Master of Science / Department of Statistics / Paul I. Nelson / Hotelling’s T2 test is the standard tool for inference about the mean of a multivariate normal population. However, this test may perform poorly when used on samples from multivariate distributions with highly skewed marginal distributions. The goal of our study was to investigate the type I error rate and power properties of Hotelling’s one sample test when sampling from a class of multivariate skew-normal (SN) distributions, which includes the multivariate normal distribution and, in addition to location and scale parameters, has a shape parameter to regulate skewness. Simulation results of tests carried out at nominal type I error rate 0.05 obtained from various levels of shape parameters, sample sizes, number of variables and fixed correlation matrix showed that Hotelling’s one sample test provides adequate control of type I error rates over the entire range of conditions studied. The test also produces suitable power levels for detecting departures from hypothesized values of a multivariate mean vector when data result from a random sample from a multivariate SN. The shape parameter of the SN family appears not to have much of an effect on the robustness of Hotelling’s test. However, surprisingly, it does have a positive impact on power.

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This study used a two-phased explanatory mixed-methods design to explore in-depth what factors are perceived by Instructional Design and Technology (IDT) professionals as impacting instructional design practice, how these factors are valued in the field, and what differences in perspectives exist between IDT managers and non-managers. For phase 1 of the study, one hundred and sixteen corporate IDT professionals (managers and non-managers) responded to a web-based survey that was designed and developed from: (a) The results of an exploratory study of the practices of corporate instructional designers, (b) the results of an extensive literature review into the theory and practice in the field of IDT, and (c) other survey instruments developed, validated and used in prior studies. Analysis of the data collected in phase 1 of the study resulted in the development of an Evaluation Model for IDT Practice that was used as a framework to answer the research questions. Quantitative analysis included the use of Hotelling’s T2 inferential statistic to test for mean differences between managers and non-managers perceptions of formal and informally trained groups of IDT personnel. Chi squared analysis test of independence, and correlation analysis was used to determine the nature and extent of the relationship between the type of training and the professional status of the participants. For phase 2 of the study, semi-structured interviews were conducted with selected participants and analyzed using the constant comparative method in order to help validate the findings from phase 1. Ensuing analysis of the survey data determined that, both managers and non-managers generally agreed that both formal and on the job training was valuable, and that their peers who were formally and informally trained were competent instructional designers. The qualitative phase of the study and a closer examination of effect sizes suggested the potential for some variation in perceptions. In addition, a statistically significant correlation showed that IDT managers who completed the survey were more likely to be formally trained. Recommendations based on the results included future studies with a larger, more diverse population; future studies to refine the Evaluation Model for ID practice; and that academic ID programs work more closely with practitioners when designing and delivering their curricula.

The classical one way MANOVA model is used to test whether the mean measurements are the same or differ across p groups, and assumes that the covariance matrix of each group is the same. This work suggests using the Olive (2017abc) bootstrap technique to develop analogs of one way MANOVA test. A large sample theory test has also been developed. The bootstrap tests can have considerable outlier resistance, and the tests do not need the population covariance matrices to be equal. The two sample Hotelling's T^2 test is the special case of the one way MANOVA model when p =2.

This dissertation comprises of three problems in the area of Political Economy and Industrial Organization. The first chapter concerns how ideologically-opposite media firms report a particular event to maximize their payoffs from advocating their ideology and strengthen reader trust which increases if the report is proximate to their beliefs. I use these facts to develop a Hotelling's linear city model of competition where the two media firms choose their respective locations which signify the impression they want to impart to its readers. I find partisan media provides accurate information while covering topics favorable to its ideology. However, for unfavourable topics, the media never provides an indifferent report, but either defends its own ideology or delivers a partially accurate report. For unfavourable issues, imparting an indifferent impression rewards a media with lowest equilibrium payoffs. I identify sufficiency conditions where readers give better assessment to news of a media located farther away from their ideology than one which is nearer. Increasing competition by the entry of a third firm does not necessarily alleviate the level of bias in the news economy. The second paper studies the pricing schedule of a monopolist while it sells a non-durable product over two time periods. The consumer's experience with the product is correlated with two possible states — good (bad) experience is more probable under a high (low) state. Given this, I study the monopolist's pricing scheme in the two periods when consumers are wishful — overly optimistic about the high state even after a bad experience. I provide a comparative study of prices in each periods when the monopolist announces prices with and without commitment when consumers are either naive or sophisticated. The final chapter provides an understanding of the efficacy of two types of trade sanctions (import and export) using a directed network model. Sanctions are common punitive measures taken by a sender player to discipline a target player. Empirical evidences in the realm of international trade show differences in the effectiveness between import and export sanctions. This paper shows that such differences can be explained by one specific centrality feature of the underlying trading network — betweenness-centrality. This measure lends insights to the trade spill-overs following sanctions underscoring why sanctions are ineffective. I highlight when a higher value of this centrality acts as a sufficient condition towards effective sanction. Based on this analysis, one can conclude whether import or export sanction will be more effective for a given trade network. / Doctor of Philosophy / Three essays spanning across topics of political economy and Industrial Organization has been studied. The first essay `Media bias in the best and worst of times' studies how ideology-motivated (partisan) media firms try to create impressions to its audience about a particular issue to increase its payoffs from either of the two sources — reader trust and advocating its ideology. This trade-off depends on the type of issue at hand which either aggravates or moderates a media's wish to generate bias in its news. I investigate not only the degree of bias for any given event, but also study how profits of media are impacted from doing so. The second chapter `Monopoly pricing under wishful thinking' investigates the pricing strategies of a seller when he sells a non-durable product to a wishful buyer twice, over two time periods. Under two possible states of the world — textit{high} and textit{low} — the buyer can derives either a good or bad experience. It is assumed that a good experience is more likely than a bad one under textit{high} state. Would the buyer re-purchase the product after having a bad experience in the first period? A wishful buyer is overly optimistic about a good experience in the future even after a bad experience in the current period. Such optimism paves the way for pricing strategies in favor of the seller under certain conditions. My aim has been to highlight these conditions and draw comparison with a pricing model with non-wishful buyers. The third chapter investigates the effectiveness of trade sanctions. Such sanctions are imposed by a sender country against a target country when the latter has taken an action which the sender disapproves — initiating domestic war, building nuclear arsenals, etc. The sanctions are enforced until the target. However, only 30% sanctions are effective in disciplining the target. This paper studies if any feature of the trade network can explain why sanctions fail and what type of trade sanction — import or export — will be optimal in any given trade network.

Diffusion tensor imaging (DTI) is a specialist MRI modality that can identify microstructural changes or abnormalities in the brain. It can also be used to show fibre tract pathways. Both of these features were used in this thesis. Firstly, standard imaging analysis techniques were used to study the effects of mild, repetitive closed head injury on a group of professional boxers. Such data is extremely rare, so the findings of regions of brain abnormalities in the boxers are important, adding to the body of knowledge about more severe traumatic brain injury. The author developed a novel multivariate analysis technique which was used on the same data. This new technique proved to be more sensitive than the standard univariate methods commonly used. An important part of diagnosing and monitoring brain damage involves the use of biomarkers. A novel investigation of whether diffusion parameters obtained from DTI data could serve as bio-markers of cognitive impairment in Parkinson's disease was conducted. This also involved developing a multivariate approach, which displayed increased sensitivity compared with any of the component parameters used singly, and suggested these diffusion measures could be robust bio-markers of cognitive impairment. Fibre tract connectivity between regions of the brain is also a potentially valuable measure for diagnosis and monitoring brain integrity. The feasibility of this was investigated in a multi-modal MRI study. Functional MRI (fMRI) identifies regions of activation associated with a particular task. DTI can then find the pathway of the fibre bundles connecting these regions. The feasibility of using regional connectivity to interrogate brain integrity was investigated using a single healthy volunteer. Fibre pathways between regions activated and deactivated by a working memory paradigm were determined. Though the results are only preliminary, they suggest that this line of research should be continued.

Diffusion tensor imaging (DTI) is a specialist MRI modality that can identify microstructural changes or abnormalities in the brain. It can also be used to show fibre tract pathways. Both of these features were used in this thesis. Firstly, standard imaging analysis techniques were used to study the effects of mild, repetitive closed head injury on a group of professional boxers. Such data is extremely rare, so the findings of regions of brain abnormalities in the boxers are important, adding to the body of knowledge about more severe traumatic brain injury. The author developed a novel multivariate analysis technique which was used on the same data. This new technique proved to be more sensitive than the standard univariate methods commonly used. An important part of diagnosing and monitoring brain damage involves the use of biomarkers. A novel investigation of whether diffusion parameters obtained from DTI data could serve as bio-markers of cognitive impairment in Parkinson's disease was conducted. This also involved developing a multivariate approach, which displayed increased sensitivity compared with any of the component parameters used singly, and suggested these diffusion measures could be robust bio-markers of cognitive impairment. Fibre tract connectivity between regions of the brain is also a potentially valuable measure for diagnosis and monitoring brain integrity. The feasibility of this was investigated in a multi-modal MRI study. Functional MRI (fMRI) identifies regions of activation associated with a particular task. DTI can then find the pathway of the fibre bundles connecting these regions. The feasibility of using regional connectivity to interrogate brain integrity was investigated using a single healthy volunteer. Fibre pathways between regions activated and deactivated by a working memory paradigm were determined. Though the results are only preliminary, they suggest that this line of research should be continued.

The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use. / Ph. D.