Applied Statistics Commons^™

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 …

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.

Cephalometric Norms For The Mexican Population Using The Ricketts, Steinar, And Tweed Analyses, Eduardo A. Velarde

Loma Linda University Electronic Theses, Dissertations & Projects

In order to investigate the characteristics of the facial complex of the Mexican and to compare them with the Caucasian, a sample of 40 subjects, 31 males and nine females, of Latin American origin from Chihuahua, Chihuahua, Mexico, with a mean age of 16.6 years, were selected for this study. The criteria for selection were visual and only individuals with clinical normal, Angle Class I occlusion were chosen.

Lateral head Roentgenograms were obtained and cephalometric evaluation of the Skeletal and Dental Pattern was carried out using the Ricketts, Steiner, and Tweed Analyses.

The mean values for the Mexican were compared …

Effects Of Cocaine, Nicotine And Diet On Voluntary Alcohol Consumption In Rats, Zaida Raquel Cordero Loayza

Loma Linda University Electronic Theses, Dissertations & Projects

The consumption of alcohol is a problem not only in this country (U.S.), but also in many other places in the world. Thus we find the Indians in Peru, Bolivia and other neighboring countries (Ecuador and northern part of Argentina) consuming alcohol to the point that they become alcoholics, in addition to this they also chew coca leaves, plant from which cocaine is extracted.

In an effort to establish the cause for this behavior, we put Sprague-Dawley albino rats on either a poor or good basal diet. Once every other day the rats were injected with a solution of cocaine. …

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 …

Grain Moisture And The Weather : What Can The Records Tell Us?, M W. Perry, P. A. Fievez

Journal of the Department of Agriculture, Western Australia, Series 4

The expansion of cereal production in areas along the south coast has exposed harvesting problems associated with high grain moisture.

A grain delivery standard of 12 per cent moisture means that, in the absence of grain drying facilities, harvesting times in the field are restricted to those hours when grain moisture falls below this figure.

Grain moisture, however, remains the major problem and for planning purposes, producers require an estimate of the harvesting time available in a given year. This will depend on all the climatic variables which affect grain moisture. These include rainfall and dew which deposit water directly …

Principal Component Factor Analysis, Kuang-Ming Chu

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

The principal-factor solution is probably the most widely used technique in factor analysis and a relatively straight forward method to determine the minimum number of independent dimensions needed to account for most of the variance in the original set of variables.

The principal components approach to parsimony was first proposed by Karl Pearson (1901) who studied the problem for the case of nonstochastic variables, and in a different context. Hotelling provided the full development of the method (1933) and Thomson (1947) was the first to apply it to the principal factor analysis.

This method was first developed to deal with …

Matrix Norms, I-Hui C. Cheng

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

In many situations it is very useful to have a single nonnegative real number to be, in some sense, the measure of the size of a vector or a matrix. As a matter of fact we do a similiar thing with scalars, we let jÀj represent the familiar absolute value or modulus of À. Fora vector x e: C , one way n of assigning magnitude is the usual definition of length, Il I 1/2 2 1/2 xl= = {jxij } , which is called the euclidean norm of x. In this case, length gives an overall estimate of 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 …

Computer Programs Supporting The Teaching Of Statistics, Chien-Hwa Liu

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

During the past few years there has been an increasing interest in developing computer packages to enhance the teaching of elementary statistics. The conventional ways of teaching statistics have used such devices as desk calculators, tables of functions, short-cut calculating formulas and electronic calculators, etc. to manipulate the involved computations. Electronic computers, in the past decade, have been broadly used in universities and colleges in many ways. It is only natural to extend the use of computers to the teaching function. Remote terminals can now be installed in any classroom and bring the computer to the students.

A Monte Carlo Comparison Of Nonparametric Reliability Estimators, Jia-Jinn Yueh

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

It is very difficult to construct a reliability model for a complex system. However, the reliability model for a series configuration is relatively simple. In the simplest case in which the components are mutually independent, the system reliability can be represented as follows:

R_s(x) = ∑ⁿ_i=1R_i(x),

where R_i is the reliability for the i^th component. It is also known that for moderate levels of system reliability for large systems, the component reliability must be high.

Extreme Value Theory indicates that under very general conditions, the initial form of the distribution function …

The Evaluation Of Glasser's Maximum Likelihood Method On Missing Data In Regression, Gayle M. Yamasaki

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

Missing data in regression is often a problem to research workers because standard regression methods are applicable only to complete data sets. At present there are three general methods for solving the problem of missing data.

At first, the reduced data method, reduces the incomplete data set to a complete data set before analyzing. Although this method is very simple to apply, substantial amounts of information are sometimes lost when data is eliminated. This results in less precise estimates of the regression parameters.

The second method, generalized least squares, estimates the missing values through least squares techniques, thus obtaining a …

Integer Programming By Cutting Planes Methods, Sung-Yen Wu

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

Linear programming is a relatively new, very important branch of modern mathematics and is about twenty five years old.

In this day and age, most planners and decision makers will acknowledge that some linear optimization problems are worth the expense and trouble to solve. Using linear programming technique as a tool to make decision plannes are able to greatly redice cost or increase profit for any project under consideration.

Since Dr. George B. Dantzig published his first paper on the simplex method in 1947, progress in that field has been rapid. Although the first applications were military in nature, it …

A Nonparametric Solution For Finding The Optimum Useful Life Of Equipment, Barry T. Stoll

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

It is often the case that equipment used by industry must be replaced with new equipment from time to time either because frequent malfunctions make it too costly to repair, or because the equipment has simply worn out. The new equipment often has the nature of either malfunctioning soon after installation due to manufacturing defects, or functioning for an extended period of time because it is free of these defects. For this reason, equipment is often given a preliminary running called the burn-in which gives no useful output but merely tests for manufacturing defects. Also, after a given amount of …

Canonical Analysis Of Several Sets Of Variables, Chong S. Kim

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

Many procedures have been proposed for analyzing and describing multivariate dependence structure.

Partial correlation, multiple correlation, canonical correlation, principal component and factor analysis are used to analyze the dependence structures of a multinormal population.

For a partial correlation analysis it is necessary to decide which variables are to be correlated and which of the remaining variables must be held constant.

Multiple correlation demands that one variable be dependent upon some or all of the remaining variates.

For a canonical correlation, the variables must be collected into two or more sets. The factor analysis technique is for explaining the covariances of …

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 …

A Simple Method For The Construction Of Empirical Confidence Limits For Economic Forecasts, William (Bill) H. Williams, M. L. Goodman

Publications and Research

A simple method for the construction of empirical confidence intervals for time series forecasts is described. The procedure is to go through the series making a forecast from each point in time. The comparison of these forecasts with the known actual observations will yield an empirical distribution of forecasting errors. This distribution can then be used to set confidence intervals for subsequent forecasts. The technique appears to be particularly useful when the mechanism generating the series cannot be fully identified from the available data or when limits based on more standard considerations are difficult to obtain.

U. S. U. Mathematical Programming Package, R. Gary Goodwin

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

Solving mathematical programming problems without the aid of electronic computers is very time consuming even for a mathematical model consisting of only a few constraints and variables. The objective of this report is to illustrate the use of mathematical programming computer routines available at Utah State University. Computer routines discussed are the International Business Machines (IBM), Mathematical Programming System (MPS) package, a quadratic programming routing, a zero-one integer programming routing, and a transportation code. The MPS package is a product of IBM; the quadratic programming routing was develop by the author: the last three routines were obtained from the IBM …

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

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

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

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 …

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.

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.

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 …

A Bayes Rule For The Symmetric Multiple Comparisons Problem, Aban Nawabi

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

Many procedures have been proposed for the symmetric multiple comparisons problem in recent years. These include a "protected" least significant difference procedure due to Fisher (FSD), a multiple range rule by Duncan, and HSD (honest significant difference) procedure by Tukey, and a procedure for testing all contrasts by Scheffe.

The tests which are mentioned above are either comparison-wise or experiment-wise approaches. The probability of Type I error is intended to be a for all comparisons made when an experiment-wise approach is used. Whereas, the probability of Type I error referred to each comparison is a comparison-wise approach. Both approaches can …

A Non-Parametric Sequential Signed-Rank Test And Comparison With The Sequential T-Test, Kuei-Mei Even Sher

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

Sequential analysis is a method of statistical inference whose characteristic feature is that the number of observations required by the procedure is not determined in advance of the experiment. The decision to terminate the experiment depends, at each stage, on the results of the observations previously made.

So far the general sequential t-test (without truncation) is a standard test for the mean of a normal distribution. A truncated sequential t-test has been developed by Suich and Iglewicz (1970). The difference between these two tests is that the former has a fixed critical value whenever the type I error (α) and …

Nonparametric Test Of Fit, Frena Nawabi

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

Most statistical methods require assumptions about the populations from which samples are taken. Usually these methods measure the parameters, such as variance, standard deviations, means, etc., of the respective populations. One example is the assumption that a given population can be approximated closely with a normal curve. Since these assumptions are not always valid, statisticians have developed several alternate techniques known as nonparametric tests. The models of such tests do not specify conditions about population parameters.

Certain assumptions, such as (1) observations are independent and (2) the variable being studied has underlying continuity, are associated with most nonparametric tests. However, …

Solutions Of The Problem Of Finding Confidence Intervals For The Two Normal Population With Unequal Variances, Ing-Haur Liu

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

Comparison of the means of two normal populations is a simpler problem when the variance (if unknown) are assumed to be equal than it is when they are not equal. The main concern of this report is the latter case also called the Behrens [4] - Fisher [5] problem.

In this report the solutions proposed by Behrens-Fisher, Scheffe [10], Welch [12], Banerjee [3] and Hajek [8], will be described and compared. To this problem Scheffe proposed a solution which has the advantage that no special table is necessary for its use, since the variate has an exact "Student's t" distribution. …

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 …