Applied Statistics Commons^™

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 …

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 …

Comparison Of Transition Matrices Between Metropolitan And Non-Metropolitan Areas In The State Of Utah Using Juvenile Court Data, Sung-Ik Song

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to use Markov Chains for the study of youths referred to the juvenile court in the metropolitan and non-metropolitan areas of the state of Utah.

Two computer programs were written for creating case histories for each person referred to the court and for testing for the significance of the difference among several transition matrices.

Another computer program, which was written by Soo Hong Uh, was used for analyzing realizations of a Markov chains up to the 4th order; a third computer program, originally written by David White, was used for interpreting Markov chains.

The …

An Investigation Of Cluster Analysis, John C. Klingel

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Three cluster analysis programs were used to group the same 64 individuals, generated so as to represent eight populations of eight individuals each. Each individual had quantitative values for seven attributes. All eight populations shared a common attribute variance-covariance matrix.

The first program, from F. J. Rohlf's MINT package, implemented single linkage. Correlation was used as the basis for similarity. The results were not satisfactory, and the further use of correlation is in question.

The second program, MDISP, bases similarity on Euclidean distance. It was found to give excellent results, in that it clustered individuals into the exact populations from …

Sequential Analysis For Tolerances Of Noxious Weed Seeds, Seung Tokko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The application of a sequential test, the sequential probability ratio test, for the tolerances of noxious weed seeds is studied. It is proved that the sequential test can give a similar power curve to that of the current fixed sample test if the test parameters are properly chosen.

The average sample size required by a sequential test, in general, is smaller than that of the existing test. However, in some cases it requires relatively a larger sample than current test.

As a solution to the problem a method of truncation is considered. A kind of mixed procedure is suggested. This …

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 …

A Two Sample Test Of The Reliability Performance Of Equipment Components, Miki Lynne Coleman

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to develop a test which can be used to compare the reliability performances of two types of equipment components to determine whether or not the new component satisfies a given feasibility criterion.

Two types of tests were presented and compared: the fixed sample size test and the truncated sequential probability ratio test. Both of these tests involve use of a statistic which is approximately distributed as F.

This study showed that the truncated sequential probability ratio test has good potential as a means of comparing two component types to see whether or not the …

Statistical Analysis For Tolerances Of Noxious Weed Seeds, Yadolah Dodge

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

An analysis of the previous method for testing tolerances of noxious weed seeds was performed. Problems of the current techniques were discussed, and the solution to these problems was given.

A new technique of testing through the sequential test ratio was developed, and results examined.

The sequential test was found to be useful enough to include the use of it in determining tolerances for noxious weed seeds.

This study did show that the use of sequential tests does have excellent potential and flexibility as a statistical tool for the tolerances of noxious weed seeds.

Fitting Some Families Of Contagious Distributions To Biological And Accident Data, Yung-Sung Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Four families of contagious distributions--generalized Poisson distributions, generalized binomial distributions, generalized Pascal distributions, and generalized log-zero distributions--are investigated in this thesis.

The family of generalized Poisson distributions contains five distributions: the Neyman Type A, the "Short," the Poisson binomial, the Poisson Pascal, and the negative binomial. The family of generalized binomial distributions contains eight distributions: the binomial Poisson, the binomial binomial, the binomial Pascal, the binomial log-zero, the Poisson with zeros, the binomial with zeros, the Pascal with zeros, and the log-zero with zeros. The family of generalized Pascal distributions contains four distributions: the Pascal Poisson, the Pascal binomial, the …

The Effectiveness Of Categorical Variables In Discriminant Function Analysis, Preston Jay Waite

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A preliminary study of the feasibility of using categorical variables in discriminant function analysis was performed. Data including both continuous and categorical variables were used and predictive results examined.

The discriminant function techniques were found to be robust enough to include the use of categorical variables.

Some problems were encountered with using the trace criterion for selecting the most discriminating variables when these variables are categorical. No monotonic relationship was found to exist between the trace and the number of correct predictions.

This study did show that the use of categorical variables does have much potential as a statistical tool …

Resource Requirements Determination (Based On Statistical Methods), Robert L. Howard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of determining resource requirements at an Air Force maintenance depot were developed.

The first method is designed for new workloads and is based on infinite queuing theory formulas. Tables have been developed for this method.

The second method is designed for workload with, at minimum, several months of historical data. An optimum fit test was designed to aid in fitting and smoothing the empirical data to the normal distribution. These data are then input to simulation model for determination of resource requirements.

Model For Bathtub-Shaped Hazard Rate: Monte Carlo Study, Glen S. Leithead

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A new model developed for the entire bathtub-shaped hazard rate curve has been evaluated as to its usefulness as a method of reliability estimation. The model is of the form:

F(t) = 1 - exp - (ϴ₁t^L + ϴ₂t + ϴ₃t^M)

where "L" and "M" were assumed known.

The estimate of reliability obtained from the new model was compared with the traditional restricted sample estimate for four different time intervals and was found to have less bias and variance for all time points.

This was a monte carlo study and the …

A Report On The Statistical Properties Of The Coefficient Of Variation And Some Applications, Howard P. Irvin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Examples from four disciplines were used to introduce the coefficient of variation which was considered to have considerable usage and application in solving Quality Control and Reliability problems.

The statistical properties were found in the statistical literature and are presented, namely, the mean and the variance of the coefficient of variation. The cumulative probability function was determined by two approximate methods and by using the noncentral t distribution. A graphical method to determine approximate confidence intervals and a method to determine if the coefficients of variation from two samples were significantly different from each other are also provided (with examples). …

Analysis Of Contingency Tables, James Joseph Biundo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of analyzing multi-dimensional frequency data are detailed.

The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴ_i's and ϴ_j's. The ϴ_i's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴ_ij are not zero, then the ϴ_i's are analogous to a main effect in a 2^m factorial analysis, (m = number of factors or classifications). The ϴ_if's may be interpreted as a measure and direction …

Design Optimization Using Model Estimation Programming, Richard Kay Brimhall

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Model estimation programming provides a method for obtaining extreme solutions subject to constraints. Functions which are continuous with continuous first and second derivatives in the neighborhood of the solution are approximated using quadratic polynomials (termed estimating functions) derived from computed or experimental data points. Using the estimating functions, an approximation problem is solved by a numerical adaptation of the method of Lagrange. The method is not limited by the concavity of the objective function.

Beginning with an initial array of data observations, an initial approximate solution is obtained. Using this approximate solution as a new datum point, the coefficients for …

Spectral Analysis Of Time-Series Associated With Control Systems, Karl Leland Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The progress of science is based to a large degree on experimentation. The scientist, engineer, or researcher is usually interested in the results of a single experiment only to the extent that he hopes to generalize the results to a class of similar experiments associated with an underlying phenomenon. The process by which this is done is called inductive inference and is always subject to uncertainty. The science of statistical inference can be used to make inductive inferences for which the degree of uncertainty can be measure in terms of probability. A second type of inference called deductive inference is …