Statistics and Probability Commons^™

Characterization Of Matrix Variate Normal Distributions, A.K. Gupta, T. Varga

Mathematical Sciences Technical Reports (MSTR)

In this paper, it is shown that two random matrices have a joint matrix variate distribution if conditioning each one on the other the resulting distributions satisfy certain conditions. A general result involving more than two matrices is also proved.

Characterization Of Joint Density By Conditional Densities, A.K. Gupta, T. Varga

Mathematical Sciences Technical Reports (MSTR)

In this paper the relationship between joint density and conditional densities is studied. An explicit formula is given for obtaining the joint density from the conditional ones. It is illustrated for the case of bivariate normal distribution.

A Small Area Simulation Approach To Determining Variation In Dental Procedure Rates, Paula Diehr

Paula Diehr

All small area analyses need to compare the observed variability in rates to that expected by chance alone, but the expected variability is usually not known. This paper uses patient-level data for five dental procedures to simulate the distributions of the summary statistics that are usually generated in such studies. These statistics are found to vary greatly even under the "null hypothesis" that all dentists are using procedures at the same rates. The simulated dentist rates are compared to observed rates obtained in a different study. These findings illustrate problems that can occur in small area analysis studies, and emphasize …

Use Of A Preferred Provider Plan By Employees Of The City Of Seattle, Paula Diehr

Paula Diehr

Little is known about the use of services in a preferred provider organization (PPO). We studied a preferred provider arrangement between Pacific Medical Center and employees of the City of Seattle. In the second 12 months of this program 8,529 subjects submitted at least one claim; of these, only 420 (4.9%) ever used the preferred provider. Those who used the PPO at least once differed significantly from those who never used it on age, sex, employee/dependent status, and utilization in the previous year. Outpatient and total charges were higher for PPO users than for nonusers before and after control for …

Student Fact Book, Fall 1990, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 1990.

Stress And Educational Administration: Variations In Stress Factors Across Administrative Levels, Cynthia R. Frick, John Fraas

John W. Fraas

No abstract provided.

Kindergarten Screening Test: Does It Predict Academic Achievement, John Fraas, D Scott Aronholt, Bettilu Fraas

John W. Fraas

No abstract provided.

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh

Mathematics and Statistics Faculty Publications

The Berry-Esseen-type bounds of order N^−1/2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.

Notions Of Relative Ubiquity For Invariant Sets Of Relational Structures, Paul Bankston, Wim Ruitenburg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is …

Modeling Mass Transport In Aquifers: The Distributed Source Problem, Sergio E. Serrano

KWRRI Research Reports

This report presents a new methodology to model the time and space evolution of groundwater variables in a system of aquifers when certain components of the model, such as the geohydrologic information, the boundary conditions, the magnitude and variability of the sources or physical parameters are uncertain and defined in stochastic terms. This facilitates a more realistic statistical representation of groundwater flow and groundwater pollution forecasting for either the saturated or the unsaturated zone. The method is based on applications of modern mathematics to the solution of the resulting stochastic transport equations. This procedure exhibits considerable advantages over the existing …

Oscillations In Lotka-Volterra Systems Of Chemical Reactions, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

For a chemical reaction system modeled by x =k₁Ax -k₂x² -k₃xy +k₄y², y =k₃xy -k₄y² -k₅y +k₆B, it is shown that for each positive choice of parameters k₁A, B there exists a unique stationary state which is globally asymptotically stable in the positive quadrant. A criterion for the non-existence of periodic solutions is given for the generalized Lotka-Volterra system:x = f(x)h(x, y), y. © 1990 J.C. Baltzer AG, Scientific Publishing Company.

Testing The Selection Effect: A New Theoretical Framework With Empirical Tests, Theodore Eisenberg

Cornell Law Faculty Publications

Recent law and economics scholarship has produced much theoretical and empirical work on how and why legal disputes are settled and litigated. One of the most significant developments in this literature, attributable to the work of William Baxter and the combined efforts of George Priest and Benjamin Klein, has been the formation of a theory about both the selection of disputes for trial and the rates of success that plaintiffs enjoy for those cases that are resolved at trial. The basic theory contains two components. The selection effect refers to the proposition that the selection of tried cases is not …

Taxonomies Of Model-Theoretically Defined Topological Properties, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.K, is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y _{E …}

A Modified Nance Unilateral Molar Distalizer, Tracy J. Reiner

Loma Linda University Electronic Theses, Dissertations & Projects

This clinical study evaluated a modified Nance appliance designed by the author to distalize molars unilaterally for Class II correction. This fixed appliance did not rely upon extraoral traction or intraoral elastics. Twelve unilateral Class II patients aged 13 to 17 were treated nonextraction with the appliance. Pretreatment and posttreatment photographs were taken of the palatal soft tissue and did not reveal any untoward changes as a result of the Nance acrylic button. All molars were corrected to an Angle's Class I relationship. Molar correction was evaluated visually and molar distalization was measured using an acrylic jig fitted to the …

Ordered Alternatives: A Means Of Improving Power, John E. Boyer Jr.

Conference on Applied Statistics in Agriculture

In analysis of variance settings it is often known that if there are any differences among the means, those differences will fall in a particular order. The usual F test used to look for the existence of differences is not sensitive to the particular order. This paper presents two procedures from the nonparametric literature which have sensitivity to the suggested ordering. The analogy is drawn between these procedures and the two-sample t test. The paper concludes with a simulation study which investigates the power properties of the proposed tests and makes comparisons with the F test.

The Aligned Rank Transform Procedure, James J. Higgins, R. Clifford Blair, Suleiman Tashtoush

Conference on Applied Statistics in Agriculture

Recent work has shown that the rank transform methodology is flawed when applied to multifactor designs with interactions. A simple fix-up is proposed and shown to apply to designs typical of those found in agricultural research including split-plots. Simulation results suggest that the fix-up provides a valid procedure for analyzing multifactor designs when error distributions are symmetric or moderately skewed. The procedure appears to have power advantages over normal theory ANOVA when error distributions are heavy tailed.

Nearest Neighbor Adjusted Best Linear Unbiased Prediction In Field Experiments, Walter W. Stroup

Conference on Applied Statistics in Agriculture

In field experiments with large numbers of treatments, inference can be affected by 1) local variation, and 2) method of analysis .

The standard approach to local, or spatial, variation in the design of experiments is blocking. While the randomized complete block design is obviously unsuitable for experiments with large numbers of treatments, incomplete block designs - even apparently well-chosen ones - may be only partial solutions. Various nearest neighbor adjustment procedures are an alternative approach to spatial variation .

Treatment effects are usually estimated using standard linear model methods. That is, linear unbiased estimates are obtained using ordinary least …

Nonlinear Regression For Split Plot Experiments, Marcia L. Gumpertz, John O. Rawlings

Conference on Applied Statistics in Agriculture

Split plot experimental designs are common in studies of the effects of air pollutants on crop yields. Nonlinear functions such the Weibull function have been used extensively to model the effect of ozone exposure on yield of several crop species. The usual nonlinear regression model, which assumes independent errors, is not appropriate for data from nested or split plot designs in which there is more than one source of random variation. The nonlinear model with variance components combines a nonlinear model for the mean with additive random effects to describe the covariance structure. We propose an estimated generalized least squares …

A Simulation Study Of Field Trial Analysis, Perry Y. Jui

Conference on Applied Statistics in Agriculture

In variety trials, lattice designs are perhaps the most popular ones used by agriculture researchers. An eight by eight lattice design in which there were 56 test cultivars and a check cultivar in each of the eight blocks, was replicated four times. A simulation was performed in which the lattice design was superimposed on two soil fertility maps, one relatively uniform (map 1) and one more heterogeneous (map 2). Ratios of soil variation to total variation (soil + error ) ranging from .1 to 1.0 were studied. The results suggest that in the present setup blocking is more effective when …

Path Analysis In Agricultural Research, K. Bondari

Conference on Applied Statistics in Agriculture

Path analysis introduced by Wright in 1921 as "correlation and causation" has been extensively used in agriculture, sociology, and epidemiology, among many other fields. This study will review path diagrams, algorithms, and the relationship to standardized and mUltivariate regression analyses. Basic assumptions underlying path analysis (e.g., cause and effect relationship, linearity of regression, complete additivity) will also be discussed. Several research examples will be presented to better acquaint statisticians invol ved in agricultural research wi th the methodology and application of path analysis suitable for agricultural data. The method of path coefficient is simple, easy to use, and if "tracing …

A Transformation Approach To Estimating Usual Intake Distributions, Sarah M. Nusser, Alicia L. Carriquiry, Helen H. Jensen, Wayne A. Fuller

Conference on Applied Statistics in Agriculture

Design of effective food and nutrition policies, efficient allocation of resources, and more precise targeting of food programs require good estimates of the percentage of the population with deficient, or excess, nutrient or other food component intake. An individual's mean daily intake of the dietary component is a good estimate of the individual's dietary status. However, to evaluate dietary adequacy of a population it is necessary to obtain an estimate of the distribution of usual intakes. Often, the distribution of usual intakes is estimated from the distribution of mean daily intakes. Two problems arise. First, distributions of usual intakes for …

Linear-Plateau Regression Analysis And Its Application To Selenite Adsorption Rate, Bahman Shafii, Kevin C. Harper, Steven L. Mcgeehan

Conference on Applied Statistics in Agriculture

Simple computational methods are presented which facilitate fitting regression models to response data exhibiting a plateau effect. The iterative statistical program (called PLATFOR) is written in FORTRAN (a SAS version is also available), and produces all relevant regression statistics, plots, and information on goodness of fit. The presented procedures are empirically valuable, since linear-plateau models have many useful applications in agriculture, especially in soil fertility and soil chemistry experiments. The technique was employed in an experiment designed to determine the effect of soil volcanic ash content on selenite adsorption. Ion chromatographic methods were used to investigate selenite adsorption in three …

Applying Principal Component Analysis To Soil-Landscape Research-Quantifying The Subjective, R. David Hammer, John W. Philpot, Jon M. Maatta

Conference on Applied Statistics in Agriculture

Principal component analysis is a multivariate statistical procedure that can be used to identify factors (correlated subsets of variables) in large data sets. This statistical method appears useful for scientists investigating soil processes, but it has received little attention. Reported applications of principal component analysis share a common fault--subjective, user-specified analytical options apparently are not recognized, for they are not discussed. Reported data sets are often small, have low observations-per-variable ratios, and lack tests of robustness. A large soil data set is used to demonstrate systematic procedures for an optimum rotated principal component solution. This solution retained 21 variables aligned …

Statistical Analysis Of Spectrophotometric Assays In The Presence Of Interference, Edward Gbur, Patti Landers, Roy Sharp

Conference on Applied Statistics in Agriculture

Indirect measurement of the amount of a specified component in a sample of a chemical compound can be accomplished by spectrophotometry. The underlying principle is Beer's Law, which states that, in a pure system, the amount of light absorbed by a chemical bond is linearly related to its concentration. In some mixtures it may not be possible to find a wavelength at which only the bond of interest absorbs light. Hence, the absorbance is composed of contributions from the bond of interest and one or more other (nuisance) bonds. Chemists refer to this situation as interference. In this paper we …

Estimating Mixture Fraction And Map Distance In A Mixed F2, Bc1 Population, Dennis L. Clason, N. Scott Urquhart, Joe Corgan, Catherine M. Cryder

Conference on Applied Statistics in Agriculture

An F₁ interspecific hybrid onion (Allium cepa x A. fistulosum) was backcrossed to the A. cepa parent line under field conditions. The progeny of this cross were shown by electrophoretic protein analysis to be a mixture of BC₁ (the desired backcross) and F₂ (A. cepa x A. fistulosum) x (A. cepa x A. fistulosum) individuals. This mixture of populations among the progeny render the usual X² test for independent segregation of loci invalid. F₂ is used to denote progeny derived from either selfing of the F₁ or from sib-crosses between two F₁ individuals. …

Genotype X Weather Interactions In Grain Yields Of Wheat, Arlin M. Feyerherm, Rollin G. Sears, Gary M. Paulsen

Conference on Applied Statistics in Agriculture

The purpose of this paper is to demonstrate the advantage of using weather elements as covariates in studying yield differentials between varieties of wheat over different climatological regions. Using regression methods, the dependence of varietal yield differences on weather elements was demonstrated with a relatively small sample consisting of yield and weather data over a 3-year period from nine locations in Kansas. For each location, the sample-derived regression equation was used to calculate predicted yield differentials and 95% confidence intervals for the mean (CLM) for each year from 1950 through 1989. The proportion of CLMs that covered positive (or negative) …

Nepotism In Honey Bees, Computer Programs And Scientific Hypotheses, Benjamin P. Oldroyd, Thomas E. Rinderer

Conference on Applied Statistics in Agriculture

Page et al. (1989) attempted to show that bees on queen cells preferentially reared their super sisters as replacement queens rather than half sisters. In support of their contention, they used computer simulation to model the biological system. We argue that the simulation did not accurately reflect the biological system in several important respects. We show that random data will produce the same kinds of statistical significance as the actual data.

Using Response Surface Methodology With A Multivariate Response To Improve The Quality Of A Food Product, George A. Milliken, Tanya W. Maclaurin, Carole S. Setser

Conference on Applied Statistics in Agriculture

Nutrition in health is a major area of focus in our national health priorities as we move into the 21st century. The government, food industry, food scientists, health professionals, and all disciplines that can assist need to work together in the development of "healthful food products" and encourage Americans to make healthful food choices (Drishell, 1990). Experimentation science provides strategies for helping food scientists improve existing food products and develop new ones. This paper describes a process where design of experiments and response surface methodology were utilized in the formulation development to guide product development of a healthful muffin that …

A Simulation Study On The Relationship Between The Abundance And Spatial Distribution Of Insects And Selected Sampling Schemes, J. L. Willers, D. L. Boykin, J. M. Hardin, T. L. Wagner, R. L. Olson, M. R. Williams

Conference on Applied Statistics in Agriculture

During the development of a Bayesian approach to estimate insect population abundance, it was necessary to compare not only the reliability of Bayesian estimates, but to also compare these estimates to those obtained by traditional methods employed by entomologists. To facilitate these comparisons it was necessary to use simulated fields apportioned into quadrats where conditions representative of insect abundance and dispersion are modeled. Thus, a simulation model was developed using SAS to derive example insect populations from which samples could be drawn. The negative binomial distribution was used to simulate the proportion of infested plants (p) with various degrees of …