published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Leung Shun-piu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 41-43). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiplicity Problem in Multiple Testing --- p.1 / Chapter 1.2 --- Family --- p.2 / Chapter 1.3 --- Family wise Error Rate --- p.2 / Chapter 1.4 --- Multiple Comparisons with a Control --- p.3 / Chapter 1.5 --- Single-step Procedures vs Stepwise Procedures --- p.4 / Chapter 1.6 --- Dunnett Procedure --- p.5 / Chapter 1.6.1 --- One-way Fixed Effect Model --- p.5 / Chapter 1.6.2 --- Simultaneous Inference and Test Statistics --- p.6 / Chapter 1.6.3 --- Calculation of the Upper and Lower Percentage Points --- p.8 / Chapter 1.7 --- Objectives --- p.10 / Chapter 2 --- Testing Procedures --- p.11 / Chapter 2.1 --- Simultaneous Inference in Mixed Families --- p.11 / Chapter 2.2 --- "Evaluation of C1,α and c2,α" --- p.13 / Chapter 2.3 --- Extension to Mixed Families with 3 Testing Groups --- p.15 / Chapter 3 --- The Calculation of Critical Values --- p.18 / Chapter 3.1 --- Calculation of Critical Values --- p.18 / Chapter 3.2 --- "Tabulation of Critical Values (c-*,α c*,α)" --- p.22 / Chapter 4 --- Numerical Example --- p.30 / Chapter 5 --- Conclusions --- p.34 / Appendix --- p.35 / References --- p.41

Lee Hang Ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 37-39). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple comparison procedures --- p.1 / Chapter 1.2 --- Multiple comparisons with a control (MCC) --- p.2 / Chapter 1.3 --- MCC in two-way designs --- p.3 / Chapter 1.4 --- Directional-mixed families --- p.4 / Chapter 1.5 --- Objectives --- p.6 / Chapter 2 --- MCC with directional-mixed families in one-way designs: a review --- p.8 / Chapter 2.1 --- The model --- p.8 / Chapter 2.2 --- The test statistics --- p.8 / Chapter 2.3 --- The evaluation of critical constants --- p.9 / Chapter 2.4 --- Testing and estimation --- p.11 / Chapter 2.5 --- An example --- p.12 / Chapter 3 --- MCC with directional-mixed families in two-way designs --- p.14 / Chapter 3.1 --- The model --- p.14 / Chapter 3.2 --- The test statistics --- p.15 / Chapter 3.3 --- Testing and estimation --- p.16 / Chapter 4 --- Evaluation and tabulation of critical values --- p.17 / Chapter 4.1 --- Evaluation of critical values --- p.17 / Chapter 4.2 --- Comparisons of computational methods --- p.19 / Chapter 4.3 --- Tabulation of critical values --- p.24 / Chapter 5 --- Power study --- p.30 / Chapter 5.1 --- Objectives --- p.30 / Chapter 5.2 --- Simulation results --- p.30 / Chapter 6 --- Numerical example --- p.33 / Chapter 7 --- Conclusions --- p.36 / Bibliography

Wang Yanhui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 46-48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparisons with a Control --- p.1 / Chapter 1.1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.1.2 --- Multiple Comparisons with a Control --- p.2 / Chapter 1.1.3 --- Single-step and Stepwise Procedures --- p.2 / Chapter 1.2 --- The Dunnett Procedure --- p.4 / Chapter 1.2.1 --- One-way Fixed Effect Model --- p.4 / Chapter 1.2.2 --- Testing Procedure --- p.4 / Chapter 1.3 --- Directional-mixed Families --- p.7 / Chapter 1.3.1 --- Definition of Directional-mixed Families --- p.7 / Chapter 1.3.2 --- Selection between One- and Two-sided Inferences --- p.7 / Chapter 1.4 --- Objectives --- p.8 / Chapter 2 --- Single-step Procedure --- p.10 / Chapter 2.1 --- SSI Procedure --- p.10 / Chapter 2.1.1 --- The Testing Procedure --- p.10 / Chapter 2.1.2 --- Computation of Optimal Critical Values --- p.11 / Chapter 2.2 --- p-value Consistency --- p.17 / Chapter 2.3 --- The SS2 Procedure --- p.18 / Chapter 3 --- Step-down Procedure --- p.24 / Chapter 3.1 --- The Testing Procedure --- p.24 / Chapter 3.2 --- Derivation of Critical p-values for the SD Procedure --- p.26 / Chapter 4 --- Simulation Study of Power --- p.30 / Chapter 5 --- Practical Example --- p.36 / Appendix --- p.39 / References --- p.46

Chan Tat-on. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.2 --- One-step MCCP --- p.2 / Chapter 1.3 --- Stepwise MCCP --- p.7 / Chapter 1.4 --- Thesis Objectives --- p.10 / Chapter Chapter 2 --- One-step MCCP with Heterogeneous Group Variances --- p.11 / Chapter 2.1 --- The Model --- p.11 / Chapter 2.2 --- Test Statistics --- p.12 / Chapter 2.3 --- Testing and Estimation --- p.15 / Chapter Chapter 3 --- Stepwise MCCP with Heterogeneous Group Variances --- p.17 / Chapter 3.1 --- The Model --- p.17 / Chapter 3.2 --- Testing Procedure --- p.17 / Chapter 3.3 --- Simulation Study --- p.18 / Chapter 3.3.1 --- Average power --- p.19 / Chapter 3.3.2 --- Family wise Type I error rate --- p.20 / Chapter 3.3.3 --- Simulation procedures --- p.21 / Chapter 3.3.4 --- Choice of parameter configurations --- p.23 / Chapter 3.3.5 --- Simulation results --- p.24 / Chapter 3.3.6 --- Summary --- p.28 / Chapter Chapter 4 --- Numerical Example --- p.33 / Chapter 4.1 --- SS procedures --- p.34 / Chapter 4.2 --- SW procedures --- p.35 / Chapter Chapter 5 --- Further Research --- p.38 / References --- p.39

The Thurstone-Mosteller and Bradley-Terry Models are commonly used to rank items from paired comparisons experiments in which one item in each pair "wins," and to assess the importance of time-independent explanatory variables on such rankings. The first part of this thesis clarifies the use of probit and logistic regression models for such designs, including the incorporation of time-dependent explanatory variables and the analysis of unbalanced designs. In addition, likelihood inference, using the EM Algorithm, is proposed for Thurstone's Case HI Model allowing the estimation of variance parameters to account for variable item performances. The second half of this thesis presents an extension of the model to permitting the "performances" or "worths" of each competitor to be serially correlated. As an example, the performance of a basketball team in its current game is allowed to be correlated with its performance from the previous game. The Thurstone-Mosteller Model is sometimes motivated through the use of an underlying, normally-distributed performance distribution for each item or competitor, with a competitor winning a trial if a draw from its performance distribution exceeds that from its competitor's. The observed outcome is solely the win or loss for each team, but regression models, using either time-dependent or time-independent explanatory variables, may be specified for the performance means. The extension in this thesis comes from supposing the error structure for the performance distribution for each team is normal with first-order autocorrelation. The EM Algorithm is used, treating the underlying draws from the performance distributions as "missing data." This provides approximate maximum likelihood estimates; the approximation is due to the use of Monte Carlo integration in the E-step of the algorithm. Unfortunately, the heavy computational requirement and the inability to calculate the maximized likelihood function or the information matrix, make the approach unattractive for practical use. Two approximations are presented, however, which can be carried out with standard routines and some minor programming. Keywords: auto-regressive model, Bradley-Terry Model, EM Algorithm, generalized linear model, logistic regression, MCEM Algorithm, probit regression, serial correlation, Thurstone-Mosteller Model. / Graduation date: 1996

Social and temporal comparison researchers to date have only looked at comparisons involving the self. The present investigation aims to extend comparison theory by examining social and temporal comparisons people make of others. Using movie reviews, the results support Festinger’s (1954) similarity hypothesis, such that lateral comparisons were more frequent than either upward or downward comparisons when the comparisons were social in nature. For temporal comparisons, on the other hand, there was no difference in the use of upward, downward, and lateral comparisons, which does not support Albert’s (1977) hypothesis that people are motivated to maintain a stable sense of self over time and should therefore prefer lateral comparisons over upward or downward comparisons. Implications about the use of between-individual comparisons as a way to expand comparison theory and the benefits of examining these types of comparisons for their own sake are discussed.

Social and temporal comparison researchers to date have only looked at comparisons involving the self. The present investigation aims to extend comparison theory by examining social and temporal comparisons people make of others. Using movie reviews, the results support Festinger’s (1954) similarity hypothesis, such that lateral comparisons were more frequent than either upward or downward comparisons when the comparisons were social in nature. For temporal comparisons, on the other hand, there was no difference in the use of upward, downward, and lateral comparisons, which does not support Albert’s (1977) hypothesis that people are motivated to maintain a stable sense of self over time and should therefore prefer lateral comparisons over upward or downward comparisons. Implications about the use of between-individual comparisons as a way to expand comparison theory and the benefits of examining these types of comparisons for their own sake are discussed.

Multiple comparisons and selection procedures are commonly studied in research and employed in application. Clinical trial is one of popular fields to which the subject of multiple comparisons is extensively applied. Based on the Federal Food, Drug, and Cosmetic Act, drug manufacturers need to not only demonstrate safety of their drug products but also establish effectiveness by substantial evidence in order to obtain marketing approval. However, the problem of error inflation occurs when there are more than two groups to compare with at the same time. How to design a test procedure with high power while controlling type I error becomes an important issue. The treatment with the largest population mean is considered to be the best one in the study. Potentially the best treatments can receive increased resources and further investigation by excluding clearly inferior treatments. Hence, a small number of possibly the best treatments is preferred. This thesis focuses on the problem of eliminating the less effective treatments among three in clinical trials. The goal is to increase the ability to identify any inferior treatment providing that the probability of excluding any best treatment is guaranteed to be less than or equal to alpha. A step-down procedure is applied to solve the problem. The general step-down procedure with fixed thresholds is conservative in our problem. The test is not efficient in rejecting the less effective treatments. We propose two methods with sharper thresholds to improve current procedures and construct a subset containing strictly inferior treatments. The first method, the restricted parameter space approach, is designed for the scenario when prior information about range of treatment means is known. The second method, the step-down procedure with feedback, utilizes observations to modify the threshold and controls error rate for the whole parameter space. The new procedures have greater ability to detect more inferior treatments than the standard procedure. In addition, type I error is also controlled under mild violation of the assumptions demonstrated by simulation.

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