Statistics and Probability Commons^™

Efficiency Of Canonical Discriminant Function Versus Mahalanobis Distance In Differentiating Groups: Screening Ovarian Cancer In A Multivariate System Analysis Using Enzyme Markers, Chinmoy K. Bose

Journal of Modern Applied Statistical Methods

Due to its low prevalence, high mortality and uniquely hidden intrapelvic position, ovarian cancer remains a subject of intense interest to researchers. Statistical calculation and new technology both have major roles to play in the effort to screen this cancer at an early stage. Advanced statistics, such as multivariate analysis, remain at the root of screening endeavors. Multivariate analysis has the power to combine many tests and to produce better results in terms high specificity and positive predictive value. Multivariate analysis techniques include Mahalanobis distance (D²), canonical stepwise discriminant function (Z) and Posterior Probability. These may have varied …

Applying Census Data For Small Area Estimation In Community And Social Service Planning, Michael Wolf-Branigin, Hyon-Sook Suh, Star Muir, Emily S. Ihara

Journal of Modern Applied Statistical Methods

Small area estimation provides a tool for community analysis. A procedure for accessing, selecting, joining and analyzing US Census data is provided. Skills acquired while completing the procedure include accessing census data, downloading boundary files and displaying themes. Such skills are valuable tools for students to possess as they enter the workforce.

A Comparative Study Of Bayesian Model Selection Criteria For Capture-Recapture Models For Closed Populations, Ross M. Gosky, Sujit K. Ghosh

Journal of Modern Applied Statistical Methods

Capture-Recapture models estimate unknown population sizes. Eight standard closed population models exist, allowing for time, behavioral, and heterogeneity effects. Bayesian versions of these models are presented and use of Akaike's Information Criterion (AIC) and the Deviance Information Criterion (DIC) are explored as model selection tools, through simulation and real dataset analysis.

Quantile Regression: On Inferences About The Slopes Corresponding To One, Two Or Three Quantiles, Rand R. Wilcox, Kathleen Costa

Journal of Modern Applied Statistical Methods

The problem of testing hypotheses about the slope of a quantile regression line when the sample size is small is considered. A modified bootstrap method is suggested that is found to have certain advantages over the inverse rank method recommended by Koenker (1994). A method is suggested that simultaneously controls the probability of at least one Type I error when performing two or three tests corresponding to two or three specific quantiles. Using data from actual studies, it is illustrated that the new method can yield substantially shorter confidence intervals than the rank inverse method and, even with a large …

A Monte Carlo Comparison Of Regression Estimators When The Error Distribution Is Long-Tailed Symmetric, Oya Can Mutan, Birdal Şenoğlu

Journal of Modern Applied Statistical Methods

The performances of the ordinary least squares (OLS), modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares (WIN), trimmed least squares (TLS), Theil’s (Theil) and weighted Theil’s (Weighted Theil) estimators are compared under the simple linear regression model in terms of their bias and efficiency when the distribution of error terms is long-tailed symmetric.

Improved Confidence Intervals For The Difference Between Two Proportions, James F. Reed Iii

Journal of Modern Applied Statistical Methods

Wald-z asymptotic methods, with and without a continuity correction, have less than nominal coverage probability characteristics but continue to be used. Newcombe's hybrid method and the Agresti-Caffo methods have coverage probabilities that are near nominal for either equal or unequal samples. Newcombe's hybrid and Agresti-Caffo methods demonstrate superior coverage properties.

Multiple Regression In Pair Correlation Solution, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Behavior of the coefficients of ordinary least squares (OLS) regression with the coefficients regularized by the one-parameter ridge (Ridge-1) and two-parameter ridge (Ridge-2) regressions are compared. The ridge models are not prone to multicollinearity. The fit quality of Ridge-2 does not decrease with the profile parameter increase, but the Ridge-2 model converges to a solution proportional to the coefficients of pair correlation between the dependent variable and predictors. The Correlation-Regression (CORE) model suggests meaningful coefficients and net effects for the individual impact of the predictors, high quality model fit, and convenient analysis and interpretation of the regression. Simulation with three …

Bayesian Inference On The Variance Of Normal Distribution Using Moving Extremes Ranked Set Sampling, Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

Journal of Modern Applied Statistical Methods

Bayesian inference of the variance of the normal distribution is considered using moving extremes ranked set sampling (MERSS) and is compared with the simple random sampling (SRS) method. Generalized maximum likelihood estimators (GMLE), confidence intervals (CI), and different testing hypotheses are considered using simple hypothesis versus simple hypothesis, simple hypothesis versus composite alternative, and composite hypothesis versus composite alternative based on MERSS and compared with SRS. It is shown that modified inferences using MERSS are more efficient than their counterparts based on SRS.

Quantifying Bimodality Part 2: A Likelihood Ratio Test For The Comparison Of A Unimodal Normal Distribution And A Bimodal Mixture Of Two Normal Distributions. Bruno D. Zumbo Is, B. W. Frankland, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Scientists in a variety of fields are often faced with the question of whether a sample is best described as unimodal or bimodal. In an earlier paper (Frankland & Zumbo, 2002), a simple and convenient method for assessing bimodality was described. That method is extended by developing and demonstrating a likelihood ratio test (LRT) for bimodality for the comparison of a unimodal normal distribution and a bimodal mixture of two normal distributions. As in Frankland and Zumbo (2002), the LRT approach is demonstrated using algorithms in SPSS.

Email: A Note On Hypothesis Tests After Correction For Autocorrelation: Solace For The Cochrane-Orcutt Method?, Terry E. Dielman

Journal of Modern Applied Statistical Methods

The behavior of the t test in small samples for coefficient significance in time-series regressions is examined after using the Prais-Winsten (PW) and Cochrane-Orcutt (CO) corrections for autocorrelation. Results are compared to ordinary least squares and generalized least squares.

Quel Test For Two Linear Restrictions In The Nonlinear Models, Krishna K. Saha

Journal of Modern Applied Statistical Methods

An alternative Wald type test called the quel test is developed for two linear restrictions by finding the critical region based on the quel utilizing the repeated values of estimated parameters of interest under the null. Simulation shows evidence that the full quel test performs best in that it holds nominal level well and shows monotonic increasing power properties.

Comparative Power Of The Independent T, Permutation T, And Wilcoxontests, Michèle Weber, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The nonparametric Wilcoxon Rank Sum (also known as the Mann-Whitney U) and the permutation t-tests are robust with respect to Type I error for departures from population normality, and both are powerful alternatives to the independent samples Student’s t-test for detecting shift in location. The question remains regarding their comparative statistical power for small samples, particularly for non-normal distributions. Monte Carlo simulations indicated the rank-based Wilcoxon test was found to be more powerful than both the t and the permutation t-tests.

Industrialization In Animal Agriculture: A Kalman Filter Analysis, Oya S. Erdogdu, Levent Ozbek

Journal of Modern Applied Statistical Methods

Studies discussing the effects of technological developments on (animal) agricultural production argue that the effective usage of chemicals and genetic engineering increase control over production processes, which in turn decreases seasonality (one significant factor defining agricultural production) significantly and brings standardization to production. Studies on broilery also show that production is not limited by nature determined seasons. Supply side changes accompanied by changes in demand have led to more healthier, standardized products. Using tools of economics and statistics, this study documents this transformation in animal agricultural production of beef, pork and milk. Results indicate decreasing seasonality, thus the industralization of …

Aligned Rank Tests For Interactions In Split-Plot Designs: Distributional Assumptions And Stochastic Heterogeneity, T. Mark Beasley, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Three aligned rank methods for transforming data from multiple group repeated measures (split-plot) designs are reviewed. Univariate and multivariate statistics for testing the interaction in split-plot designs are elaborated. Computational examples are presented to provide a context for performing these ranking procedures and statistical tests. SAS/IML and SPSS syntax code to perform the procedures is included in the Appendix.

Pain As A Predictor Of Depression Treatment Outcomes In Women With Childhood Sexual Abuse, Ellen L. Poleshuck, Nancy L. Talbot, Haiyan Su, Xin Tu, Linda Chaudron, Stephanie Gamble, Donna E. Giles

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Objectives: Childhood sexual abuse (CSA) increases risk for both depression and pain in women. Pain is associated with worse depression treatment response. The contribution of pain to depression treatment outcomes in women with histories of CSA is unknown. This study examined whether clinically significant pain would be associated with worse depression and functioning outcomes among women with CSA histories treated with interpersonal psychotherapy. Method: Participants were 66 women with major depression and CSA who presented to a community mental health center. An interpersonal psychotherapy protocol planned for 14 weekly sessions followed by 2 biweekly sessions. Patients were classified as experiencing …

The Comparison Of Model Selection Criteria When Selecting Among Competing Hierarchical Linear Models, Tiffany A. Whittaker, Carolyn F. Furlow

Journal of Modern Applied Statistical Methods

Little is known about the use and accuracy of model selection criteria when selecting among a set of competing multilevel models. The practices of applied researchers and the performance of five model selection criteria are examined when selecting the correct multilevel model using simulation techniques.

Bias In Stabilized Sieve Sampling, Liming Guan, John P. Wendell

Journal of Modern Applied Statistical Methods

The stabilized sieve sample selection method (SSM) is considered to be a probability proportional to size (PPS) sampling method with an unbiased estimator (Horgan 1997, 1998). This article demonstrates that SSM does not select items with PPS and that the point estimator is biased.

A New Approximate Bayesian Approach For Decision Making About The Variance Of A Gaussian Distribution Versus The Classical Approach, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

Rules of decision-making about the variance of a Gaussian distribution are obtained and compared. Considering the square error loss function, an approximate Bayesian decision rule for the variance of a normal population is derived. Using normal data and SAS software, the obtained approximate Bayesian test results were compared to their counterparts obtained with the well-known classical decision rule. It is shown that the proposed approximate Bayesian decision rule relies only on observations. The classical decision rule, which uses the Chi-square statistic, does not always yield the best results: the proposed approach often performs better.

Which Is The Best Parametric Statistical Method For Analyzing Delphi Data?, Hiral A. Shah, Sema A. Kalaian

Journal of Modern Applied Statistical Methods

This study compares the three parametric statistical methods: coefficient of variation, Pearson correlation coefficient, and F-test to obtain reliability in a Delphi study that involved more than 100 participants. The results of this study indicated that coefficient of variation was the best procedure to obtain reliability in such a study.

A Socratic Dialogue, Vance W. Berger

Journal of Modern Applied Statistical Methods

Socrates has found some aspects of medical biostatistics a bit confusing, and wishes to discuss some of these issues with Simplicio, a prominent medical researcher. This Socratic dialogue will shed some light on the errant use of parametric analyses in clinical trials.

A Comparison Of Maximum Likelihood And Expected A Posteriori Estimation For Polychoric Correlation Using Monte Carlo Simulation, Jinsong Chen, Jaehwa Choi

Journal of Modern Applied Statistical Methods

This study aims to compare the maximum likelihood (ML) and expected a posterior (EAP) estimation for polychoric correlation (PCC) under diverse conditions, especially when considering a sample size. As the ML is the classical solution to estimate PCC, the EAP is a new method based on Bayes’ theorem. Different types of prior distributions are also adapted to investigate the sensitivity of prior distribution onto the PCC estimate for the EAP case. The Monte Carlo simulation is used for this comparison by a specialized program code in MATLAB.

Tandem Queues With Non-Stationary Arrivals, Senthil Balaji Girimurugan

All Theses

We consider a network of K queues in tandem labeled Q₁, Q₂, ..,Q_K. The arrivals to Q ₁ form a non-homogeneous Poisson process whose intensity is periodic. We conjecture that asymptotically the arrival process A_j to Q_j, j= 1,2,..,K is cycle stationary. In addition, we conjecture that asymptotically as 'j' gets larger, the arrival process at the jth queue gets closer to a stationary point process. Hence, the queue performance measures become more stationary as 'j' increases. We perform Monte-Carlo simulations and design statistical tests whose results support the conjecture.

The Effectiveness Of Institutional Intervention At Minimizing Demographic Inertia And Improving The Representation Of Women Faculty In Higher Education, Amanda V. Bakian

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

Across all science and engineering disciplines, women currently receive 46% of the doctoral degrees granted annually. Despite gains in doctoral degrees earned by women over the past 30 years, they remain under-represented among full time tenured /tenure-track science and engineering faculty compared to their presence among degree recipients. The inequality gap is widest among full professors at 4 year research universities where women account for a mere 16% of all S&E full time full professors. Multiple hypothesis have been proposed to account for women's under-representation relative to men including those based on human capital/economic theory, feminist theory, innate biological gender …

Time Series Analysis: A New Look At Some Old Problems, Ferebee Tunno

All Dissertations

This dissertation gives a comprehensive report of my doctoral research in time series analysis from summer 2006 to spring 2009. It is comprised of two main efforts: interval estimation for an autoregressive parameter and arc length tests for equivalent ARIMA dynamics. Such problems are traditional in statistics, but three new theorems and several simulations are presented here that help elucidate new ways to handle them.

Investigations Of Variable Importance Measures Within Random Forests, Andrew C. Merrill

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Random Forests (RF) (Breiman 2001; Breiman and Cutler 2004) is a completely nonparametric statistical learning procedure that may be used for regression analysis and. A feature of RF that is drawing a lot of attention is the novel algorithm that is used to evaluate the relative importance of the predictor/explanatory variables. Other machine learning algorithms for regression and classification, such as support vector machines and artificial neural networks (Hastie et al. 2009), exhibit high predictive accuracy but provide little insight into predictive power of individual variables. In contrast, the permutation algorithm of RF has already established a track record for …

Resampling-Based Multiple Hypothesis Testing With Applications To Genomics: New Developments In The R/Bioconductor Package Multtest, Houston N. Gilbert, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

The multtest package is a standard Bioconductor package containing a suite of functions useful for executing, summarizing, and displaying the results from a wide variety of multiple testing procedures (MTPs). In addition to many popular MTPs, the central methodological focus of the multtest package is the implementation of powerful joint multiple testing procedures. Joint MTPs are able to account for the dependencies between test statistics by effectively making use of (estimates of) the test statistics joint null distribution. To this end, two additional bootstrap-based estimates of the test statistics joint null distribution have been developed for use in the …

A Class Of Semiparametric Mixture Cure Survival Models With Dependent Censoring, Megan Othus, Yi Li, Ram C. Tiwari

Harvard University Biostatistics Working Paper Series

No abstract provided.

Application Of Time-To-Event Methods In The Assessment Of Safety In Clinical Trials, Kelly L. Moore, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Since randomized controlled trials (RCT) are typically designed and powered for efficacy rather than safety, power is an important concern in the analysis of the effect of treatment on the occurrence of adverse events (AE). These outcomes are often time-to-event outcomes which will naturally be subject to right-censoring due to early patient withdrawals. In the analysis of the treatment effect on such an outcome, gains in efficiency, and thus power, can be achieved by exploiting covariate information. We apply the targeted maximum likelihood methodology to the estimation of treatment specific survival at a fixed end point for right-censored survival outcomes. …

Interval Estimation For The Difference In Paired Areas Under The Roc Curves In The Absence Of A Gold Standard Test, Hsin-Neng Hsieh, Hsiu-Yuan Su, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard test on the true disease status is required to estimate the AUC. However, a gold standard test may sometimes be too expensive or infeasible. Therefore, in many medical research studies, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, using the expectation-maximization …

Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …