Statistics and Probability Commons^™

Effects Of Population Distribution, Sample Size And Correlation Structure On Huberty’S Effect Size R, James B. Hittner

Journal of Modern Applied Statistical Methods

Huberty’s (1994) R² is derived by subtracting the expected value of R² from an adjusted R², and the square root of Huberty’s R² is Huberty’s effect size R. The present study examined the effects of population distribution, sample size and population correlation structure on the statistical power of Huberty’s R.

Estimating Task Duration In Pert Using The Weibull Probability Distribution, Edward L. Mccombs, Matthew E. Elam, David B. Pratt

Journal of Modern Applied Statistical Methods

The Weibull probability distribution can be used as an alternative model for task time estimates in the PERT estimating methodology. It has the same advantages as the traditional beta distribution for this application. It has additional benefits, however, that make it a preferred option.

Beyond Kappa: Estimating Inter-Rater Agreement With Nominal Classifications, Nol Bendermacher, Pierre Souren

Journal of Modern Applied Statistical Methods

Cohen’s Kappa and a number of related measures can all be criticized for their definition of correction for chance agreement. A measure is introduced that derives the corrected proportion of agreement directly from the data, thereby overcoming objections to Kappa and its related measures.

Some Estimators For The Population Mean Using Auxiliary Information Under Ranked Set Sampling, Walid A. Abu-Dayyeh, M. S. Ahmed, R. A. Ahmed, Hassen A. Muttlak

Journal of Modern Applied Statistical Methods

Auxiliary information is used along with ranking information to derive several classes of estimators to estimate the population mean of a variable of interest based on RSS (ranked set sample). The properties of these newly suggested estimators were examined. Comparisons between special cases of these estimators and other known estimators are made using a real data set. Some of the new estimators are superior to the old ones in terms of bias and mean square error.

A Heteroscedastic, Rank-Based Approach For Analyzing 2 X 2 Independent Groups Designs, Laura Mills, Robert A. Cribbie, Wei-Ming Luh

Journal of Modern Applied Statistical Methods

The ANOVA F is a widely used statistic in psychological research despite its shortcomings when the assumptions of normality and variance heterogeneity are violated. A Monte Carlo investigation compared Type I error and power rates of the ANOVA F, Alexander-Govern with trimmed means and Johnson transformation, Welch-James with trimmed means and Johnson Transformation, Welch with trimmed means, and Welch on ranked data using Johansen’s interaction procedure. Results suggest that the ANOVA F is not appropriate when assumptions of normality and variance homogeneity are violated, and that the Welch/Johansen on ranks offers the best balance of empirical Type I error …

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.

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.

Barriers Encountered During Enrollment In An Internet-Mediated Randomized Controlled Trial, Lorraine R. Buis, Adrienne W. Janney, Michael L. Hess, Silas A. Culver, Caroline R. Richardson

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Online technology is a promising resource for conducting clinical research. While the internet may improve a study's reach, as well as the efficiency of data collection, it may also introduce a number of challenges for participants and investigators. The objective of this research was to determine the challenges that potential participants faced during the enrollment phase of a randomized controlled intervention trial of Stepping Up to Health, an internet-mediated walking program that utilized a multi-step online enrollment process.

Methods

We conducted a quantitative content analysis of 623 help tickets logged in a participant management database during the enrollment …

Multi-Group Confirmatory Factor Analysis For Testing Measurement Invariance In Mixed Item Format Data, Kim H. Koh, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

This simulation study investigated the empirical Type I error rates of using the maximum likelihood estimation method and Pearson covariance matrix for multi-group confirmatory factor analysis (MGCFA) of full and strong measurement invariance hypotheses with mixed item format data that are ordinal in nature. The results indicate that mixed item formats and sample size combinations do not result in inflated empirical Type I error rates for rejecting the true measurement invariance hypotheses. Therefore, although the common methods are in a sense sub-optimal, they don’t lead to researchers claiming that measures are functioning differently across groups – i.e., a lack of …

Estimating Explanatory Power In A Simple Regression Model Via Smoothers, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

Consider the regression model Y = γ(X) + ε , where γ(X) is some conditional measure of location associated with Y , given X. Let Υ̂ be some estimate of Y, given X, and let τ² (Y) be some measure of variation. Explanatory power is η² = τ² (Υ̂) /τ²(Y) . When γ(X) = β₀ + β₁X and τ²(Y) is the variance of Y , η² = ρ² , …

Data Mining Ceo Compensation, Susan M. Adams, Atul Gupta, Dominique M. Haughton, John D. Leeth

Journal of Modern Applied Statistical Methods

The need to pre-specify expected interactions between variables is an issue in multiple regression. Theoretical and practical considerations make it impossible to pre-specify all possible interactions. The functional form of the dependent variable on the predictors is unknown in many cases. Two ways are described in which the data mining technique Multivariate Adaptive Regression Splines (MARS) can be utilized: first, to obtain possible improvements in model specification, and second, to test for the robustness of findings from a regression analysis. An empirical illustration is provided to show how MARS can be used for both purposes.

Least Squares Percentage Regression, Chris Tofallis

Journal of Modern Applied Statistical Methods

In prediction, the percentage error is often felt to be more meaningful than the absolute error. We therefore extend the method of least squares to deal with percentage errors, for both simple and multiple regression. Exact expressions are derived for the coefficients, and we show how such models can be estimated using standard software. When the relative error is normally distributed, least squares percentage regression is shown to provide maximum likelihood estimates. The multiplicative error model is linked to least squares percentage regression in the same way that the standard additive error model is linked to ordinary least squares regression.