Applied Statistics Commons^™

An Evaluation Of Truncated Sequential Test, Ryh-Thinn Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of sequential analysis has led to the proposal of tests that are more economical in that the Average Sample Number (A. S. N.) of the sequential test is smaller than the sample size of the fixed sample test. Although these tests usually have a smaller A. S. N. than the equivelent fixed sample procedure, there still remains the possibility that an extremely large sample size will be necessary to make a decision. To remedy this, truncated sequential tests have been developed.

A method of truncation for testing a composite hypotheses is studied. This method is formed by mixing …

A Study Of Four Statistics, Used In Analysis Of Contingency Tables, In The Presence Of Low Expected Frequencies, Jane R. Post

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Four statistics used for the analysis of categorical data were observed in the presence of many zero cell frequencies in two way classification contingency tables. The purpose of this study was to determine the effect of many zero cell frequencies upon the distribution properties of each of the four statistics studied. It was found that Light and Margolin's C and Pearson's Chi-square statistic closely approximated the Chi-square distribution as long as less than one-third of the table cells were empty. It was found that the mean and variance of Kullbach's 2I were larger than the expected values in the presence …

The Computation Of Eigenvalues And Eigenvectors Of An Nxn Real General Matrix, Yeh-Hao Ma

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The eigenvalues of the matrix eigenproblem Ax = λx are computed by the QR double-step method and the eigenvectors by inverse power method.

The matrix A is preliminarily scaled by the equilibration and normalization procedure. The scaled matrix is then reduced to an upper-Hessenberg form by Householder's method. The QR double-step iteration is performed on the upper-Hessenberg matrix. After all the eigenvalues are found, the inverse power method is performed on the upper-Hessenberg matrix to obtain the corresponding eigenvectors.

The program consists of five subroutines which is able to find real and/or complex eigen value/vector of an nxn real matrix.

Program For Missing Data In The Multivariate Normal Distribution, Chi-Ping Lu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Missing data can often cause many problems in research work. Therefore for carrying out analysis, some procedure for obtaining estimates in the presence of missing data should be applied. Various theories and techniques have been developed for different types of problems.

Analysis of the Multivariate Normal Distribution with missing data is one of the areas studied. It has been discussed earlier by Wilkes (1932), Lord (1955), Edgett (1956) and Hartley (1958). They have established some basic concepts and an outline in the way of estimation.

In the last ten years, A. A. Afifi and R. M. Elasfoff also have contributed …

Discriminant Function Analysis, Kuo Hsiung Su

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The technique of discriminant function analysis was originated by R.A. Fisher and first applied by Barnard (1935). Two very useful summaries of the recent work in this technique can be found in Hodges (1950) and in Tosuoka and Tiedeman (1954). The techniques have been used primarily in the fields of anthropology, psychology, biology, medicine, and education, and have only begun to be applied to other fields in recent years.

Classification and discriminant function analyses are two phases in the attempt to predict which of several populations an observation might be a member of, on the basis of multivariate measurements. Both …

An Evaluation Of Bartlett's Chi-Square Approximation For The Determinant Of A Matrix Of Sample Zero-Order Correlation Coefficients, Stephen M. Hattori

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The single equation least-squares regression model has been extensively studied by economists and statisticians alike in order to determine the problems which arise when particular assumptions are violated. Much literature is available in terms of the properties and limitations of the model. However, on the multicollinearity problem, there has been little research, and consequently, limited literature is available when the problem is encountered. Farrar & Glauber (1967) present a collection of techniques to use in order to detect or diagnose the occurrence of multicollinearity within a regression analysis. They attempt to define multicollinearity in terms of departures from a hypothesized …

Multivariate Analysis Of Variance For Simple Designs, Yin-Yin Chen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The analysis of variance is a well known tool for testing how treatments change the average response of experimental units. The essence of the procedure is to compare the variation among means of groups of units subjected to the same treatment with the within treatment variation. If the variation among means is large with respect to the within group variation we are likely to conclude that the treatments caused the variation and hence we say the treatments cause some change in the group means.

The usual analysis of variance checks how far apart the group means are in a single …