The problem of detecting monotonic increasing/decreasing trends in variances from k samples is widely met in many applications, e.g. financial data analysis, medical and environmental studies. However, most of the tests for equality of variances against ordered alternatives rely on the assumption of normality. Such tests are often non-robust to departures from normality, which eventually leads to unreliable conclusions. In this thesis, we propose a combination of a robust Levene-type test and a finite-intersection method, which relaxes the assumption of normality. The new combined procedure yields a more accurate estimate of sizes of the test and provides competitive powers. In addition, we discuss various modifications of the proposed test for unbalanced design cases. We present theoretical justifications of the new test and illustrate its applications by simulations and case studies.

The problem of detecting monotonic increasing/decreasing trends in variances from k samples is widely met in many applications, e.g. financial data analysis, medical and environmental studies. However, most of the tests for equality of variances against ordered alternatives rely on the assumption of normality. Such tests are often non-robust to departures from normality, which eventually leads to unreliable conclusions. In this thesis, we propose a combination of a robust Levene-type test and a finite-intersection method, which relaxes the assumption of normality. The new combined procedure yields a more accurate estimate of sizes of the test and provides competitive powers. In addition, we discuss various modifications of the proposed test for unbalanced design cases. We present theoretical justifications of the new test and illustrate its applications by simulations and case studies.

The purpose of this thesis is to examine the relationships between personality-centered and issue-centered approaches to a study of attitudes. The relationships will be sought through examination of the essential characteristics of the ideas behind each approach and by exposing the same population to both of the data-gathering methods employed by these researchers, i.e., Rokeach's Dogmatism Scale, and Sherif, et al.'s Method of Ordered Alternatives.

Ordered alternatives tests are sometimes used in life-testing experiments and drug-screening studies. An ordered alternative test is sometimes used to gain power if the researcher thinks parameters will be ordered in a certain way if they are different. This research proposal focuses on developing new nonparametric tests for the nondecreasing ordered alternative problem for k (k?3) populations when testing for differences in both location and scale. Six nonparametric tests are proposed for the nondecreasing ordered alternative when testing for a difference in either location or scale. The six tests are various combinations of a well-known ordered alternatives test for location and a test based on the Moses test technique for testing differences in scale. A simulation study is conducted to determine how well the proposed tests maintain their significance levels. Powers are estimated for the proposed tests under a variety of conditions for three, four and five populations. Several types of variable parameters are considered: when the location parameters are different and the scale parameters are equal; when the location parameters are equal and the scale parameters are different; when the location and scale parameters are both different. Equal and unequal samples sizes of 18 and 30 are considered. Subgroup sizes of 3 and 6 are both used when applying the Moses test technique. Recommendations are given for which test should be used for various situations.