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Full-Text Articles in Statistics and Probability

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data, Alfred A. Bartolucci, Shimin Zheng, Sejong Bae, Karan P. Singh Nov 2003

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data, Alfred A. Bartolucci, Shimin Zheng, Sejong Bae, Karan P. Singh

Journal of Modern Applied Statistical Methods

We generalize Lyles et al.’s (2000) random regression models for longitudinal data, accounting for both undetectable values and informative drop-outs in the distribution assumptions. Our models are constructed on the generalized multivariate theory which is based on the Elliptically Contoured Distribution (ECD). The estimation of the fixed parameters in the random regression models are invariant under the normal or the ECD assumptions. For the Human Immunodeficiency Virus Epidemiology Research Study data, ECD models fit the data better than classical normal models according to the Akaike (1974) Information Criterion. We also note that both univariate distributions of the random intercept and …

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Statistical Pronouncements Ii, Jmasm Editors Nov 2003

Statistical Pronouncements Ii, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

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Jmasm8: Using Sas To Perform Two-Way Analysis Of Variance Under Variance Heterogeneity, Scott J. Richter, Mark E. Payton Nov 2003

Jmasm8: Using Sas To Perform Two-Way Analysis Of Variance Under Variance Heterogeneity, Scott J. Richter, Mark E. Payton

Journal of Modern Applied Statistical Methods

We present SAS code to implement the method proposed by Brunner et al. (1997) for performing two-way analysis of variance under variance heterogeneity.

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Type I Error Rates Of Four Methods For Analyzing Data Collected In A Groups Vs Individuals Design, Stephanie Wehry, James Algina Nov 2003

Type I Error Rates Of Four Methods For Analyzing Data Collected In A Groups Vs Individuals Design, Stephanie Wehry, James Algina

Journal of Modern Applied Statistical Methods

Using previous work on the Behrens-Fisher problem, two approximate degrees of freedom tests, that can be used when one treatment is individually administered and one is administered to groups, were developed. Type I error rates are presented for these tests, an additional approximate degrees of freedom test developed by Myers, Dicecco, and Lorch (1981), and a mixed model test. The results indicate that the test that best controls the Type I error rate depends on the number of groups in the group-administered treatment. The mixed model test should be avoided.

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Variable Selection For Poisson Regression Model, Felix Famoye, Daniel E. Rothe Nov 2003

Variable Selection For Poisson Regression Model, Felix Famoye, Daniel E. Rothe

Journal of Modern Applied Statistical Methods

Poisson regression is useful in modeling count data. In a study with many independent variables, it is desirable to reduce the number of variables while maintaining a model that is useful for prediction. This article presents a variable selection technique for Poisson regression models. The data used is log-linear, but the methods could be adapted to other relationships. The model parameters are estimated by the method of maximum likelihood. The use of measures of goodness-of-fit to select appropriate variables is discussed. A forward selection algorithm is presented and illustrated on a numerical data set. This algorithm performs as well if …

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Bootstrapping Confidence Intervals For Robust Measures Of Association, Jason E. King Nov 2003

Bootstrapping Confidence Intervals For Robust Measures Of Association, Jason E. King

Journal of Modern Applied Statistical Methods

A Monte Carlo simulation study compared four bootstrapping procedures in generating confidence intervals for the robust Winsorized and percentage bend correlations. Results revealed the superior resiliency of the robust correlations over r, with neither outperforming the other. Unexpectedly, the bootstrapping procedures achieved roughly equivalent outcomes for each correlation.

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Letters To The Editor, Jmasm Editors Nov 2003

Letters To The Editor, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

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On Treating A Survey Of Convenience Sample As A Simple Random Sample, W. Gregory Thatcher, J. Wanzer Drane Nov 2003

On Treating A Survey Of Convenience Sample As A Simple Random Sample, W. Gregory Thatcher, J. Wanzer Drane

Journal of Modern Applied Statistical Methods

Threat of bias has kept many from using data gathered in less than optimal conditions. We maintain that when convenience sampling represents race and gender at nearly correct proportions and can be beneficial, as these two variables are quite often used as stratification variables. We compared a convenience sample with a proven sample. Race and Sex were nearly proportional as was found in the proven sample. We conclude that the convenience sample can be used as though it is simple random.

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Fortune Cookies, Measurement Error, And Experimental Design, Greogry R. Hancock Nov 2003

Fortune Cookies, Measurement Error, And Experimental Design, Greogry R. Hancock

Journal of Modern Applied Statistical Methods

This article pertains to the theoretical and practical detriments of measurement error in traditional univariate and multivariate experimental design, and points toward modern methods that facilitate greater accuracy in effect size estimates and power in hypothesis testing.

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Correcting Publication Bias In Meta-Analysis: A Truncation Approach, Guillermo Montes, Bohdan S. Lotyczewski Nov 2003

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.

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Comparison Of Viral Trajectories In Aids Studies By Using Nonparametric Mixed-Effects Models, Chin-Shang Li, Hua Liang, Ying-Hen Hsieh, Shiing-Jer Twu Nov 2003

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.

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Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky Nov 2003

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.

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A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly T. Perry Nov 2003

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).

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Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi Nov 2003

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.

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Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara Nov 2003

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 …

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A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes, Christopher J. Mecklin Nov 2003

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.

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Random Number Generators, George Marsaglia May 2003

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.

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Without Supporting Statistical Evidence, Where Would Reported Measures Of Substantive Importance Lead? To No Good Effect, Anthony J. Onwuegbuzie, Joel R. Levin May 2003

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 …

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Bayesian Analysis Of Poverty Rates: The Case Of Vietnamese Provinces, Dominique Haughton, Nguyen Phong May 2003

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 …

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Not All Effects Are Created Equal: A Rejoinder To Sawilowsky, J. Kyle Roberts, Robin K. Henson May 2003

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.

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Comparison Of Estimates Of Proprietary And Syndicated Methods In Auto Industry Surveys, Daniel X. Wang May 2003

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.

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Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations, Kailash C. Madan, Walid Abu-Dayyeh, Firas Tayyan May 2003

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.

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A Different Future For Social And Behavioral Science Research, Shlomo S. Sawilowsky May 2003

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.

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The Trouble With Interpreting Statistically Nonsignificant Effect Sizes In Single-Study Investigations, Joel R. Levin, Daniel H. Robinson May 2003

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.

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A Recursive Algorithm For Fractionally Differencing Long Data Series, Joseph Mccarthy, Robert Disario, Hakan Saraoglu May 2003

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.

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Modeling Correlated Time-Varying Covariate Effects In A Cox-Type Regression Model, Mourad Tighiouart May 2003

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.

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Performing Two-Way Analysis Of Variance Under Variance Heterogeneity, Scott J. Richter, Mark E. Payton May 2003

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.

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The Way Ahead In Qualitative Computing, Tom Richards, Lyn Richards May 2003

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.

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Homogeneous Markov Processes For Breast Cancer Analysis, Ricardo Ocaña-Rilola, Emilio Sanchez-Cantalejo, Carmen Martinez-Garcia May 2003

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.

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Incorporating Sampling Weights Into The Generalizability Theory For Large-Scale Analyses, Christopher W. T. Chiu, Ronald S. Fesco May 2003

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 …

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