This study sought to determine the effect of varying degrees of disproportionality of four methods of handling disproportionality cell frequencies in two-way analysis of variance. A Monte Carlo simulation procedure was employed. Two multiple linear regression techniques and two "approximate" techniques were compared.

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The additive-plus-multiplicative model, Y_ij = μ + α_i + β_j + ∑_p=1^kλ_pτ_piγ_pj, has been used to describe multiplicative interaction in an unreplicated experiment. Outlier effects often appear as interaction in a two-way analysis of variance with one observation per cell. I use this model in the same setting to study outliers. In data sets with significant interaction, one may be interested in determining whether the cause of the interaction is due to a true interaction, outliers or both. I develop a new technique which can show how outliers can be distinguished from interaction when there are simple outliers in a two-way table. Several examples illustrating the use of this model to describe outliers and interaction are presented. I briefly address the topics of leverage and influence. Leverage measures the impact a change in an observation has on fitted values, whereas influence evaluates the effect deleting an observation has on model estimates. I extend the leverage tables for an additive-plus-multiplicative model of rank 1 to a rank k model. Several examples studying the influence in a two-way nonreplicated table are given. / Ph. D.

The purpose of this work is to investigate methods of obtaining special percentage points of the studentized range, In fulfilling this purpose, two new methods are developed and used. / Master of Science

The problem discussed in this paper is the estimation of a single missing observation, two missing observations and several missing observations in a Group Visible (Singular) for Shirley balanced incomplete blocks design with two associate classes. Subsequently the analysis of variance, of the data augmented by the estimates of the missing observations, is derived. The method, first employed by Yates (1933), was followed to minimize the error sum of squares. Explicit formulae were developed, for the estimates of one missing observation, two missing observations occurring in various configurations and general formulae for z (= n) missing observations for certain particular configurations. Analysis of the data augmented by the estimates of the missing observations lead to positive bias in the case of treatment sum of squares, a method of analysis was discussed to eliminate this bias. A numerical example of illustrating the technique of estimating missing observations in a GDS P.B.I.B. design was given. The approximate and exact tests were performed, for the null hypothesis of no treatment differences, using the intra-block error mean square. / Master of Science

A method has been proposed for obtaining confidence intervals for the differences between treatment means in an analysis of variance. The intervals have the following properties: (1) The probability that the interval will cover the parameter is greater than or equal to (1 - α), and (2) If the same procedure is applied simultaneously to each of the pO2 differences among p means, the probability that all confidence intervals will cover the parameters correctly is at least (1 - α) ^{p - 1}. The same properties hold if the procedure is simultaneously applied to special linear comparisons among the means as well as to differences between single means. The intervals are complex in that the limits are dependent on the values of nuisance parameters. Three alternatives for handling these nuisance parameters are discussed, and one is preferred for use in practice. / Master of Science

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