Date of Award

Spring 2020

Document Type

Thesis Restricted

Degree Name

Master of Science (MS)


Applied Statistics

Committee Chairperson

Randall Rieger, PhD

Committee Member

Scott D. McClintock, PhD

Committee Member

Andrew J. Crossett, PhD


Group sequential designs allow for performing multiple sequential hypotheses as data accumulates while also controlling the type-1 error rate. Most of the existing literature assumes that the data follows a normal (or approximately) distribution and that the sample sizes are large. For small samples, however, several publications pointed to the fact that these methods lead to type-1 error inflation (Shao and Feng, 2007). Exact critical values for any sample size have been constructed before, but only for single treatment arm group designs (Jennison and Turnbull (1991) and Stallard and Todd (2000)). Most common, though, are situations of group designs where there are two treatment arms, like a placebo and treatment. For these cases, exact critical values are not available. In this paper, we will show how researchers at a local statistical consulting company, LogEcal Data Analytics, derived the exact critical values for any sample size for a single or two treatment arm group design. We will show how they distributed the critical values for 2-5 stage designs based on popular alpha spending functions, such as Obrien-Fleming and Pocock. We also discuss how to implement these critical values in a practical setting based on various group sequential designs and power restrictions.