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The primary problem considered was to what degree anxiety and sociopathy are found in groups that, by external criteria, differ in level of adjustment.

Typescript (photocopy). / Digitized by Kansas Correctional Industries / Department: Statistics.

Abstract not available

Testing main effects and interaction effects in factorial designs are basic content in statistics textbooks and widely used in various fields. In balanced designs there is general agreement on the appropriate main effect and interaction sums of squares and these are typically displayed in an analysis of variance (ANOVA). A number of methods for analyzing unbalanced designs have been developed, but in general they do not lead to unique results. For example, in SAS one can get three different main effect sums of squares in an unbalanced design. I, If these results are viewed from the theory of the general linear model, then it is typically the case that the different sums of squares all lead to F-tests, but they are testing different linear hypotheses. In particular, if one clearly specifies the linear hypothesis being tested, then linear model theory leads to one unique deviation sum of squares. One exception to this statement is an ANOVA, called an unweighted means ANOVA (UANOVA) introduced by Yates (1934). The deviation sum of squares in a UNANOVA typically does not lead to an F-test and hence does not reduce to a usual deviation sum of squares for some linear hypothesis. The UANOVA tests have been suggested by several writers as an alternative to the usual tests. Almost all of these results are limited to the one-way model or a two-way model with interaction, and hence the UANOVA procedure is not available for a general linear model. This thesis generalizes the UANOVA test prescribed in the two-way model with interaction to a general linear model. In addition, the properties of the test are investigated. It is found, similar to the usual test, that computation of the UANOVA test statistic does not depend on how the linear hypothesis is formulated. It is also shown that the numerator of the UANOVA test is like a linear combination of independent chi-squared random variables as opposed to a single chi-squared random variable in the usual test. In addition we show how the Imhof (1961) paper can be used to determine critical values, p-values and power for the UANOVA test. Comparisons with the usual test are also included. It is found that neither test is more powerful than the other. Even so, for most circumstances our general recommendation is that the usual test is probably superior to the UANOVA test. / Graduation date: 2002

This thesis is about multiple hypothesis testing and its relation to the P-value. In Chapter 1, the methodologies of hypothesis testing among the three inference schools are reviewed. Jeffreys, Fisher, and Neyman advocated three different approaches for testing by using the posterior probabilities, P-value, and Type I error and Type II error probabilities respectively. In Berger's words ``Each was quite critical of the other approaches." Berger proposed a potential methodological unified conditional frequentist approach for testing. His idea is to follow Fisher in using the P-value to define the strength of evidence in data and to follow Fisher's method of conditioning on strength of evidence; then follow Neyman by computing Type I and Type II error probabilities conditioning on strength of evidence in the data, which equal the objective posterior probabilities of the hypothesis advocated by Jeffreys. Bickis proposed another estimate on calibrating the null and alternative components of the distribution by modeling the set of P-values as a sample from a mixed population composed of a uniform distribution for the null cases and an unknown distribution for the alternatives. For tackling multiplicity, exploiting the empirical distribution of P-values is applied. A variety of density estimators for calibrating posterior probabilities of the null hypothesis given P-values are implemented. Finally, a noninterpolatory and shape-preserving estimator based on B-splines as smoothing functions is proposed and implemented.

This thesis is about multiple hypothesis testing and its relation to the P-value. In Chapter 1, the methodologies of hypothesis testing among the three inference schools are reviewed. Jeffreys, Fisher, and Neyman advocated three different approaches for testing by using the posterior probabilities, P-value, and Type I error and Type II error probabilities respectively. In Berger's words ``Each was quite critical of the other approaches." Berger proposed a potential methodological unified conditional frequentist approach for testing. His idea is to follow Fisher in using the P-value to define the strength of evidence in data and to follow Fisher's method of conditioning on strength of evidence; then follow Neyman by computing Type I and Type II error probabilities conditioning on strength of evidence in the data, which equal the objective posterior probabilities of the hypothesis advocated by Jeffreys. Bickis proposed another estimate on calibrating the null and alternative components of the distribution by modeling the set of P-values as a sample from a mixed population composed of a uniform distribution for the null cases and an unknown distribution for the alternatives. For tackling multiplicity, exploiting the empirical distribution of P-values is applied. A variety of density estimators for calibrating posterior probabilities of the null hypothesis given P-values are implemented. Finally, a noninterpolatory and shape-preserving estimator based on B-splines as smoothing functions is proposed and implemented.

Thesis (M.A.)--York University, 1999. Graduate Programme in Psychology. / Typescript. Includes bibliographical references (leaves 161-176). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pMQ59127.