do not generalize to all statistics, such as noncontinuous and nonfunctional data. Here, we use the robust effect size index (RESI) framework, which is generally defined across many different types of models. We use RESI to develop a general approach to effect size-based inference for neuroimaging data using confidence sets derived from simultaneous confidence intervals (SCI) using bootstrapping from the pbj (parametric bootstrap joint) R package. From a given effect size threshold, this approach will identify regions of the brain that belong to the null set (areas where the effect size is less than the threshold) or the target set (areas where the effect size is greater than the threshold), with a prespecified confidence level. We then conduct simulations to evaluate this approach, using a parametric standard error normalization, and one method without any normalization. The coverage, average interval width, and the maximum interval width are reported to evaluate the SCIs. This approach can be applied to areas of research that focus on multivariate outcomes, such as genomics and imaging.