Thesis (Ph.D.)--University of Melbourne, Dept. of Mathematics and Statistics, 2007. / Typescript. Includes bibliographical references.

Thesis (Ph. D.)--University of California, San Diego, 2004. / Vita. Includes bibliographical references.

Thesis (M. Soc. Sc.)--University of Hong Kong, 1993. / Includes bibliographical references (leaves 58-59).

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 124-133).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 179-183).

Thesis (M.Sc.)--Memorial University of Newfoundland, 2004. / Bibliography: leaves 91-92.

Thesis (M.Soc.Sc.)--University of Hong Kong, 1993. / Includes bibliographical references (leaves 58-59) Also available in print.

Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability. Monte Carlo simulation methodology was used to fulfill the purpose of this study. Initially, data populations with various manipulated conditions were generated (N = 100,000). Subsequently, 500 random samples were drawn with replacement from each population, and data was subjected to canonical correlation analyses. The canonical correlation results were then analyzed using descriptive statistics and an ANOVA design to determine under which condition(s) the squared canonical correlation coefficient was most attenuated when compared to population Rc2 values. This information was analyzed and used to determine what effect, if any, the different conditions considered in this study had on Rc2. The results from this Monte Carlo investigation clearly illustrated the importance of score reliability when interpreting study results. As evidenced by the outcomes presented, the more measurement error (lower reliability) present in the variables included in an analysis, the more attenuation experienced by the effect size(s) produced in the analysis, in this case Rc2. These results also demonstrated the role between and within set correlation, variable set size, and sample size played in the attenuation levels of the squared canonical correlation coefficient.

I. A Comparison of the Effectiveness of Tournaments. A paired-comparison experiment involving t treatments is analogous to a tournament with t players. A balanced experiment, in which every possible pair occurs once per replication, is the counterpart of a round robin tournament. When the objective is to pick the best treatment, the balanced design may prove to be more expensive than necessary. The knock-out tournament has been suggested as an alternative requiring fewer units of each treatment per replication. In this paper round robin, replicated knock-out, and double elimination tournaments are investigated for their effectiveness in selecting the best one or tour players. Effectiveness is gauged in terms of the two criteria (a) the probability that the best player wins and (b) the expected number of games. For general values of the parameters involved, expressions are derived for the evaluation of the criteria. Comparisons are made on the basis of series of assigned parameter values. Possibilities for the extension of the study are briefly discussed. II. Ties in Paired-Comparison Experiments. In making paired comparisons a judge frequently is unable to express a real preference in a number of the pairs he judges. In spite of this, some or the methods in current use do not permit the judge to declare a tie. In other methods tied observations are either ignored or divided equally or randomly between the tied members. It appears that there is a need, at least in the estimation of response-scale values, for a method which takes tied observations into account. In the Thurstone-Mosteller method the standardized distribution of the difference of two stimulus responses is normal with unit variance and mean equal to the difference or the two mean stimulus responses. In prohibiting ties the assumption is in effect made that all differences, however small, are perceptible to the judge. In this paper the assumption is made that a tie will occur whenever the difference between the judge's responses to the two stimuli lie below a certain threshold, i.e. if the difference lies between -t and t the judge will declare a tie. The parameter t and the mean stimulus responses are estimated by least squares. To overcome a difficulty presented by correlated data, an angular response law is postulated for the response-scale differences. In the resulting transformed data non-homogeneity of variances is encountered. In effecting a weighted solution, weights are first determined by using a preliminary unweighted analysis, and an iterative procedure is proposed. Large-sample variances and covariances of the estimates are obtained. A test of the validity of the model is described. A computational procedure is set up, and exemplified through application to experimental data. / Ph. D.

To reduce the variance of metamodel coefficients, simulation analysts often advocate the use of correlation induction strategies. Under certain conditions, these strategies have been shown to reduce the variance of metamodel coefficients without producing significant bias in the coefficient estimates. Although these procedures are very useful for estimating metamodels, the application of many statistical analysis techniques is inappropriate unless the analyst is assured that a pure error component is present in the response. Crenshaw and Tew have demonstrated the absence of pure error in experiments in which all random number streams are used to induce correlations. Mihram argues that a pure error component can be maintained by selecting the seeds for at least one random component randomly and non-repetitively for all design points and replications. In this thesis, random components for which seeds are randomly and non-repetitively selected are referred to as pure error generators. This thesis examines the selection of pure error generators in the context of univariate response, replicated simulation experiments. To assess the impact of pure error generator selection, we give the results of an extensive series of Monte-Carlo experiments in which the Schruben-Margolin strategy is applied for each possible pure error generator in each of two simulation models. To determine causes for the differences in pure error generator performance, four pure error generator selection methods are outlined, tested, and compared to the results of the Monte-Carlo experiments. The results strongly suggest the importance of careful pure error generator selection and indicate that the primary difference in their performance is related to their ability to maintain the prescribed correlation structures of the correlation induction strategy. / Master of Science