Statistics and Probability Commons^™

A More Efficient Way Of Obtaining A Unique Median Estimate For Circular Data, B. Sango Otieno, Christine M. Anderson-Cook

Journal of Modern Applied Statistical Methods

The procedure for computing the sample circular median occasionally leads to a non-unique estimate of the population circular median, since there can sometimes be two or more diameters that divide data equally and have the same circular mean deviation. A modification in the computation of the sample median is suggested, which not only eliminates this non-uniqueness problem, but is computationally easier and faster to work with than the existing alternative.

You Think You’Ve Got Trivials?, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

Effect sizes are important for power analysis and meta-analysis. This has led to a debate on reporting effect sizes for studies that are not statistically significant. Contrary and supportive evidence has been offered on the basis of Monte Carlo methods. In this article, clarifications are given regarding what should be simulated to determine the possible effects of piecemeal publishing trivial effect sizes.

A Semiparametric Regression Model For Oligonucleotide Arrays, Jianhua Hu, Guosheng Yin

Journal of Modern Applied Statistical Methods

A semiparametric model incorporating the spline smoothing technique is proposed to study oligonucleotide gene expression data. No specific parametric functional form is assumed for mismatch probe intensities, which allows much more flexibility in the fitted model. The new approach improves the model fitting, hence the estimation of expression indexes. The method is applied to a data set of 18 HuGeneFL arrays.

Jmasm6: An Algorithm For Generating Exact Critical Values For The Kruskal-Wallis One-Way Anova, Todd C. Headrick

Journal of Modern Applied Statistical Methods

A Fortran 77 subroutine is provided for computing exact critical values for the Kruskal-Wallis test on k independent groups with equal or unequal samples sizes. The subroutine requires the user to provide sorting and ranking routines and a uniform pseudo-random number generator. The program is available from the author on request.

Randomization Technique, Allocation Concealment, Masking, And Susceptibility Of Trials To Selection Bias, Vance W. Berger, Costas A. Christophi

Journal of Modern Applied Statistical Methods

It is widely believed that baseline imbalances in randomized clinical trials must necessarily be random. Yet even among masked randomized trials conducted with allocation concealment, there are mechanisms by which patients with specific covariates may be selected for inclusion into a particular treatment group. This selection bias would force imbalance in those covariates, measured or unmeasured, that are used for the patient selection. Unfortunately, few trials provide adequate information to determine even if there was allocation concealment, how the randomization was conducted, and how successful the masking may have been, let alone if selection bias was adequately controlle d. In …

Improved Multiple Comparisons With The Best In Response Surface Methodology, Laura K. Miller, Ping Sa

Journal of Modern Applied Statistical Methods

A method to construct simultaneous confidence intervals about the difference in mean responses at the stationary point and at x for all x within a sphere with radius I R is proposed. Results of an efficiency study to compare the new method and the existing method by Moore and Sa (1999) are provided.

Pain And Distress Associated With Polyclonal Antibody Production: Discussion And Recommendations, The Humane Society Of The United States

ANIMAL RESEARCH

The Humane Society of the United States (HSUS) held a workshop in August 2002 in order to develop recommendations for minimizing pain and distress associated with polyclonal antibody (Pab) production. A small group of experts in the fields of antibody production, animal welfare, in vitro alternatives, and/or regulatory compliance participated in the roundtable discussion. The workshop was a scientifically based meeting, and recommendations were based on the extensive experience of the workshop participants as well as published literature regarding the relevant issues.

Participants recognized that insufficient attention has been paid to animal welfare aspects of Pab production, in part because …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Census 2000 Demographic Profile Report Of The Older Adult Population In Cuyahoga, Lake, Geauga, Lorain And Medina Counties, Mark Salling, Sharon Bliss, Mcnamara, Brian

All Maxine Goodman Levin School of Urban Affairs Publications

No abstract provided.

On The Misuse Of Confidence Intervals For Two Means In Testing For The Significance Of The Difference Between The Means, George W. Ryan, Steven D. Leadbetter

Journal of Modern Applied Statistical Methods

Comparing individual confidence intervals of two population means is an incorrect procedure for determining the statistical significance of the difference between the means. We show conditions where confidence intervals for the means from two independent samples overlap and the difference between the means is in fact significant.

Constructive Criticism, Ronald C. Serlin

Journal of Modern Applied Statistical Methods

Attempts to attain knowledge as certified true belief have failed to circumvent Hume’s injunction against induction. Theories must be viewed as unprovable, improbable, and undisprovable. The empirical basis is fallible, and yet the method of conjectures and refutations is untouched by Hume’s insights. The implications for statistical methodology is that the requisite severity of testing is achieved through the use of robust procedures, whose assumptions have not been shown to be substantially violated, to test predesignated range null hypotheses. Nonparametric range null hypothesis tests need to be developed to examine whether or not effect sizes or measures of association, as …

Extensions Of The Concept Of Exchangeability And Their Applications, Phillip I. Good

Journal of Modern Applied Statistical Methods

Permutation tests provide exact p-values in a wide variety of practical testing situations. But permutation tests rely on the assumption of exchangeability, that is, under the hypothesis, the joint distribution of the observations is invariant under permutations of the subscripts. Observations are exchangeable if they are independent, identically distributed (i.i.d.), or if they are jointly normal with identical covariances. The range of applications of these exact, powerful, distribution-free tests can be enlarged through exchangeability- preserving transforms, asymptotic exchangeability, partial exchangeability, and weak exchangeability. Original exact tests for comparing the slopes of two regression lines and for the analysis of …

A Test Of Symmetry, Abdul R. Othman, H. J. Keselman, Rand R. Wilcox, Katherine Fradette, A. R. Padmanabhan

Journal of Modern Applied Statistical Methods

When data are nonnormal in form classical procedures for assessing treatment group equality are prone to distortions in rates of Type I error and power to detect effects. Replacing the usual means with trimmed means reduces rates of Type I error and increases sensitivity to detect effects. If data are skewed, say to the right, then it has been postulated that asymmetric trimming, to the right, should be better at controlling rates of Type I error and power to detect effects than symmetric trimming from both tails of the data distribution. Keselman, Wilcox, Othman and Fradette (2002) found that Babu, …

Best Regression Model Using Information Criteria, Phill Gagné, C. Mitchell Dayton

Journal of Modern Applied Statistical Methods

The accuracy of AIC and BIC is evaluated under simulated multiple regression conditions, varying number of total and valid predictors, R², and n. AIC and BIC were increasingly accurate as n increased and as total predictors decreased. Interactions of the ratio of valid/total predictors affected accuracy.

The Statistical Modeling Of The Fertility Of Chinese Women, Dudley L. Poston Jr.

Journal of Modern Applied Statistical Methods

This article is concerned with the statistical modeling of children ever born (CEB) fertility data. It is shown that in a low fertility population, such as China, the use of linear regression approaches to model CEB is statistically inappropriate because the distribution of the CEB variable is often heavily skewed with a long right tail. For five sub-groups of Chinese women, their fertility is modeled using Poisson, negative binomial, and ordinary least squares (OLS) regression models. It is shown that in almost all instances there would have been major errors of statistical inference had the interpretations of the results been …

Fermat, Schubert, Einstein, And Behrens-Fisher: The Probable Difference Between Two Means When Σ_1^2≠Σ_2^2, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The history of the Behrens-Fisher problem and some approximate solutions are reviewed. In outlining relevant statistical hypotheses on the probable difference between two means, the importance of the Behrens- Fisher problem from a theoretical perspective is acknowledged, but it is concluded that this problem is irrelevant for applied research in psychology, education, and related disciplines. The focus is better placed on “shift in location” and, more importantly, “shift in location and change in scale” treatment alternatives.

Double Median Ranked Set Sample: Comparing To Other Double Ranked Samples For Mean And Ratio Estimators, Hani M. Samawi, Eman M. Tawalbeh

Journal of Modern Applied Statistical Methods

Double median ranked set sample (DMRSS) and its properties for estimating the population mean, when the underlying distribution is assumed to be symmetric about its mean, are introduced. Also, the performance of DMRSS with respect to other ranked set samples and double ranked set samples, for estimating the population mean and ratio, is considered. Real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The analysis and simulation indicate that using DMRSS for estimating the population mean is more efficient than using the other ranked samples and double ranked samples schemes except in …

Robust Estimation Of Multivariate Failure Data With Time-Modulated Frailty, Pingfu Fu, J. Sunil Rao, Jiming Jiang

Journal of Modern Applied Statistical Methods

A time-modulated frailty model is proposed for analyzing multivariate failure data. The effect of frailties, which may not be constant over time, is discussed. We assume a parametric model for the baseline hazard, but avoid the parametric assumption for the frailty distribution. The well-known connection between survival times and Poisson regression model is used. The parameters of interest are estimated by generalized estimating equations (GEE) or by penalized GEE. Simulation studies show that the procedure is successful to detect the effect of time-modulated frailty. The method is also applied to a placebo controlled randomized clinical trial of gamma interferon, a …

Some Reflections On Significance Testing, Thomas R. Knapp

Journal of Modern Applied Statistical Methods

This essay presents a variation on a theme from my article “The use of tests of statistical significance”, which appeared in the Spring, 1999, issue of Mid-Western Educational Researcher.

Null Distribution Of The Likelihood Ratio Statistic For Feed-Forward Neural Networks, Douglas Landsittel, Harshinder Singh, Vincent C. Arena, Stewart J. Anderson

Journal of Modern Applied Statistical Methods

Despite recent publications exploring model complexity with modern regression methods, their dimensionality is rarely quantified in practice and the distributions of related test statistics are not well characterized. Through a simulation study, we describe the null distribution of the likelihood ratio statistic for several different feed-forward neural network models.

Combining Quantum Mechanical Calculations And A Χ^2 Fit In A Potential Energy Function For The Co_2 + O^+ Reaction, Ellen F. Sawilowsky

Journal of Modern Applied Statistical Methods

In order to compute a highly accurate statistical rate constant for the CO2 + O⁺ reaction, it is necessary to first calculate the potential energy of the system at many different geometric configurations. Quantum mechanical calculations are very time-consuming, making it difficult to obtain a sufficient number to allow for accurate interpolation. The number of quantum mechanical calculations required can be significantly reduced by using known relations in classical physics to calculate energy for configurations where the oxygen is relatively far from the CO2. A chi-squared fit to quantum mechanical points is obtained for these configurations, and the resulting …

Type I Error Rates For Rank-Based Tests Of Homogeneity Of Slopes, Alan J. Klockars, Tim P. Moses

Journal of Modern Applied Statistical Methods

The purpose of this study was to explicate two issues concerning the standard and rank based test of homogeneity of slopes. Two alternative ranking methods intended to address nonnormality and additive treatment effect patterns were developed and compared in terms of their ability to control Type I error. The results replicated previous findings of inflated Type I error rates with leptokurtic curves and with rank based tests with some patterns of additive treatment effects. The new nonparametric procedures generally control Type I error although they were slightly inflated with skewed distributions.

Exploration Of Distributions Of Ratio Of Partial Sum Of Sample Eigenvalues When All Population Eigenvalues Are The Same, Moonseong Heo

Journal of Modern Applied Statistical Methods

This paper explores empirically the first two moments of ratio of the partial sum of the first two sample eigenvalues to the sum of all eigenvalues when the population eigenvalues of a covariance matrix are all the same. Estimation of the first two moments can be practically crucial in assessing non-randomness of observed patterns on planar graphical displays based on lower rank approximations of data matrices. For derivation of the moments, exact and large sample asymptotic distributions of the sample ratios are reviewed but neither can be applicable to derivation of the moments. Therefore, I rely on simulations, where data …

Chronic Disease Data And Analysis: Current State Of The Field, Ralph D'Agostino Sr., Lisa M. Sullivan

Journal of Modern Applied Statistical Methods

Chronic disease usually spans years of a person’s lifetime and includes a disease free period, a preclinical, or latent period, where there are few overt signs of disease, a clinical period where the disease manifests and is eventually diagnosed, and a follow-up period where the disease might progress steadily or remain stable. It is often of interest to investigate the relationship between risk factors measured at a point in time (usually during the disease free or preclinical period), and the development of disease at some future point (e.g., 10 years later). We outline some popular designs for the identification of …

Twenty Nonparametric Statistics And Their Large Sample Approximations, Gail F. Fahoome

Journal of Modern Applied Statistical Methods

Nonparametric procedures are often more powerful than classical tests for real world data which are rarely normally distributed. However, there are difficulties in using these tests. Computational formulas are scattered throughout the literature, and there is a lack of availability of tables and critical values. The computational formulas for twenty commonly employed nonparametric tests that have large-sample approximations for the critical value are brought together. Because there is no generally agreed upon lower limit for the sample size, Monte Carlo methods were used to determine the smallest sample size that can be used with the respective large-sample approximation. The statistics …

Trimming, Transforming Statistics, And Bootstrapping: Circumventing The Biasing Effects Of Heterescedasticity And Nonnormality, H. J. Keselman, Rand R. Wilcox, Abdul R. Othman, Katherine Fradette

Journal of Modern Applied Statistical Methods

Researchers can adopt different measures of central tendency and test statistics to examine the effect of a treatment variable across groups (e.g., means, trimmed means, M-estimators, & medians. Recently developed statistics are compared with respect to their ability to control Type I errors when data were nonnormal, heterogeneous, and the design was unbalanced: (1) a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically, (2) two different transformations to eliminate skewness, (3) the accuracy of assessing statistical significance with a bootstrap methodology was examined, and (4) statistics that use a robust measure of the typical …

A Simulation Study Of The Impact Of Forecast Recovery For Control Charts Applied To Arma Processes, John N. Dyer, B. Michael Adams, Michael D. Conerly

Journal of Modern Applied Statistical Methods

Forecast-based schemes are often used to monitor autocorrelated processes, but the resulting forecast recovery has a significant effect on the performance of control charts. This article describes forecast recovery for autocorrelated processes, and the resulting simulation study is used to explain the performance of control charts applied to forecast errors.

Determining Predictor Importance In Multiple Regression Under Varied Correlational And Distributional Conditions, Tiffany A. Whittaker, Rachel T. Fouladi, Natasha J. Williams

Journal of Modern Applied Statistical Methods

This study examines the performance of eight methods of predictor importance under varied correlational and distributional conditions. The proportion of times a method correctly identified the dominant predictor was recorded. Results indicated that the new methods of importance proposed by Budescu (1993) and Johnson (2000) outperformed commonly used importance methods.

A Program For Generating All Permutations Of {1, 2, ..., N}, Robert Disario

Journal of Modern Applied Statistical Methods

A Visual Basic program that generates all permutations of {1, 2, ..., n} is presented. The procedure for running the program as an Excel macro is described. An application is presented which involves selecting permutations which meet a specific constraint.

A Comparison Of The D’Agostino S_U Test To The Triples Test For Testing Of Symmetry Versus Asymmetry As A Preliminary Test To Testing The Equality Of Means, Kimberly T. Perry, Michael R. Stoline

Journal of Modern Applied Statistical Methods

This paper evaluates the D’Agostino S_U test and the Triples test for testing symmetry versus asymmetry. These procedures are evaluated as preliminary tests in the selection of the most appropriate procedure for testing the equality of means with two independent samples under a variety of symmetric and asymmetric sampling situations. Key words: symmetry; asymmetry; preliminary testing.