Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD


Most statistical tests are fully developed for univariate data, but when inference is required for multivariate data, univariate tests risk information loss and interpretability. This research 1) derives and extends the multivariate Komolgorov Smirnov test for 2 and into m-dimensions, 2) derives small sample critical values for the KS test that are not reliant on sample size simulations or correlation between variables, 3) extends large sample estimations and current KS implementations, and 4) provides sample size and power calculations in order to enable experimental design with respect to testing for differences in distributions. Through extensive simulation, we demonstrate that our new multidimensional KS test generally has more power for smaller sample sizes and comparable power for larger sample sizes and maintains desirable statistical properties. Furthermore, we improve and extend current implementations of the KS test to sample sizes upwards of n = 5000. Finally, we demonstrate how to compute critical values to any size dimensional data and provide power and sample size criterion for designing studies using 2 and 3 dimensional distributions. These results enable statistical testing of multidimensional features, irrespective of correlation, thus improving our ability to understand large data sets for rapid and efficient decision making and analysis.

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