Statistics and Probability Commons^™

Hotelling's T2 Vs. The Rank Transform With Real Likert Data, Michael J. Nanna

Journal of Modern Applied Statistical Methods

Monte Carlo research has demonstrated that there are many applications of the rank transformation that result in an invalid procedure. Examples include the two dependent samples, the factorial analysis of variance, and the factorial analysis of covariance layouts. However, the rank transformation has been shown to be a valid and powerful test in the two independent samples layout. This study demonstrates that the rank transformation is also a robust and powerful alternative to the Hotellings T² test when the data are on a Likert scale.

Applying Spatial Randomness To Community Inclusion, Michael Wolf-Branigin

Journal of Modern Applied Statistical Methods

A spatial analytic methodology incorporating true locations is demonstrated using Monte Carlo simulations as a complement to current psychometric and quality of life indices for measuring community inclusion. Moran's I, a measure of spatial autocorrelation, is used to determine spatial dependencies in housing patterns for multiple variables, including family/friends involvement in future planning, home size, and earned income. Simulations revealed no significant spatial autocorrelation, which is a socially desirable result for housing locations for people with disabilities. Assessing the absence of clustering provides a promising methodology for measuring community inclusion.

Shifting Goals And Mounting Challenges For Statistical Methodology, Pranab K. Sen

Journal of Modern Applied Statistical Methods

Modern interdisciplinary research in statistical science encompasses a wide field: agriculture, biology, biomedical sciences along with bioinformatics, clinical sciences, education, environmental and public health disciplines, genomic science, industry, molecular genetics, socio-behavior, socio-economics, toxicology, and a variety of other disciplines. Statistical science has historically had mathematical perspectives dominating theoretical and methodological developments. Yet, the advent of modern information technology has opened the doors for highly computation intensive statistical tools (i.e., software), wherein mathematical aspects are often de-emphasized. Knowledge discovery and data mining (KDDM) is now becoming a dominating force, with bioinformatics as a notable example. In view of this apparent discordance …

The Q-Sort Method: Assessing Reliability And Construct Validity Of Questionnaire Items At A Pre-Testing Stage, Abraham Y. Nahm, S. Subba Rao, Luis E. Solis-Galvan, T. S. Ragu-Nathan

Journal of Modern Applied Statistical Methods

This paper describes the Q-sort, which is a method of assessing reliability and construct validity of questionnaire items at a pre-testing stage. The method uses Cohen's Kappa and Moore and Benbasat's Hit Ratio in assessing the questionnaire.

Using The T Test With Uncommon Sample Sizes, Shlomo S. Sawilowsky, Barry S. Markman

Journal of Modern Applied Statistical Methods

Monte Carlo techniques were used to determine the effect of using common critical values as an approximation for uncommon sample sizes. Results indicate there can be a significant loss in statistical power. Therefore, even though many instructors now rely on computer statistics packages, the recommendation is made to provide more specificity (i.e., values between 30 and 60) in tables of critical values published in textbooks.

Modeling Strategies In Logistic Regression With Sas, Spss, Systat, Bmdp, Minitab, And Stata, Chao-Ying Joanne Peng, Tak-Shing Harry So

Journal of Modern Applied Statistical Methods

This paper addresses modeling strategies in logistic regression within the context of a real-world data set. Six commercially available statistical packages were evaluated in how they addressed modeling issues and in the accuracy of their regression results. Recommendations are offered for data analysts in terms of each package's strengths and weaknesses.

Rank-Based Procedures For Mixed Paired And Two-Sample Designs, Suzanne R. Dubnicka, R. Clifford Blair, Thomas P. Hettmansperger

Journal of Modern Applied Statistical Methods

This paper presents a rank-based procedure for parameter estimation and hypothesis testing when the data are a mixture of paired observations and independent samples. Such a situation may arise when comparing two treatments. When both treatments can be applied to a subject, paired data will be generated. When it is not possible to apply both treatments, the subject will be randomly assigned to one of the treatment groups. Our rank-based procedure allows us to use the data from the paired sample and the independent samples to make inferences about the difference in the mean responses. The rank-based procedure uses both …

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=^N\ω is an exterior domain in ^N, ω⊂^N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈C^α_loc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|^l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

Secured Debt And The Likelihood Of Reorganization, Clas Bergström, Theodore Eisenberg, Stefan Sundgren

Cornell Law Faculty Publications

Theory suggests that secured creditors may increasingly oppose a debtor’s reorganization as the value of their collateral approaches the amount of their claims. If reorganization occurs and the value of the firm appreciates, the secured creditor receives only part of the gain. But if the firm’s value depreciates, the secured creditor bears all of the cost. Secured claimants, thus, often have more to lose than to gain in reorganizations. This study of Finnish reorganizations filed in districts that account for most of the country’s reorganizations finds that creditor groups most likely to be well-secured are most likely to oppose reorganization. …

Comparative Genomic Hybridization Array Analysis, Annette M. Molinaro, Mark J. Van Der Laan, Dan H. Moore

U.C. Berkeley Division of Biostatistics Working Paper Series

At the present time, there is increasing evidence that cancer may be regulated by the number of copies of genes in tumor cells. Through microarray technology it is now possible to measure the number of copies of thousands of genes and gene segments in samples of chromosomal DNA. Microarray comparative genomic hybridization (array CGH) provides the opportunity to both measure DNA sequence copy number gains and losses and map these aberrations to the genomic sequence. Gains can signify the over-expression of oncogenes, genes which stimulate cell growth and have become hyperactive, while losses can signify under-expression of tumor suppressor genes, …

A Method To Identify Significant Clusters In Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Clustering algorithms have been widely applied to gene expression data. For both hierarchical and partitioning clustering algorithms, selecting the number of significant clusters is an important problem and many methods have been proposed. Existing methods for selecting the number of clusters tend to find only the global patterns in the data (e.g.: the over and under expressed genes). We have noted the need for a better method in the gene expression context, where small, biologically meaningful clusters can be difficult to identify. In this paper, we define a new criteria, Mean Split Silhouette (MSS), which is a measure of cluster …

Miscellaneous Publication 8/2002 - Statistics Report For The Western Australian Floriculture Industry - August 2000, Department Of Agriculture, Western Australia

Horticulture published reports

Statistical data plays an important role in many decisions faced by both established and prospective businesses within all industry sectors. In order to offer a better service to its customers, the Department of Agriculture (the Department) requires information regarding the cutflower and nursery industry within Australia and Western Australia.

Though there are many avenues available in order to obtain this statistical information, both locally and nationally, there is no concise summary available. In addition, information obtained must be assessed in detail to determine its reliability and relevance.

Current statistics for both the Australian and Western Australian nursery and cutflower industries …

Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny

Doctoral Dissertations

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …

A Comparison Of Coalescent Estimation Software, Kristen Piggott Shepherd

Theses and Dissertations

Coalescent theory is a method often used by population geneticists in order to make inferences about evolutionary parameters. The coalescent is a stochastic model that approximates ancestral relationships among genes. An understanding of the coalescent pattern of a sample of sequences, along with some knowledge of the mutations that have occurred, provides information about the evolutionary forces that have acted on the population. Processes such as migration, recombination, variable population size, or natural selection are the forces that affect the genealogies and lead to genetic variability in a sample. Coalescent theory provides a statistical description of the variability in the …

Boundary Layers Associated With Incompressible Navier-Stokes Equations: The Noncharacteristic Boundary Case, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

The goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly non-characteristic, i.e., there is injection and/or suction everywhere at the boundary. Following earlier work on the boundary layer for linearized Navier-Stokes equations in the case where the boundaries are characteristic (non-slip at the boundary and non-permeable), we consider here the case where the boundary is permeable and thus non-characteristic. the form of the boundary layer and convergence results are derived in two cases: linearized equation and full nonlinear equations. We prove that there exists …

An Adaptive Analysis Of Covariance Using Tree-Structured Regression, Gary L. Gadbury, H. K. Iyer, H. T. Schreuder

Mathematics and Statistics Faculty Research & Creative Works

In this article, we propose an adaptive procedure for testing for the effect of a factor of interest in the presence of one or more confounding variables in observational studies. It is especially relevant for applications where the factor of interest has a suspected causal relationship with a response. This procedure is not tied to linear modeling or normal distribution theory, and it offers a valuable alternative to traditional methods. It is suitable for applications where a factor of interest is categorical, and the response is continuous. Confounding variables may be continuous or categorical. The method is comprised of two …

Five-Hundred Life-Saving Interventions And Their Misuse In The Debate Over Regulatory Reform, Lisa Heinzerling

RISK: Health, Safety & Environment (1990-2002)

The author argues that John D. Graham, administrator of the Office of Information and Regulatory Affairs, holds strong anti-environmental biases and has perpetuated and encouraged a misrepresentation of his own research, which has largely influenced health, safety, and environmental regulation.

L-Arginine Uptake And Metabolism Following In Vivo Silica Exposure In Rat Lungs, Leif D. Nelin, Gary S. Krenz, Louis G. Chicoine, Christopher A. Dawson, Ralph M. Schapira

Mathematics, Statistics and Computer Science Faculty Research and Publications

Pulmonary inflammation increases nitric oxide (NO) production via inducible nitric oxide synthase (iNOS). This study was performed to determine some of the factors that affect the availability of the NOS substrate, L-arginine (L-arg), in the intact lung subjected to silica-induced inflammation. Nitrate production, as an index of NO production, was significantly greater in silica-exposed lungs (53.5 ± 12.1 nmol/90 min) compared with controls (22.5 ±5.1 nmol/90 min, P < 0.05). This was accompanied by greater (P< 0.0001) 90-min [³H]L-arg uptake (62 ± 3% control, 82 ± 1% silica), a significantly (P < 0.005) increased permeability-surface area product for L-arg(0.28 ± 0.05 ml/min control, 0.63 ± 0.07 ml/min silica), and asignificantly (P < 0.001) increased urea production (1.16 ± 0.08µmol/90 min control, 1.77 ± 0.06 µmol/90 min silica). There was no difference in eNOS protein between groups and eNOS mRNA was not detectable in either group, whereas silica exposure resulted in the appearance of both iNOS protein and mRNA. Silica exposure increased CAT-1 and CAT-2 mRNA ~ 8-fold compared with controls. We conclude that the increase in NO production in silica-exposed lungs was associated with increased L-arg uptake from the vasculature, presumably resulting from increased CAT-1 and CAT-2, and by increased L-arg metabolism via arginase.

Inconsistency Of Resampling Algorithms For High Breakdown Regression Estimators And A New Algorithm, Douglas M. Hawkins, David J. Olive

Articles and Preprints

Since high breakdown estimators are impractical to compute exactly in large samples, approximate algorithms are used. The algorithm generally produces an estimator with a lower consistency rate and breakdown value than the exact theoretical estimator. This discrepancy grows with the sample size, with the implication that huge computations are needed for good approximations in large high-dimensioned samples

The workhorse for HBE has been the ‘elemental set’, or ‘basic resampling’ algorithm. This turns out to be completely ineffective in high dimensions with high levels of contamination. However, enriching it with a “concentration” step turns it into a method that is able …

Prevalence Of Various Upper Extremity Disorders In Patients With Carpal Tunnel Syndrome Versus Patients Without Carpal Tunnel Syndrome, Daniel C. Buda

Loma Linda University Electronic Theses, Dissertations & Projects

Background and Purpose: Increasingly larger numbers of patients present with repetitive strain injuries of the upper extremities, especially carpal tunnel syndrome (CTS). A large number of these patients appear to have more than one upper extremity condition. The purpose of this study was to determine the probability that a patient diagnosed with carpal tunnel syndrome will also be diagnosed with other upper extremity and/or cervical spine disorders.

Subjects: A group of 188 subjects diagnosed with carpal tunnel syndrome and a group of 203 subjects without carpal tunnel syndrome were selected through a chart review of patients at Loma Linda …

Juries, Judges, And Punitive Damages: An Empirical Study, Theodore Eisenberg, Neil Lafountain, Brian Ostrom, David Rottman, Martin T. Wells

Cornell Law Faculty Publications

This Article, the first broad-based analysis of punitive damages in judge-tried cases, compares judge and jury performance in awarding punitive damages and in setting their levels. Data covering one year of judge and jury trial outcomes from forty-five of the nation's largest counties yield no substantial evidence that judges and juries differ in the rate at which they award punitive damages or in the central relation between the size of punitive awards and compensatory awards. The relation between punitive and compensatory awards in jury trials is strikingly similar to the relation in judge trials. For a given level of compensatory …

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

Orthogonal Arrays Of Strength Three From Regular 3-Wise Balanced Designs, Charles J. Colbourn, D. L. Kreher, John P. Mcsorley, D. R. Stinson

Articles and Preprints

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction.

Applications Of Robust Distances For Regression, David J. Olive

Articles and Preprints

The DD plot, introduced by Rousseeuw and Van Driessen (1999), is a plot of classical vs robust Mahalanobis distances: MD_i vs RD_i. The DD plot can be used as a diagnostic for multivariate normality and elliptical symmetry, and to assess the success of numerical transformations towards elliptical symmetry. In the regression context, many procedures can be adversely affected if strong nonlinearities are present in the predictors. Even if strong nonlinearities are present, the robust distances can be used to help visualize important regression models such as generalized linear models.

Comparative Molecular Field Analysis (Comfa) Of Protonated Methylphenidate Phenyl-Substituted Analogs, Kathleen Mary Gilbert

Theses

Protonated methylphenidate (pMP) and several phenyl-substituted pMP analogs were analyzed using Comparative Molecular Field Analysis (CoMFA) to develop a pharmacophore for dopamine transporter (DAT) binding. This research is a part of an interdisciplinary study on using methylphenidate (MP) analogs to block the binding of cocaine to the DAT as a treatment for addiction.

A random search conformational analysis using key pMP torsional angles was performed to create conformer families representing possible bioactive conformations. The lowest energy pMP conformer of each family was used as a template to create phenyl-substituted pMP analogs.

Partial least squares analysis was used to determine the …

On Size Mappings, W. J. Charatonik, Alicja Samulewicz

Mathematics and Statistics Faculty Research & Creative Works

A real-valued mapping r from the hyperspace of all compact subsets of a givenmetric space X is called a size mapping if r({x}) = 0 for x ∈ X and r(A) ≤ r(B) if a ⊂ B. We investigate what continua admit an open or a monotone size mapping. Special attention is paid to the diameter mappings.

Regression Analysis Of Recurrent Gap Times With Time-Dependent Covariates, Ying Qing Chen, Mei-Cheng Wang, Yijian Huang

U.C. Berkeley Division of Biostatistics Working Paper Series

Individual subjects may experience recurrent events of same type over a relatively long period of time in a longitudinal study. Researchers are often interested in the distributional pattern of gaps between the successive recurrent events and their association with certain concomitant covariates as well. In this article, their probability structure is investigated in presence of censoring. According to the identified structure, we introduce the proportional reverse-time hazards models that allow arbitrary baseline function for every individual in the study, when the time-dependent covariates effect is of main interest. Appropriate inference procedures are proposed and studied to estimate the parameters of …

Estimating Causal Parameters In Marginal Structural Models With Unmeasured Confounders Using Instrumental Variables, Tanya A. Henneman, Mark Johannes Van Der Laan, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

For statisticians analyzing medical data, a significant problem in determining the causal effect of a treatment on a particular outcome of interest, is how to control for unmeasured confounders. Techniques using instrumental variables (IV) have been developed to estimate causal parameters in the presence of unmeasured confounders. In this paper we apply IV methods to both linear and non-linear marginal structural models. We study a specific class of generalized estimating equations that is appropriate to these data, and compare the performance of the resulting estimator to the standard IV method, a two-stage least squares procedure. Our results are applied to …

On The Existence Of Nontrivial Solutions To Some Elliptic Variational Inequalities, Vy Khoi Le, Klaus Schmitt

Mathematics and Statistics Faculty Research & Creative Works

The paper is concerned with the existence of nontrivial solutions of the obstacle problem: u ε K: ∫Ω ▽u▽ (v - u) dx - λ ∫ Ω u (v - u) dx ≥ ∫ Ω p (x, u) (v - u) dx ∀x ε K, where K = {v ε Ho1(Ω): v ≤ Ψ a.e. on Ω}. By using a generalized mountain pass theorem for inequalities, we prove, subject to some restrictions on the obstacle Ψ, the existence of nontrivial solutions of the above inequality.

An Interactive Tutorial For Teaching Statistical Power, Christopher L. Aberson '99, Dale E. Berger, Michael R. Healy '04, Victoria L. Romero '07

CGU Faculty Publications and Research

This paper describes an interactive Web-based tutorial that supplements instruction on statistical power. This freely available tutorial provides several interactive exercises that guide students as they draw multiple samples from various populations and compare results for populations with differing parameters (for example, small standard deviation versus large standard deviation). The tutorial assignment includes diagnostic multiple-choice questions with feedback addressing misconceptions, and follow-up questions suitable for grading. The sampling exercises utilize an interactive Java applet that graphically demonstrates relationships between statistical power and effect size, null and alternative populations and sampling distributions, and Type I and II error rates. The applet …