Date of Award


Document Type

Open Access Master's Report

Degree Name

Master of Science in Mathematical Sciences (MS)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Jianping Dong

Committee Member 1

Yu Cai

Committee Member 2

Renfang Jiang


Testing of hypotheses about the population parameter is one of the most fundamental tasks in the empirical sciences and is often conducted by using parametric tests (e.g., the t-test and F-test), in which they assume that the samples are from populations that are normally distributed. When the normality assumption is violated, nonparametric tests are employed as alternatives for making statistical inference. In recent years, the Bayesian versions of parametric tests have been well studied in the literature, whereas in contrast, the Bayesian versions of nonparametric tests are quite scant (for exception, Yuan and Johnson (2008) ) in the literature, mainly due to the lack of sampling distribution of data.

It is well known that like the frequentist counterparts, the Bayesian tests perform well in practical applications, whereas unlike the frequentist ones, they are generally fail to control the Type I error and can even result in different decisions from them. To avoid these issues, we integrate the ideas of Yuan and Johnson (2008) and Goddard and Johnson (2016) and develop Bayes factor tests for comparing the difference between the means among several populations, which can not only control the Type I error, but also allow researchers to make the identical decisions between frequentists and Bayesians on the basis of the observed data. In addition, they depend on the data only through nonparametric statistics and can thus be easily computed, so long as one has conducted the nonparametric tests. More importantly, they can quantify evidence from empirical data favoring the null hypothesis, and this property is not shared by the frequentist counterparts, which lack the ability to quantify evidence favoring the null hypothesis in the case of failing to reject the null hypothesis.