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The purpose of this paper was to present the exact analysis of variance with unequal variances. Bishop presented the new procedure for the r-way layout ANOVA. In this paper, one and two way layout ANOVA were explained and Bishop's method and Standard method were compared by using a Monte Carlo method.

In the past decades there has been onsiderable commercial and academic interest in methods for monitoring control system performance for linear systems. Far less has been written on control system performance for nonlinear dynamic / stochastic systems. This thesis presents research results on three control performance monitoring topics for the nonlinear systems: i) Controller assessment of a class of nonlinear systems: The use of autoregressive moving average (ARMA) models to assess the control loop performance for linear systems is well known. Classes of nonlinear dynamic / stochastic systems for which a similar result can be obtained are established for SISO discrete systems. For these systems, the performance lower bounds can be estimated from closed-loop routine operating data using nonlinear autoregressive moving average with exogenous inputs (NARMAX) models. ii) Variance decomposition of nonlinear systems / time series: We develop a variance decomposition approach to quantify the effects of different sources of disturbances on the nonlinear dynamic / stochastic systems. A method, called ANOVA-like decomposition, is employed to achieve this variance decomposition. Modifications of ANOVA-like decomposition are proposed so that the NOVA-like decomposition can be used to deal with the time dependency and the initial condition. iii) Parameter uncertainty effects on the variance decomposition: For the variance decomposition in the second part, the model parameters are assumed to be exactly known. However, parameters of empirical or mechanistic models are uncertain. The uncertainties associated with parameters should be included when the model is used for variance analysis. General solutions of the parameter uncertainty effects on the variance decomposition for the general nonlinear systems are proposed. Analytical solutions of the parameter uncertainty effects on the variance decomposition are provided for models with linear parameters. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2007-10-17 16:02:26.376 / This work was sponsored by NSERC Discovery, NSERC Equipment, Shell Global Solutions, OGSST and QGA

Surgical scheduling is complicated by naturally occurring, and human-induced variability in the demand for surgical services. We used time series methods to detect, model and forecast these behaviors in surgical demand time series to help improve the scheduling of scarce surgical resources. With institutional approval, we studied 47,752 surgeries undertaken at a large academic medical center over a six-year time frame. Each daily sample in this time series represented the aggregate total hours of surgeries worked on a given day. Linear terms such as periodic cycles, trends, and serial correlations explained approximately 80 percent of the variance in the raw data. We used a moving variance filter to help explain away a large share of the heteroscedastic behavior mainly attributable to surgical activities on specific US holidays, which we defined as holiday variance. In the course of this research, we made a thoughtful attempt to understand the time series structure within our surgical demand data. We also laid a foundation, for further development, of two time series techniques, the multiwindow variance filter and cyclostatogram that can be applied not only to surgical demand time series, but also to other time series problems from other disciplines. We believe that understanding the non-stationarity, in surgical demand time series, may be an important initial step in helping health care managers save critical health care dollars. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-09 11:55:42.494

When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.

Master of Science / Department of Statistics / Dallas E. Johnson / Variability is inherent in most data and often it is useful to study the variability so scientists are able to make more accurate statements about their data. One of the most popular ways of analyzing variance in data is by making use of a one-way ANOVA which consists of partitioning the variability among observations into components of variability corresponding to between groups and within groups. One then has σ(subY)(superscript 2)=σ (sub A) (superscript)2+σ(sub e)(superscript 2). Thus there are two variance components. In certain situations, in addition to estimating these components of variance, it is important to estimate functions of the variance components. This report is devoted to methods for constructing confidence intervals for three particular functions of variance components in the unbalanced One- way random effects models. In order to compare the performance of the methods, simulations were conducted using SAS® and the results were compared across several scenarios based on the number of groups, the number of observations within each group, and the value of sigma (sub A)(superscript 2).