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Item Comparison of Proposed K Sample Tests with Dietz's Test for Nondecreasing Ordered Alternatives for Bivariate Normal Data(North Dakota State University, 2011) Zhao, YanchunThere are many situations in which researchers want to consider a set of response variables simultaneously rather than just one response variable. For instance, a possible example is when a researcher wishes to determine the effects of an exercise and diet program on both the cholesterol levels and the weights of obese subjects. Dietz (1989) proposed two multivariate generalizations of the Jonckheere test for ordered alternatives. In this study, we propose k-sample tests for nondecreasing ordered alternatives for bivariate normal data and compare their powers with Dietz's sum statistic. The proposed k-sample tests are based on transformations of bivariate data to univariate data. The transformations considered are the sum, maximum and minimum functions. The ideas for these transformations come from the Leconte, Moreau, and Lellouch (1994). After the underlying bivariate normal data are reduced to univariate data, the Jonckheere-Terpstra (JT) test (Terpstra, 1952 and Jonckheere, 1954) and the Modified Jonckheere-Terpstra (MJT) test (Tryon and Hettmansperger, 1973) are applied to the univariate data. A simulation study is conducted to compare the proposed tests with Dietz's test for k bivariate normal populations (k=3, 4, 5). A variety of sample sizes and various location shifts are considered in this study. Two different correlations are used for the bivariate normal distributions. The simulation results show that generally the Dietz test performs the best for the situations considered with the underlying bivariate normal distribution. The estimated powers of MJT sum and JT sum are often close with the MJT sum generally having a little higher power. The sum transformation was the best of the three transformations to use for bivariate normal data.Item A Comparison of the Ansari-Bradley Test and the Moses Test for the Variances(North Dakota State University, 2011) Yuni, ChenThis paper is aimed to compare the powers and significance levels of two well known nonparametric tests: the Ansari-Bradley test and the Moses test in both situations where the equal-median assumption is satisfied and where the equal-median assumption is violated. R-code is used to generate the random data from several distributions: the normal distribution, the exponential distribution, and the t-distribution with three degrees of freedom. The power and significance level of each test was estimated for a given situation based on 10,000 iterations. Situations with the equal samples of size 10, 20, and 30, and unequal samples of size 10 and 20, 20 and 10, and 20 and 30 were considered for a variety of different location parameter shifts. The study shows that when two location parameters are equal, generally the Ansari-Bradley test is more powerful than the Moses test regardless ofthe underlying distribution; when two location parameters are different, the Moses is generally preferred. The study also shows that when the underlying distribution is symmetric, the Moses test with large subset size k generally has higher power than the test with smaller k; when the underlying distribution is not symmetric, the Moses test with larger k is more powerful for relatively small sample sizes and the Moses test with medium k has higher power for relatively large sample sizes.Item Comparison of Proposed K Sample Tests with Dietz's Test For Nondecreasing Ordered Alternatives for Bivariate Exponential Data(North Dakota State University, 2011) Pothana, JyothsnadeviComparison of powers is essential to determine the best test that can be used for data under certain specific conditions. Likewise, several nonparametric methods have been developed for testing the ordered alternatives. The Jonckheere-Terpstra (JT) test and the Modified Jonckheere-Terpstra (MJT) test are for testing nondecreasing ordered alternatives for univariate data. The Dietz test is for testing nondecreasing alternatives based on bivariate data. This paper compares various tests when testing for nondecreasing alternatives specifically when the underlying distributions are bivariate exponential. The JT test and the MJT test are applied to univariate data which is derived by reducing bivariate data to univariate data using various transformations. A Monte Carlo simulation study is conducted comparing the estimated powers of JT tests and MJT tests (based on a variety of transformed univariate data) with the estimated powers of Dietz test (based on bivariate data) under a variety of location shifts and sample sizes. The results are compared with Zhao' s (2011) results for bivariate normal data. The overall best test statistic for bivariate data ordered alternatives is discussed in this paper.Item Comparison of Classification Rates among Logistic Regression, Neural Network and Support Vector Machines in the Presence of Missing Data(North Dakota State University, 2014) Upadhyaya, SudhiStatistical models such as Logistic Regression (LR), Neural Network (NN) and Support Vector Machines (SVM) often use datasets with missing values while making inferences regarding the population. When inferences are made based on the data set used, the presence of missing data can severely skew the results and distort the efficiency of the model. Our objective was to identify a robust model among LR, NN, SVM in the presence of missing data. The study was conducted by simulating observations based on Monte Carlo methods and missing data was introduced randomly at 10% level. Single mode imputation was used to impute missing values. Simple random samples of 120, 240 and 500 observations were chosen and these three models were fit for two scenarios. Results showed that the performance of SVM was far superior compared to LR or NN models. However, the classification accuracy of SVM gradually decreased as sample size increased.