Physical Sciences and Mathematics Commons^™

The Use Of Contingency Table Analysis As A Robust Technique For Analysis Of Variance, Mei-Eing Chiu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to compare Analysis of Variance with Contingency Table Analysis when the data being analyzed do not satisfy Analysis of Variance assumptions. The criteria for comparison are the powers of the Standard variance-ratio and the Chi-square test.

The test statistic and powers were obtained by Monte Carlo.

1. Calculate test statistic for each of 100 trials, this process was repeated 12 times. Each time different combination of means and variances were used.

2. Powers were obtained for each of 12 combinations of means and variances.

Whether Analysis of Variance or Contingency Table Analysis is a …

Exact Analysis Of Variance With Unequal Variances, Noriaki Yanagi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

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.

A Μ-Model Approach On The Cell Means: The Analysis Of Full, Design Models With Non-Orthogonal Data, Richard Van Koningsveld

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This work considers the application of a µ-model approach on the cell means to a special yet important class of experimental designs. These include full factorial, completely nested, and mixed models with one or more observations per cell. By limiting attention to full models, an approach to the general data situation is developed which is both conceptually simple and computationally advantageous.

Conceptually, the method is simple because the design related effects are defined as if the cell means are single observations. This leads to a rather simple algorithm for generating main effect contrasts, from which associated interaction contrasts can also …

Selecting The Best Linear Model From A Subset Of All Possible Models For A Given Set Of Predictors In A Multiple Linear Regression Analysis, David L. Jensen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Sixteen "model building" and "model selection" procedures commonly encountered in industry, all of which were initially alleged to be capable of identifying the best model from the collection of 2^k possible linear models corresponding to a given set of k predictors in a multiple linear regression analysis, were individually summarized and subsequently evaluated by considering their comparative advantages and limitations from both a theoretical and a practical standpoint. It was found that none of the proposed procedures were absolutely infallible and that several were actually unsuitable. However, it was also found that most of these techniques could still be …