by Ying-wang Wong. / Year shown on spine: 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 41-44). / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.2 --- Familywise Error Rate --- p.3 / Chapter 1.3 --- One-step Procedures Versus Stepwise Procedures --- p.4 / Chapter 1.4 --- Pairwise Multiple Comparisons --- p.5 / Chapter 1.5 --- Pairwise Multiple Comparisons in Two-Way Designs --- p.6 / Chapter 1.6 --- Objectives --- p.8 / Chapter 2. --- Pairwise Multiple Comparisons in One-Way Designs with Covariates --- p.9 / Chapter 2.1 --- The General ANCOVA Model --- p.9 / Chapter 2.2 --- Pairwise Comparisons --- p.12 / Chapter 3. --- Pairwise Comparisons in Two-Way Layout with Covariates --- p.15 / Chapter 3.1 --- The Model --- p.15 / Chapter 3.2 --- The Test Statistics --- p.16 / Chapter 3.3 --- Computation of Upper Percentage Points --- p.17 / Chapter 3.4 --- Approximation Procedure --- p.21 / Chapter 3.5 --- Two-Way Layout with One Covariate --- p.21 / Chapter 4. --- Numerical Examples --- p.23 / Appendix A - An Algorithm in Solving Equation (3.2.4) for the value of ta --- p.35 / Appendix B - Evaluation of Multivariate Normal Probabilities --- p.38 / References --- p.41

Lau, Sin Yi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 64-66). / 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 --- p.2 / Chapter 1.3 --- Multiple Comparisons with a control in directional- mixed families --- p.5 / Chapter 1.4 --- Examples --- p.8 / Chapter 1.5 --- Thesis Objectives --- p.10 / Chapter 2 --- Evaluation of Power --- p.12 / Chapter 2.1 --- Definition and the Use of Power --- p.12 / Chapter 2.2 --- Computational Details --- p.13 / Chapter 2.3 --- All-pairs Power --- p.13 / Chapter 2.4 --- Any-pair Power --- p.15 / Chapter 2.5 --- Average Power --- p.16 / Chapter 2.6 --- Algorithm --- p.16 / Chapter 2.7 --- Results --- p.19 / Chapter 2.7.1 --- All-pairs Power --- p.20 / Chapter 2.7.2 --- Any-pair Power --- p.23 / Chapter 2.7.3 --- Average Power --- p.26 / Chapter 3 --- Sample Size Determination --- p.29 / Chapter 3.1 --- The required sample size for a pre-assigned all-pairs power --- p.31 / Chapter 3.2 --- The required sample size for a pre-assigned any-pair power --- p.41 / Chapter 3.3 --- The required sample size for a pre-assigned average power --- p.51 / Chapter 4 --- An Illustrative Example --- p.61 / Chapter 5 --- Conclusions --- p.63 / References --- p.64

Introduction: A typical task in quantitative data analysis is to derive estimates of population parameters based on sample statistics. For manifest variables this is usually a straightforward process utilising suitable measurement instruments and standard statistics such the mean, median and standard deviation. Latent variables on the other hand are typically more elusive, making it difficult to obtain valid and reliable measurements. One of the most widely used methods of estimating the parameter value of a latent variable is to use a summated score derived from a set of individual scores for each of the various attributes of the latent variable. A serious limitation of this method and other similar methods is that the validity and reliability of measurements depend on whether the statements included in the questionnaire cover all characteristics of the variable being measured and also on respondents’ ability to correctly indicate their perceived assessment of the characteristics on the scale provided. Methods without this limitation and that are especially useful where a set of objects/entities must be ranked based on the parameter values of one or more latent variables, are methods of paired comparisons. Although the underlying assumptions and algorithms of these methods often differ dramatically, they all rely on data derived from a series of comparisons, each consisting of a pair of specimens selected from the set of objects/entities being investigated. Typical examples of the comparison process are: subjects (judges) who have to indicate for each pair of objects which of the two they prefer; sport teams that compete against each other in matches that involve two teams at a time. The resultant data of each comparison range from a simple dichotomy to indicate which of the two objects are preferred/better, to an interval or ratio scale score for e d Bradley-Terry models, and were based on statistical theory assuming that the variable(s) being measured is either normally (Thurstone-Mosteller) or exponentially (Bradley-Terry) distributed. For many years researchers had to rely on these PCM’s when analysing paired comparison data without any idea about the implications if the distribution of the data from which their sample were obtained differed from the assumed distribution for the applicable PCM being utilised. To address this problem, PCM’s were subsequently developed to cater for discrete variables and variables with distributions that are neither normal or exponential. A question that remained unanswered is how the performance, as measured by the accuracy of parameter estimates, of PCM's are affected if they are applied to data from a range of discrete and continuous distribution that violates the assumptions on which the applicable paired comparison algorithm is based. This study is an attempt to answer this question by applying the most popular PCM's to a range of randomly derived data sets that spans typical continuous and discrete data distributions. It is hoped that the results of this study will assist researchers when selecting the most appropriate PCM to obtain accurate estimates of the parameters of the variables in their data sets.

The method of paired comparisons can be found all the way back to 1860, where Fechner made the first publication in this method, using it for his psychometric investigations [4]. Thurstone formalised the method by providing a mathematical background to it [9-11] and in 1927 the method’s birth took place with his psychometric publications, one being “a law of comparative judgment” [12-14]. The law of comparative judgment is a set of equations relating the proportion of times any stimulus k is judged greater on a given attribute than any other stimulus j to the scales and discriminal dispersions of the two stimuli on the psychological continuum. The amount of research done for discrete models of paired comparisons is not a lot. This study develops a new discrete model, the SL-model for paired comparisons. Paired comparisons data processing in which objects have an upper limit to their scores was also not yet developed, and making such a model is one of the aims of this report. The SLmodel is thus developed in this context; however, the model easily generalises to not necessarily having an upper limit on scores.

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Chan Ka Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 46-48). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple comparison procedures and their applications --- p.1 / Chapter 1.2 --- Different types of error control --- p.3 / Chapter 1.3 --- Single-step and stepwise procedures --- p.5 / Chapter 1.4 --- From familywise error rate control to false discovery rate control --- p.8 / Chapter 1.5 --- The FDR procedure of BH --- p.10 / Chapter 1.6 --- Application of the FDR procedure --- p.11 / Chapter 1.7 --- Family size and family size robustness --- p.16 / Chapter 1.8 --- Objectives of the thesis --- p.17 / Chapter 2 --- The Familywise Robustness Criteria --- p.18 / Chapter 2.1 --- The basic idea of familywise robustness --- p.18 / Chapter 2.2 --- Definitions and notations --- p.19 / Chapter 2.3 --- The measurement of robustness to changing family size --- p.21 / Chapter 2.4 --- Main Theorems --- p.21 / Chapter 2.5 --- Example --- p.23 / Chapter 2.6 --- Summary --- p.24 / Chapter 3 --- FDR and FWR --- p.26 / Chapter 3.1 --- Positive false discovery rate --- p.26 / Chapter 3.2 --- A unified approach to FDR --- p.29 / Chapter 3.3 --- The S procedure --- p.30 / Chapter 3.4 --- Family wise robustness criteria and the S procedure --- p.32 / Chapter 4 --- Simulation Study --- p.41 / Chapter 4.1 --- The setup --- p.41 / Chapter 4.2 --- Simulation result --- p.43 / Chapter 4.3 --- Conclusions --- p.44 / Bibliography --- p.46

Chan, Kin Kwok. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 68-69). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The effect of using a default error model --- p.8 / Chapter 2.1 --- Formulae to measure the prediction error --- p.9 / Chapter 2.2 --- The effect of autoregressive parameter on SD of prediction error --- p.10 / Chapter 2.3 --- Misspecification error of SD of prediction error when using a default error model --- p.12 / Chapter 2.4 --- Reporting error of SD of prediction error when using a default error model --- p.23 / Chapter 3 --- Error modelling by using benchmarks --- p.30 / Chapter 3.1 --- Review of an existing method --- p.30 / Chapter 3.2 --- Introduction of Benchmark Forecasting Method --- p.32 / Chapter 3.3 --- Comparison of estimation methods --- p.36 / Chapter 4 --- Performance of using fitted error model --- p.41 / Chapter 4.1 --- Fitted value and reporting value of SD of prediction error when using a fitted error model --- p.41 / Chapter 4.2 --- Misspecification error and reporting error when using a fitted error model --- p.45 / Chapter 4.3 --- Suggestions on the selection of default and fitted error model --- p.51 / Chapter 5 --- Benchmarking performance of using fitted AR(1) model for usual ARMA survey error --- p.55 / Chapter 5.1 --- Model settings for two usual ARMA survey error --- p.56 / Chapter 5.2 --- Simulation studies --- p.57 / Chapter 6 --- An illustrative example: Traveller Accommodation series --- p.62 / Chapter 7 --- Conclusion --- p.66 / Bibliography --- p.68

It is shown that a limitation of the various collation methods for paired comparison data currently available is their lack of validity when used in cases where the experiment is incomplete and particularly when the judgements are not replicated. Presented in this thesis is a reasonably thorough background to the method of paired comparisons and an overview of the existing methods for collating paired comparison data into a final ranking. As a result of the extensive review of existing collation methods, the thesis progresses logically to a new collation method that utilises all the available information from a set of pairwise preferences. The performance of the new collation method is extensively tested against existing methods by way of a simulation exercise which highlights the performance of the collation methods under different scenarios in terms of experiment size, experiment completeness and judgement consistency, as well as by considering the number of direct comparisons and the strength of competition. The new collation method and the existing collation method of Allen (1992) are applied to a set of real world data and the outcomes of the two methods are compared. The usefulness of paired comparisons in understanding the way judges use information to construct their own criteria when instructed to make preference decisions at a broad level is also considered and a real world application of this approach is performed. The main findings of this thesis are: „FƒnThe new methodology generally provides an improved performance when there are more than 10 objects to be ranked; „FƒnReplication of each pairwise judgement certainly improves the accuracy of the overall ranking, regardless of the level of judgement inconsistency; „FƒnIn the case of non-replication, the accuracy of the final ranking greatly improves as judgement consistency improves. In other words, if it is not possible to replicate individual pairwise judgements then high judgement consistency is important for a reasonable result; In the case of replication, the accuracy of the returned ranking improves with judgement consistency only in the case of the new method. For the existing methods, the accuracy actually decreases marginally with the improvement of judgement consistency, particularly if there is a low level of experiment completeness; In terms of experiment completeness, for non-replicated experiments, there is an increase in the accuracy of the returned ranking as the proportion of possible pairwise preferences completed increases, but not to the same extent as an increase in judgement consistency. That is, judgement consistency is actually more important than experiment completeness. This suggests that control over the design of the experiment (the extent of completeness and which pairwise preferences are completed) is less important than judgement consistency and replication ¡V certainly a finding not found reported in the literature; The new method outperforms the existing methods when there is perfect or very high judgement consistency.

The brain undergoes structural changes in response to new experiences like learning a new skill. Skilled motor movements depend greatly on the primary motor cortex for their execution. Recent studies describe rat strain differences in motor performance related to differential synaptic efficacy in the motor cortex of rats. Previous studies identified differences in motor performance related to differential dendritic morphology and strain related differences in synaptic function in the motor cortex. Strain differences are one way of investigating anatomical organization and behaviour of the motor system. The object of this research was to examine strain related differences in dendritic morphology in layer II / III pyramidal cells of the forelimb area of the sensory motor cortex in both Long-Evans and Fischer 344 rats after reach training. This research also examined whether changes in reaching behaviour could be attributed to changes in dendritic morphology. Rats were trained once a day for 30 days to reach for a food pellet through a slot in a reaching box. Pyramidal cells in the motor sensory forelimb (MSF) cortex were stained with the Golgi Cox method. Subsequent analysis of Sholl and branch order data of cell drawings determined that there were no significant differences in any measure of dendritic length or dendritic length at branch order 3, 4, 5 of pyramidal cells in layer II/III of the MSF cortex between the Long Evans and Fischer 344 rat strain. The only significant strain related difference was that the Fischer 344 strain exhibited fewer reaches for each food pellet obtained, demonstrating greater reaching proficiency than similarly trained Long-Evans rats. These findings suggest that further research examining strain comparisons is required to understand the neural mechanisms underlying the differences in motor behaviour observed in these rat strains. / October 2006