Applied Statistics Commons^™

Correcting Publication Bias In Meta-Analysis: A Truncation Approach, Guillermo Montes, Bohdan S. Lotyczewski

Journal of Modern Applied Statistical Methods

Meta-analyses are increasingly used to support national policy decision making. The practical implications of publications bias in meta-analysis are discussed. Standard approaches to correct for publication bias require knowledge of the selection mechanism that leads to publication. In this study, an alternative approach is proposed based on Cohen’s corrections for a truncated normal. The approach makes less assumptions, is easy to implement, and performs well in simulations with small samples. The approach is illustrated with two published meta-analyses.

Comparison Of Viral Trajectories In Aids Studies By Using Nonparametric Mixed-Effects Models, Chin-Shang Li, Hua Liang, Ying-Hen Hsieh, Shiing-Jer Twu

Journal of Modern Applied Statistical Methods

The efficacy of antiretroviral therapies for human immunodeficiency virus (HIV) infection can be assessed by studying the trajectory of the changing viral load with treatment time, but estimation of viral trajectory parameters by using the implicit function form of linear and nonlinear parametric models can be problematic. Using longitudinal viral load data from a clinical study of HIV-infected patients in Taiwan, we described the viral trajectories by applying a nonparametric mixed-effects model. We were then able to compare the efficacies of highly active antiretroviral therapy (HAART) and conventional therapy by using Young and Bowman’s (1995) test.

Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The main purpose of this article is to contest the propositions that (1) hypothesis tests should be abandoned in favor of confidence intervals, and (2) science has not benefited from hypothesis testing. The minor purpose is to propose (1) descriptive statistics, graphics, and effect sizes do not obviate the need for hypothesis testing, (2) significance testing (reporting p values and leaving it to the reader to determine significance) is subjective and outside the realm of the scientific method, and (3) Bayesian and qualitative methods should be used for Bayesian and qualitative research studies, respectively.

A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly T. Perry

Journal of Modern Applied Statistical Methods

This paper explores the appropriateness of testing the equality of two means using either a t test, the Welch test, or the Wilcoxon-Mann-Whitney test for two independent samples based on the results of using two classes of preliminary tests (i.e., tests for population variance equality and symmetry in underlying distributions).

Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi

Journal of Modern Applied Statistical Methods

The problem considered is interval estimation of the stress - strength reliability R = P(Xθ and λ respectively and a common location parameter μ . Several types of asymptotic, approximate and bootstrap intervals are investigated. Performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their usage are given.

Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

The aim of the present study is to obtain and compare confidence intervals for the variance of a Gaussian distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the variance of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with the well known classical method. The Bayesian approach relies only on the observations. It is shown that the proposed approximate Bayesian approach relies only on the observations. The classical method, that uses the Chi-square statistic, does …

A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes, Christopher J. Mecklin

Journal of Modern Applied Statistical Methods

Equivalence testing, an alternative to testing for statistical significance, is little used in educational research. Equivalence testing is useful in situations where the researcher wishes to show that two means are not significantly different. A simulation study assessed the relationships between effect size, sample size, statistical significance, and statistical equivalence.

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Mathematics and Statistics Faculty Publications

In this paper, we study the following Duffing-type equation:

x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

Ranked Set Sampling Based On Binary Water Quality Data With Covariates, Paul Kvam

Department of Math & Statistics Faculty Publications

A ranked set sample (RSS) is composed of independent order statistics, formed by collecting and ordering independent subsamples, then measuring only one item from each subsample. If the cost of sampling is dominated by data measurement rather than collection or ranking, the RSS technique is known to be superior to ordinary sampling. Experiments based on binary data are not designed to exploit the advantages of ranked set sampling because categorical data typically are as easily measured as ranked, making RSS methods impractical. However, in some environmental and biological studies, the success probability of a bivariate outcome is related to one …

On Adaptive Estimation In Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

A simple method is provided to construct a general class of individual and simultaneous confidence intervals for the effects in orthogonal saturated designs. These intervals use the data adaptively, maintain the confidence levels sharply at 1 - α at the least favorable parameter configuration, work effectively under effect sparsity, and include the intervals by Wang and Voss (2001) as a special case.

On The Stability Of The Positive Radial Steady States For A Semilinear Cauchy Problem, Yinbin Deng, Yi Li, Yi Liu

Mathematics and Statistics Faculty Publications

No abstract provided.

What Is A Reasonable Attorney Fee? An Empirical Study Of Class Action Settlements, Theodore Eisenberg, Geoffrey P. Miller

Cornell Law Faculty Publications

Determining an appropriate fee is a difficult task facing trial court judges in class action litigation. But courts rarely rely on empirical research to assess a fee’s reasonableness, due, at least in part, to the relative paucity of available information. Existing empirical studies of attorney fees in class action cases are limited in scope, and generally do not control for important variables. To help fill this gap, we analyzed data from all state and federal class actions with reported fee decisions from 1993 to 2002 in which the fee and class recovery could be determined with reasonable confidence.

We find …

The Consequences Of Race-Blindness: Revisiting Prediction Models With Current Law School Data, Linda F. Wightman

Journal of Legal Education

No abstract provided.

Assessing Left-Handedness With Exact And Approximate Confidence Intervals Appropriate For Samples Of Different Sizes, Virginia Gardner

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Random Number Generators, George Marsaglia

Journal of Modern Applied Statistical Methods

The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit.

Without Supporting Statistical Evidence, Where Would Reported Measures Of Substantive Importance Lead? To No Good Effect, Anthony J. Onwuegbuzie, Joel R. Levin

Journal of Modern Applied Statistical Methods

Although estimating substantive importance (in the form of reporting effect sizes) has recently received widespread endorsement, its use has not been subjected to the same degree of scrutiny as has statistical hypothesis testing. As such, many researchers do not seem to be aware that certain of the same criticisms launched against the latter can also be aimed at the former. Our purpose here is to highlight major concerns about effect sizes and their estimation. In so doing, we argue that effect size measures per se are not the hoped-for panaceas for interpreting empirical research findings. Further, we contend that if …

Bayesian Analysis Of Poverty Rates: The Case Of Vietnamese Provinces, Dominique Haughton, Nguyen Phong

Journal of Modern Applied Statistical Methods

This paper presents a Bayesian analysis of poverty rates in urban Ho Chi Minh City and rural Nghe An province in Vietnam. Using mixtures of beta distributions as priors for the poverty rates, we find that, when the prior is reasonably informative, our approach yields more accurate estimated poverty rates than a frequentist approach. On the other hand, we find that, in the presence of poor/non-poor misclassification, average probabilities of posterior credible intervals for poverty rates can fall well short of .95 even with sample sizes such as 2000 or 3000 when the width of the interval is for example …

Not All Effects Are Created Equal: A Rejoinder To Sawilowsky, J. Kyle Roberts, Robin K. Henson

Journal of Modern Applied Statistical Methods

In the continuing debate over the use and utility of effect sizes, more discussion often helps to both clarify and syncretize methodological views. Here, further defense is given of Roberts & Henson (2002) in terms of measuring bias in Cohen’s d, and a rejoinder to Sawilowsky (2003) is presented.

Comparison Of Estimates Of Proprietary And Syndicated Methods In Auto Industry Surveys, Daniel X. Wang

Journal of Modern Applied Statistical Methods

Proprietary and syndicate surveys are often used in assessing appeal and initial quality of new vehicles for automobile manufactures. This study discusses the difference between the two types of studies, and proposes a computer simulation based method for checking the appropriateness of the comparisons.

Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations, Kailash C. Madan, Walid Abu-Dayyeh, Firas Tayyan

Journal of Modern Applied Statistical Methods

We examine an M/D/2 queue with Bernoulli schedules and a single vacation policy. We have assumed Poisson arrivals waiting in a single queue and two parallel servers who provide identical deterministic service to customers on first-come, first-served basis. We consider two models; in one we assume that after completion of a service both servers can take a vacation while in the other we assume that only one may take a vacation. The vacation periods in both models are assumed to be exponential. We obtain steady state probability generating functions of system size for various states of the servers.

A Different Future For Social And Behavioral Science Research, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The dissemination of intervention and treatment outcomes as effect sizes bounded by conf idence intervals in order to think meta-analytically was promoted in a recent article in Educational Researcher. I raise concerns with unfettered reporting of effect sizes, point out the con in confidence interval, and caution against thinking meta-analytically. Instead, cataloging effect sizes is recommended for sample size estimation and power analysis to improve social and behavioral science research.

The Trouble With Interpreting Statistically Nonsignificant Effect Sizes In Single-Study Investigations, Joel R. Levin, Daniel H. Robinson

Journal of Modern Applied Statistical Methods

In this commentary, we offer a perspective on the problem of authors reporting and interpreting effect sizes in the absence of formal statistical tests of their chanceness. The perspective reinforces our previous distinction between single-study investigations and multiple-study syntheses.

A Recursive Algorithm For Fractionally Differencing Long Data Series, Joseph Mccarthy, Robert Disario, Hakan Saraoglu

Journal of Modern Applied Statistical Methods

We propose a recursive algorithm to fractionally difference time series data. The algorithm eliminates the need to evaluate the gamma function directly, and hence avoids the overflow problem that arises when fractionally differencing a long data series. The proposed algorithm can be implemented using any general matrix programming language. An implementation using SAS is presented. The algorithm and the code provide a practical approach to including fractional differencing as part of a time series data analysis.

Modeling Correlated Time-Varying Covariate Effects In A Cox-Type Regression Model, Mourad Tighiouart

Journal of Modern Applied Statistical Methods

In this paper, I extend the proposed model by McKeague and Tighiouart (2000) to handle time-varying correlated covariate effects for the analysis of survival data. I use the conditional predictive ordinates (CPO’s) for model comparison and the methodology is illustrated by an application to nasopharynx cancer survival data. A reversible jump MCMC sampler to estimate the CPO’s will be presented.

Performing Two-Way Analysis Of Variance Under Variance Heterogeneity, Scott J. Richter, Mark E. Payton

Journal of Modern Applied Statistical Methods

Small sample properties of the method proposed by Brunner et al. (1997) for performing two-way analysis of variance are compared to those of the normal based ANOVA method for factorial arrangements. Different effect sizes, sample sizes, and error structures are utilized in a simulation study to compare type I error rates and power of the two methods. An SAS program is also presented to assist those wishing to implement the Brunner method to real data.

The Way Ahead In Qualitative Computing, Tom Richards, Lyn Richards

Journal of Modern Applied Statistical Methods

Specialized computer programs for Qualitative Research in social sciences have greatly changed ways of doing QR, the reliability and comprehensiveness of results, the ability to inspect and challenge a researcher’s working, and the relationship with quantitative methods in social research. This article explores these claims in the context of N6 (NUD*IST) and NVivo, the two programs designed by the authors; and considers possible future developments in the field.

Homogeneous Markov Processes For Breast Cancer Analysis, Ricardo Ocaña-Rilola, Emilio Sanchez-Cantalejo, Carmen Martinez-Garcia

Journal of Modern Applied Statistical Methods

Sometimes, the introduction of covariates in stochastic processes is required to study their effect on disease history events. However these types of models increase the complexity of analysis, even for simpler processes, and standard software to analyse stochastic processes is limited. In this paper, a method for fitting homogeneous Markov models with covariates is proposed for analysing breast cancer data. Specific software for this purpose has been implemented.

Incorporating Sampling Weights Into The Generalizability Theory For Large-Scale Analyses, Christopher W. T. Chiu, Ronald S. Fesco

Journal of Modern Applied Statistical Methods

Large scale studies frequently use complex sampling procedures, disproportionate sampling weights, and adjustment techniques to account for potential bias due to nonresponses and to ensure that results from the sample can be generalized to a larger population. Survey researchers are concerned about measurement error and the use of weights in developing models. Consequently, multiple weighting factors are used and these weighting factors are manifested as a final survey (composite) weight available for analysis. We developed a method to incorporate an external weighting factor like this for analyses of measurement errors in the theory of generalizability to provide researchers with a …

Using Multinomial Logistic Models To Predict Adolescent Behavioral Risk, Chao-Ying Joanne Peng, Rebecca Naegle Nichols

Journal of Modern Applied Statistical Methods

Multinomial logistic regression was applied to data comprising 432 adolescents’ self reports of engagement in risky behaviors. Results showed that gender, intention to drop from the school, family structure, self-esteem, and emotional risk were effective predictors collectively. Three methodological issues were highlighted: (1) the use of odds ratio, (2) the absence of an extension of the Hosmer and Lemeshow test for multinomial logistic models, and (3) the missing data problem. Psychologists and educators can utilize findings to plan prevention programs, as well as to apply the versatile and effective logistic technique in psychological, educational, and health research concerning adolescents.

Was Monte Carlo Necessary?, Thomas R. Knapp

Journal of Modern Applied Statistical Methods

In the critique that follows, I have attempted to summarize the principal disagreements between Sawilowsky and Roberts & Henson regarding the reporting and interpreting of statistically non-significant effect sizes, and to provide my own personal evaluations of their respective arguments.