Statistics and Probability Commons^™

Using Exploratory Factor Analysis For Locating Invariant Referents In Factor Invariance Studies, W. Holmes Finch, Brian F. French

Journal of Modern Applied Statistical Methods

Model identification in multi-group confirmatory factor analysis (MCFA) requires an equality constraint of referent variables across groups. Invariance assumption violations make it difficult to locate parameters that actually differ. Suggested procedures for locating invariant referents are cumbersome, complex, and provide imperfect results. Exploratory factor analysis (EFA) may be an alternative because of its ease of use, yet empirical evaluation of its effectiveness is lacking. EFAs accuracy for distinguishing invariant from non-invariant referents was examined.

Probability Of Coverage And Interval Length For Two-Group Techniques Assessing The Median And Trimmed Mean, S. Jonathan Mends-Cole

Journal of Modern Applied Statistical Methods

The purpose of the present study was to assess the probability of coverage and interval length of selected statistical techniques that have a higher finite sample breakdown point than the mean and appropriate levels of probability of coverage when using Bradley’s (1978) criterion. The techniques were examined using real education and psychology datasets (Sawilowsky & Fahoome, 2003, Sawilowsky & Blair, 1992). Welch’s test exhibited appropriate coverage for the smooth symmetric, mass at zero, digit preference, and extreme bimodal distributions. Yuen’s technique performed well under an extreme bimodal distribution. Results concerning the Maritz-Jarrett and the McKean-Schrader techniques are also presented.

Test For Spatio-Temporal Counts Being Poisson, Haiyan Chen, Howard H. Stratton

Journal of Modern Applied Statistical Methods

The new Log-Linear Test (T_L) is proposed to identify when the Poisson model fails for a collection of count random variables. T_L is shown to have better rejection rate with small sample size and essentially the same power compared to a classical Fisher-Bohning’s Statistic T_F for standard alternatives to Poisson.

Measuring Overall Heterogeneity In Meta-Analyses: Application To Csf Biomarker Studies In Alzheimer’S Disease, Chengjie Xiong, Feng Gao, Yan Yan, Jingqin Luo, Yunju Sung, Gang Shi

Journal of Modern Applied Statistical Methods

The interpretations of statistical inferences from meta-analyses depend on the degree of heterogeneity in the meta-analyses. Several new indices of heterogeneity in meta-analyses are proposed, and assessed the variation/difference of these indices through a large simulation study. The proposed methods are applied to biomakers of Alzheimer’s disease.

When Sensitivity Is A Function Of Age And Time Spent In The Preclinical State In Periodic Cancer Screening, Dongfeng Wu, Ricolindo L. Cariño, Xiaoqin Wu

Journal of Modern Applied Statistical Methods

Probability models are extended for periodic cancer screening trials to model sensitivity when it is changing with an individual’s age and time spent in the preclinical state. Wu et al. (2005) showed that sensitivity is monotone increasing with age, but intuitively, sensitivity is also a function of the time one has spent in the preclinical stage. This allows us to infer sensitivity at a late stage, just before symptoms manifest. We developed the probability model and applied Bayesian inference to the HIP study group data. The methodology we developed is also applicable to other kinds of chronic diseases.

Log-Linear Model To Assess Socioeconomic And Environmental Factors With Childhood Diarrhea Using Hospital Based Surveillance, Krishnan Rajendran, Thandavarayan Ramamurthy, Sujit Kumar Bhattacharya

Journal of Modern Applied Statistical Methods

Categorical outcomes with environment factors analyzed by log linear model are frequent in the environmental epidemiological literature. Epidemiological and socio-economical factors were obtained on 1,119 children below the age of 5 from Infectious Diseases Hospital (IDH) at the Kolkata, India. Significant associations of diarrhea were observed in the rural areas with family income, father’s occupation as a daily labor, literacy of parents, non-cemented floor and wall constructed of mud, and type of storage (wide mouthed earthen pot). The results of the study with specific Log linear model confirm environmental factors were important implications for childhood diarrhea in the rural community. …

Robust General Linear Models And Graphics Via A User Interface (Web Rglm), Kimberly Crimin, Asheber Abebe, Joseph W. Mckean

Journal of Modern Applied Statistical Methods

Rank-based procedures provide superior estimation and testing techniques when the data deviate from normality or contain gross outliers. However, these robust techniques are rarely incorporated in a nonparametric statistics or methods courses due to the lack of computational tools. One reason for this is the existence of certain unavoidable complexities in the numerical methods due to the absence of a closedform solution for the rank estimation problem. This article introduces a user interface, Web RGLM, which may be used to perform rank-based analyses of linear models across the World Wide Web. These models include simple location problems to complicated ANOVA …

Effect On Recreation Benefit Estimates From Correcting For On-Site Sampling Biases And Heterogeneous Trip Overdispersion In Count Data Recreation Demand Models (Stata), Roberto Martínez-Espiñeira, Joseph M. Hilbe

Journal of Modern Applied Statistical Methods

Correction procedures (STATA commands NBSTRAT and GNBSTRAT) are applied to simultaneously account for zero-truncation, endogenous stratification, and overdispersion, and also consider heterogeneity in the overdispersion parameter. Their effect is shown on welfare estimates from previous studies, confirming that the routines perform the appropriate correction and only when endogenous stratification is expected.

Computing Multivariate Process Capability Indices (Excel), Michele Scagliarini, Raffaele Vermiglio

Journal of Modern Applied Statistical Methods

In manufacturing industry there is growing interest in measures of process capability under multivariate setting. Although there are many statistical packages to assess univariate capability, a current problem with the multivariate measures of capability is the shortage of user friendly software. In this article a Visual Basic program has been developed to realize an Excel spreadsheet that may be used to compute two multivariate measures of capability. The aim of this article is to provide a useful tool for practitioners dealing with multivariate capability assessment problems. The features of the program include easy data entry and clear report format.

Logit Estimation Using Warner’S Randomized Response Model, Zawar Hussain, Javid Shabbir

Journal of Modern Applied Statistical Methods

A modified hidden logit estimation procedure is presented based on Warner (1965) randomized response model. Monte Carlo simulations explore the behavior of this estimator and compare its performance with the ordinary logits estimator. Warner’s model is more protective and less jeopardizing.

Estimation Of Covariance Matrix In Signal Processing When The Noise Covariance Matrix Is Arbitrary, Madhusudan Bhandary

Journal of Modern Applied Statistical Methods

An estimator of the covariance matrix in signal processing is derived when the noise covariance matrix is arbitrary based on the method of maximum likelihood estimation. The estimator is a continuous function of the eigenvalues and eigenvectors of the matrix Σ̂₁^1/2S^∗Σ̂₁^1/2, where S^∗ is the sample covariance matrix of observations consisting of both noise and signals and Σ̂₁ is the estimator of covariance matrix based on observations consisting of noise only. Strong consistency and asymptotic normality of the estimator are briefly discussed.

On The Length Of Nhl Shootouts, W. J. Hurley

Journal of Modern Applied Statistical Methods

When NHL teams are tied after 60 minutes of regulation time and 5 minutes of sudden-death overtime, they go to a shootout to determine who gets the overtime point. Teams alternate shots until a winner is determined. The probability of observing shootouts of various lengths is calculated.

Scramjet Fuel Injection Array Optimization Utilizing Mixed Variable Pattern Search With Kriging Surrogates, Bryan Sparkman

Theses and Dissertations

Fuel-air mixing analysis of scramjet aircraft is often performed through ex- perimental research or Computational Fluid Dynamics (cfd) algorithms. Design optimization with these approaches is often impossible under a limited budget due to their high cost per run. This investigation uses jetpen, a known inexpensive analysis tool, to build upon a previous case study of scramjet design optimization. Mixed Variable Pattern Search (mvps) is compared to evolutionary algorithms in the optimization of two scramjet designs. The ¯rst revisits the previously stud- ied approach and compares the quality of mvps to prior results. The second applies mvps to a new scramjet …

Delay-Induced Instabilities In Self-Propelling Swarms, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by …

Statistical Approach To The Characterization And Recognition Of Human Gaits, Derrick M. Chelliah

Theses and Dissertations

This thesis addresses the final portion of a complete process for human gait recognition. The thesis takes as input information that has been generated from videotaping walking individuals and converting their gaits into numerical data that measures the locations of various points on the body through time. Beginning with this data, this thesis uses a variety of mathematical and statistical methods to create identifying signatures for each individual and identify them on the basis of that signature. The end goal is to achieve under controlled laboratory conditions human gait recognition, an identification method which does not require contact or cooperation …

Predicting Cost And Schedule Growth For Military And Civil Space Systems, Christina F. Rusnock

Theses and Dissertations

Military and civil space acquisitions have received much criticism for their inability to produce realistic cost and schedule estimates. This research seeks to provide space systems cost estimators with a forecasting tool for space system cost and schedule growth by identifying factors contributing to growth, quantifying the relative impact of these factors, and establishing a set of models for predicting space system cost and schedule growth. The analysis considers data from both Department of Defense (DoD) and National Aeronautics and Space Administration (NASA) space programs. The DoD dataset includes 21 space programs that submitted developmental Selected Acquisition Reports between 1969 …

Why Divide By (N-1) For Sample Standard Deviation?, Paul Savory

Department of Industrial and Management Systems Engineering: Instructional Materials

In statistics, the sample standard deviation is a widely used measure of the variability or dispersion of a data set. The standard deviation of a data set is the square root of its variance. In calculating the sample standard deviation, the divisor is the number of samples in the data set minus one (n-1) rather than n. This often confuses students. This paper offers a quick overview of why the divisor is (n-1) for calculating the sample standard deviation.

Multi-Algorithmic Cryptography Using Deterministic Chaos With Applications To Mobile Communications, Jonathan Blackledge

Articles

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of …

Mathematical Analysis Of The Transmission Dynamics Of Hiv/Tb Coinfection In The Presence Of Treatment, Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

This paper addresses the synergistic interaction between HIV and mycobacterium tuberculosis using a deterministic model, which incorporates many of the essential biological and epidemiological features of the two diseases. In the absence of TB infection, the model (IIIV-only model) is shown to have a globally asymptotically stable, disease-free equilibrium whenever the associated reproduction number is less than unity and has a unique endemic equilibrium whenever this number exceeds unity. On the other hand, the model with TB alone (TB-only model) undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated …

How Do You Interpret A Confidence Interval?, Paul Savory

Department of Industrial and Management Systems Engineering: Instructional Materials

A confidence interval (CI) is an interval estimate of a population parameter. Instead of estimating the parameter by a single value, a point estimate, an interval likely to cover the parameter is developed. Many student incorrectly interpret the meaning of a confidence interval. This paper offers a quick overview of how to correctly interpret a confidence interval.

Origin Of Conductive Surface Layer In Annealed Zno, David C. Look, B. Claflin, Helen Smith

Mathematics and Statistics Faculty Publications

The highly conductive surface layers found in nearly all as-grown or annealed bulk ZnO wafers are studied by temperature-dependent Hall-effect and secondary-ion mass spectroscopy (SIMS) measurements. In this work, we have used annealing in N₂ at 900 degrees C, and forming gas (5% H₂ in N₂) at 600 degrees C, to cause a large enough surface conduction that SIMS measurements can be reliably employed. The increased near-surface donor density, as determined from two-layer Hall-effect modeling, is consistent with an increased near-surface concentration of Al, Ga, and In atoms, resulting from diffusion. There is no evidence for …

Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam

Department of Math & Statistics Faculty Publications

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …

Degradation Models, Suk Joo Bae, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Reliability testing typically generates product lifetime data, but for some tests, covariate information about the wear and tear on the product during the life test can provide additional insight into the product’s lifetime distribution. This usage, or degradation, can be the physical parameters of the product (e.g., corrosion thickness on a metal plate) or merely indicated through product performance (e.g., the luminosity of a light emitting diode). The measurements made across the product’s lifetime are degradation data, and degradation analysis is the statistical tool for providing inference about the lifetime distribution from the degradation data.

Load Sharing Models, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

Consider a system of components whose lifetimes are governed by a probability distribution. Load sharing refers to a model of stochastic interdependency between components that operate within a system. If components are set up in a parallel system (see Parallel, Series, and Series–Parallel Systems) for example, the system survives as long as at least one component is operating. In a typical load-sharing system, once a component fails, the remaining components suffer an increase in failure rate due to the extra “load” they must encumber due to the failed component.

Comparison Of Roadside Crash Injury Metrics Using Event Data Recorders, Doug Gabauer, Hampton C. Gabler

Faculty Journal Articles

The occupant impact velocity (OIV) and acceleration severity index (ASI) are competing measures of crash severity used to assess occupant injury risk in full-scale crash tests involving roadside safety hardware, e.g. guardrail. Delta-V, or the maximum change in vehicle velocity, is the traditional metric of crash severity for real world crashes. This study compares the ability of the OIV, ASI, and delta-V to discriminate between serious and non-serious occupant injury in real world frontal collisions. Vehicle kinematics data from event data recorders (EDRs) were matched with detailed occupant injury information for 180 real world crashes. Cumulative probability of injury risk …

Empirical Processes And Roc Curves With An Application To Linear Combinations Of Diagnostic Tests, Costel Chirila

University of Kentucky Doctoral Dissertations

The Receiver Operating Characteristic (ROC) curve is the plot of Sensitivity vs. 1- Specificity of a quantitative diagnostic test, for a wide range of cut-off points c. The empirical ROC curve is probably the most used nonparametric estimator of the ROC curve. The asymptotic properties of this estimator were first developed by Hsieh and Turnbull (1996) based on strong approximations for quantile processes. Jensen et al. (2000) provided a general method to obtain regional confidence bands for the empirical ROC curve, based on its asymptotic distribution.

Since most biomarkers do not have high enough sensitivity and specificity to …

Examining Significant Differences Of Gunshot Residue Patterns Using Same Make And Model Of Firearms In Forensic Distance Determination Tests., Heather Lewey

Electronic Theses and Dissertations

In many cases of crimes involving a firearm, police investigators need to know how far the firearm was held from the victim when it was discharged. Knowing this distance, vital questions regarding the re-construction of the crime scene can be known. Often, the original firearm used in commission of a suspected crime is not available for testing or is damaged. Crime laboratories require the original firearm in order to conduct distance determination tests. However, no empirical research has ever been conducted to determine if same make and model firearms produce different results in distance determination testing. It was the purpose …

Statistics In The Jury Box: How Jurors Respond To Mitochondrial Dna Match Probabilities, David H. Kaye, Valerie P. Hans, B. Michael Dann, Erin J. Farley, Stephanie Albertson

Cornell Law Faculty Publications

This article describes parts of an unusually realistic experiment on the comprehension of expert testimony on mitochondrial DNA (mtDNA) sequencing in a criminal trial for robbery. Specifically, we examine how jurors who responded to summonses for jury duty evaluated portions of videotaped testimony involving probabilities and statistics. Although some jurors showed susceptibility to classic fallacies in interpreting conditional probabilities, the jurors as a whole were not overwhelmed by a 99.98% exclusion probability that the prosecution presented. Cognitive errors favoring the defense were more prevalent than ones favoring the prosecution. These findings lend scant support to the legal argument that mtDNA …

An Omnibus Test When Using A Regression Estimator With Multiple Predictors, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

In quantile regression, the goal is to estimate theγ quantile of Y given values for p predictors. Methods for making inferences about the individual slope parameters have been proposed, some of which have been found to perform very well in simulations. But for an omnibus test that all slope parameters are zero, it appears that little is known about how best to proceed. For the special case γ =.5, a drop-in-dispersion test has been recommended, but it requires a large sample size to control the probability of a Type I error and it assumes that the usual error term is …

Bayesian Subset Selection Of Binomial Parameters Using Possibly Misclassified Data, James D. Stamey, Thomas L. Bratcher, Dean M. Young

Journal of Modern Applied Statistical Methods

Three Bayesian approaches are considered for the selection of binomial proportion parameters when data is subject to misclassification. The cases where the misclassification is non-differential and differential were considered, thus extending previous work which considered only non-differential misclassification. In this article, various selection criteria are applied to a simulated data set and a real data set.