Physical Sciences and Mathematics Commons^™

The Use Of Hierarchical Ancova In Curriculum Studies, Show-Mann Liou, Chao-Ying Joanne Peng

Journal of Modern Applied Statistical Methods

Many educational studies are carried out in intact settings, such as classrooms or groups in which individual data were collected before and after a treatment. Researchers advocate either the use of individual scores as the unit of analysis or class means. Both approaches suffer from conceptual and methodological limitations. In this article, the use of hierarchical ANCOVA for analyzing quasiexperimental data including baseline measures is designed and promoted. It is illustrated with a realworld data set collected from a curriculum study. Results showed that the hierarchical ANCOVA is a conceptually and methodologically sound approach, and is better than ANCOVA based …

A Combined Standard Deviation Based Data Clustering Algorithm, Kuttiannan Thangavel, Durairaj Ashok Kumar

Journal of Modern Applied Statistical Methods

The clustering problem has been widely studied because it arises in many knowledge management oriented applications. It aims at identifying the distribution of patterns and intrinsic correlations in data sets by partitioning the data points into similarity clusters. Traditional clustering algorithms use distance functions to measure similarity centroid, which subside the influences of data points. Hence, in this article a novel non-distance based clustering algorithm is proposed which uses Combined Standard Deviation (CSD) as measure of similarity. The performance of CSD based K-means approach, called K-CSD clustering algorithm, is tested on synthetic data sets. It compared favorably to widely used …

Jmasm23: Cluster Analysis In Epidemiological Data (Matlab), Andrés M. Alonso

Journal of Modern Applied Statistical Methods

Matlab functions for testing the existence of time, space and time-space clusters of disease occurrences are presented. The classical scan test, the Ederer, Myers and Mantel’s test, the Ohno, Aoki and Aoki’s test, and the Knox’s test are considered.

Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer

Journal of Modern Applied Statistical Methods

No abstract provided.

Statistical Pronouncements V, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

Properties Of The Gar(1) Model For Time Series Of Counts, Vasiliki Karioti, Chrys Caroni

Journal of Modern Applied Statistical Methods

Models for time series count data include several proposed by Zeger and Qaqish (1988), subsequently generalized into the GARMA family. The GAR(1) model is examined in detail. The maximum likelihood estimation of the parameters will be discussed and the properties of Pearson and randomized residuals will be examined.

Joseph Liouville’S ‘Mathematical Works Of Évariste Galois’, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Liouville’s 1846 introduction to the mathematical works of Galois is translated from French to flowing (American) English. It gave an overview of the tragic circumstances of the undergraduate mathematician whose originality led to major advances in abstract Algebra.

Variational Analysis In Nonsmooth Optimization And Discrete Optimal Control, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern methods of variational· analysis to constrained optimization and control problems generally formulated in infinite-dimensional spaces. The main attention is paid to the study of problems with nonsmooth structures, which require the usage of advanced tools of generalized differentiation. In this way we derive new necessary optimality conditions in optimization problems with functional and. operator constraints and then apply them to optimal control problems governed by discrete-time inclusions in infinite dimensions. The principal difference between finite-dimensional and infinite-dimensional frameworks of optimization and control consists of the "lack of compactness" in infinite dimensions, which …

Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield

Journal of Modern Applied Statistical Methods

Confidence intervals must be robust in having nominal and actual probability coverage in close agreement. This article examined two ways of computing an effect size in a two-group problem: (a) the classic approach which divides the mean difference by a single standard deviation and (b) a variant of a method which replaces least squares values with robust trimmed means and a Winsorized variance. Confidence intervals were determined with theoretical and bootstrap critical values. Only the method that used robust estimators and a bootstrap critical value provided generally accurate probability coverage under conditions of nonnormality and variance heterogeneity in balanced as …

Nonparametric Bayesian Multiple Comparisons For Dependence Parameter In Bivariate Exponential Populations, M. Masoom Ali, J. S. Cho, Munni Begum

Journal of Modern Applied Statistical Methods

A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied. A simple method for pairwise comparisons of these parameters is also suggested. The methodology by Gopalan and Berry (1998) is extended using Dirichlet process priors, applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through a Markov Chain Monte Carlo, Gibbs sampling, due to the intractability of analytic evaluation. The process of MCP for the dependent parameters of bivariate exponential populations is illustrated with a numerical …

Jmasm22: A Convenient Way Of Generating Normal Random Variables Using Generalized Exponential Distribution, Debasis Kundu, Anubhav Manglick

Journal of Modern Applied Statistical Methods

A convenient method to generate normal random variable using a generalized exponential distribution is proposed. The new method is compared with the other existing methods and it is observed that the proposed method is quite competitive with most of the existing methods in terms of the K − S distances and the corresponding p-values.

Variational Analysis Of Evolution Inclusions, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such roblems mainly based on their discrete approximations and the usage of advanced tools of generalized differentiation satisfying comprehensive calculus rules in the framework of Asplund (and hence any reflexive Banach) spaces. In this way we establish extended results on stability of discrete approximations (with the strong W^1,2-convergence of optimal solutions under consistent perturbations of …

Optimization And Equilibrium Problems With Equilibrium Constraints In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern variational f).nalysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as MPECs (mathematical programs with equilibrium constraints) and EPECs (equilibrium problems with equilibrium constraints) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The …

Photoionized HΒ Emission In Ngc 5548: It Breathes!, Edward M. Cackett, Keith Horne

Physics and Astronomy Faculty Research Publications

Emission-line regions in active galactic nuclei (AGNs) and other photoionized nebulae should become larger in size when the ionizing luminosity increases. This `breathing' effect is observed for the Hβ emission in NGC 5548 by using Hβ and optical continuum light curves from the 13-yr (1989-2001) AGN Watch monitoring campaign. To model the breathing, we use two methods to fit the observed light curves in detail: (i) parametrized models and, (ii) the MEMECHO reverberation-mapping code. Our models assume that optical continuum variations track the ionizing radiation, and that the Hβ variations respond with time-delays τ due to light travel-time. By fitting …

Decentralized Convex-Type Equilibrium In Nonconvex Models Of Welfare Economics Via Nonlinear Prices, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving nonconvex economies with infinite-dimensional commodity spaces. The main results relate to generalized/ extended second welfare theorems ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of generalized differentiation, we establish refined results of this type with the novel usage of nonlinear prices at the three types to optimal allocations: weak Pareto, Pareto, and strong Pareto. The usage of nonlinear (vs. standard linear) prices allow us to decentralized price equilibria in fully nonconvex models similarly to linear prices …

Fm-Test: A Fuzzy-Set-Theory-Based Approach To Differential Gene Expression Data Analysis, Lily R. Liang, Shiyong Lu, Xuena Wang, Yi Lu, Vinay Mandal, Dorrelyn Patacsil, Deepak Kumar

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Microarray techniques have revolutionized genomic research by making it possible to monitor the expression of thousands of genes in parallel. As the amount of microarray data being produced is increasing at an exponential rate, there is a great demand for efficient and effective expression data analysis tools. Comparison of gene expression profiles of patients against those of normal counterpart people will enhance our understanding of a disease and identify leads for therapeutic intervention.

Results

In this paper, we propose an innovative approach, fuzzy membership test (FM-test), based on fuzzy set theory to identify disease associated genes from microarray …

Limited Proteolysis Of Human Histone Deacetylase 1, Nayana Kamath, Paulina Karwowska-Desaulniers, Mary Kay H. Pflum

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Histone deacetylase (HDAC) proteins are associated with cell proliferation, differentiation, apoptosis, and cancer. Specifically, HDAC1 is linked with cell growth, a hallmark of cancer formation. HDAC1 is a phosphoprotein and phosphorylation at S421 and S423 promotes HDAC1 enzymatic activity and protein association. While single and double point mutants of HDAC1 at S421 and S423 appear functionally similar, the evidence suggests that HDAC1 is phosphorylated simultaneously at both S421 and S423 in vivo. Additional experiments are necessary to probe the role of double phosphorylation of HDAC1 at S421 and S423.

Results

To characterize HDAC1 phosphorylation at S421 and S423, …

A Database And Tool, Im Browser, For Exploring And Integrating Emerging Gene And Protein Interaction Data For Drosophila, Svetlana Pacifico, Guozhen Liu, Stephen Guest, Jodi R. Parrish, Farshad Fotouhi, Russell L. Finley Jr

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Biological processes are mediated by networks of interacting genes and proteins. Efforts to map and understand these networks are resulting in the proliferation of interaction data derived from both experimental and computational techniques for a number of organisms. The volume of this data combined with the variety of specific forms it can take has created a need for comprehensive databases that include all of the available data sets, and for exploration tools to facilitate data integration and analysis. One powerful paradigm for the navigation and analysis of interaction data is an interaction graph or map that represents proteins …

Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel

Mathematics Faculty Research Publications

These notes developed from a one semester course at Wayne State University, taught several times in the last three decades of the 1900s. The subject matter is analysis on manifolds, consisting of the theory of smooth manifolds, differential forms, integration of forms, the generalized Stokes' Theorem, de Rham cohomology, and some related topics. The course is intended for first or second year graduate students in Mathematics with a background in Advanced Calculus, General Topology, linear algebra (including quotient spaces), and a little elementary group theory (including some familiarity with the symmetric groups). Given the above background, the notes are self-contained. …

K-Spmm: A Database Of Murine Spermatogenic Promoters Modules & Motifs, Yi Lu, Adrian E. Platts, G Charles Ostermeier, Stephen A. Krawetz

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Understanding the regulatory processes that coordinate the cascade of gene expression leading to male gamete development has proven challenging. Research has been hindered in part by an incomplete picture of the regulatory elements that are both characteristic of and distinctive to the broad population of spermatogenically expressed genes.

Description

K-SPMM, a database of murine Spermatogenic Promoters Modules and Motifs, has been developed as a web-based resource for the comparative analysis of promoter regions and their constituent elements in developing male germ cells. The system contains data on 7,551 genes and 11,715 putative promoter regions …

The Influence Of Reliability On Four Rules For Determining The Number Of Components To Retain, Gibbs Y. Kanyongo

Journal of Modern Applied Statistical Methods

Imperfectly reliable scores impact the performance of factor analytic procedures. A series of Monte Carlo studies was conducted to generate scores with known component structure from population matrices with varying levels of reliability. The scores were submitted to four procedures: Kaiser rule, scree plot, parallel analysis, and modified Horn’s parallel analysis to find if each procedure accurately determines the number of components at the different reliability levels. The performance of each procedure was judged by the percentage of the number of times that the procedure was correct and the mean components that each procedure extracted in each cell. Generally, the …

A Method For Analyzing Unreplicated Experiments Using Information On The Intraclass Correlation Coefficient, Jamis J. Perrett

Journal of Modern Applied Statistical Methods

Many studies are performed on units that cannot be replicated; however, there is often an abundance of subsampling. By placing a reasonable upper bound on the intraclass correlation coefficient (ICC), it is possible to carry out classical tests of significance that have conservative levels of significance.

Jmasm24: Numerical Computing For Third-Order Power Method Polynomials (Excel), Todd C. Headrick

Journal of Modern Applied Statistical Methods

The power method polynomial transformation is a popular procedure used for simulating univariate and multivariate non-normal distributions. It requires software that solves simultaneous nonlinear equations. Potential users of the power method may not have access to commercial software packages (e.g., Mathematica, Fortran). Therefore, algorithms are presented in the more commonly available Excel 2003 spreadsheets. The algorithms solve for (1) coefficients for polynomials of order three, (2) intermediate correlations and Cholesky factorizations for multivariate data generation, and (3) the values of skew and kurtosis for determining if a transformation will produce a valid power method probability density function (pdf). The Excel …

Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test.

Second-Order Accurate Inference On Simple, Partial, And Multiple Correlations, Robert J. Boik, Ben Haaland

Journal of Modern Applied Statistical Methods

This article develops confidence interval procedures for functions of simple, partial, and squared multiple correlation coefficients. It is assumed that the observed multivariate data represent a random sample from a distribution that possesses infinite moments, but there is no requirement that the distribution be normal. The coverage error of conventional one-sided large sample intervals decreases at rate 1√n as n increases, where n is an index of sample size. The coverage error of the proposed intervals decreases at rate 1/n as n increases. The results of a simulation study that evaluates the performance of the proposed intervals is …

Inference For P(Y, Vee Ming Ng

Journal of Modern Applied Statistical Methods

Some tests and confidence bounds for the reliability parameter R=P(Y

An Alternative To Warner’S Randomized Response Model, Sat Gupta, Javid Shabbir

Journal of Modern Applied Statistical Methods

A modification to Warner’s (1965) Randomized Response Model is suggested. The suggested model is more efficient than the original model.

Determining Parallel Analysis Criteria, Marley W. Watkins

Journal of Modern Applied Statistical Methods

Determining the number of factors to extract is a critical decision in exploratory factor analysis. Simulation studies have found the Parallel Analysis criterion to be accurate, but it is computationally intensive. Two freeware programs that implement Parallel Analysis on Macintosh and Windows operating systems are presented.

Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu

Journal of Modern Applied Statistical Methods

Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is then reconstructed by solving the nonlinear least squares problem subject to linear inequality constraints, with starting values provided by the local extremas of the derivative of the convolved signal from discrete noisy data. Simulation results show a considerable …

Applications Of Some Improved Estimators In Linear Regression, B. M. Golam Kibria

Journal of Modern Applied Statistical Methods

The problem of estimation of the regression coefficients under multicollinearity situation for the restricted linear model is discussed. Some improve estimators are considered, including the unrestricted ridge regression estimator (URRE), restricted ridge regression estimator (RRRE), shrinkage restricted ridge regression estimator (SRRRE), preliminary test ridge regression estimator (PTRRE), and restricted Liu estimator (RLIUE). The were compared based on the sampling variance-covariance criterion. The RRRE dominates other ridge estimators when the restriction does or does not hold. A numerical example was provided. The RRRE performed equivalently or better than the RLIUE in the sense of having smaller sampling variance.