Paper Type

Master's Thesis


College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)


Mathematics & Statistics

First Advisor

Dr. Peter Wludyka

Second Advisor

Dr. Adel Boules

Third Advisor

Dr. Ping Sa


The advent of powerful computers has brought about the randomization technique for testing statistical hypotheses. Randomization tests are based on shuffles or rearrangements of the (combined) sample. Putting each of the I samples "in a bowl" forms the combined sample. Drawing samples "from the bowl" forms a shuffle. Shuffles can be made with or without replacement.

In this thesis, analysis of means type randomization tests will be presented to solve the homogeneity of variance problem. An advantage of these tests is that they allow the user to graphically present the results via a decision chart similar to a Shewhart control chart. The focus is on finding tests that are robust to departures from normality. The proposed tests will be compared against commonly used nonrandomization tests. The type I error stability across several nonnormal distributions and the power of each test will be studied via Monte Carlo simulation.

Included in

Mathematics Commons