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- Monte Carlo simulation (3)
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Articles 31 - 60 of 64
Full-Text Articles in Social and Behavioral Sciences
A Note On Probability Trees, W. J. Hurley
A Note On Probability Trees, W. J. Hurley
Journal of Modern Applied Statistical Methods
Not many introductory probability and statistics textbooks emphasize the use of probability trees to make complex probability calculations. This is puzzling in view of the power that trees bring to organizing such calculations for students. An effective classroom technique is discussed is this note.
Effects Of Physical Activity On Psychological Change In Advanced Age: A Multivariate Meta-Analysis, Meng-Jia Wu, Betsy Jane Becker, Yael Netz
Effects Of Physical Activity On Psychological Change In Advanced Age: A Multivariate Meta-Analysis, Meng-Jia Wu, Betsy Jane Becker, Yael Netz
Journal of Modern Applied Statistical Methods
An example of multivariate meta-analysis is demonstrated by synthesizing the treatment effects of exercise of 15 groups on six mood state changes in elders measured by the Profile of Mood States (POMS) scale. Two different methods were used to analyze this multivariate dataset. The SAS codes for two set of the analyses were provided. Results showed that exercise has a modest and positive impact on elders mood change.
Analyses Of Unbalanced Groups-Versus-Individual Research Designs Using Three Alternative Approximate Degrees Of Freedom Tests: Test Development And Type I Error Rates, Stephanie Wehry, James Algina
Analyses Of Unbalanced Groups-Versus-Individual Research Designs Using Three Alternative Approximate Degrees Of Freedom Tests: Test Development And Type I Error Rates, Stephanie Wehry, James Algina
Journal of Modern Applied Statistical Methods
Three approximate degrees of freedom quasi-F tests of treatment effectiveness were developed for use in research designs when one treatment is individually delivered and the other is delivered to individuals nested in groups of unequal size. Imbalance in the data was studied from the prospective of subject attrition. The results indicated the test that best controls the Type I error rate depends on the number of groups in the group-administered treatment but does not depend on the subject attrition rates included in the study.
Type I Error Rates Of The Kenward-Roger Adjusted Degree Of Freedom F-Test For A Split-Plot Design With Missing Values, Miguel A. Padilla, James Algina
Type I Error Rates Of The Kenward-Roger Adjusted Degree Of Freedom F-Test For A Split-Plot Design With Missing Values, Miguel A. Padilla, James Algina
Journal of Modern Applied Statistical Methods
The Type I error rate of the Kenward-Roger (KR) test, implemented by PROC MIXED in SAS, was assessed through a simulation study for a one between- and one within-subjects factor split-plot design with ignorable missing values and covariance heterogeneity. The KR test controlled the Type I error well under all of the simulation factors, with all estimated Type I error rates between .040 and .075. The best control was for testing the between-subjects main effect (error rates between .041 and .057) and the worst control was for the between-by-within interaction (.040 to .075). The simulated factors had very small effects …
Application Of A New Procedure For Power Analysis And Comparison Of The Adjusted Univariate And Multivariate Tests In Repeated Measures Designs, Sean W. Mulvenon, M. Austin Betz, Kening Wang, Bruno D. Zumbo
Application Of A New Procedure For Power Analysis And Comparison Of The Adjusted Univariate And Multivariate Tests In Repeated Measures Designs, Sean W. Mulvenon, M. Austin Betz, Kening Wang, Bruno D. Zumbo
Journal of Modern Applied Statistical Methods
A relationship between the multivariate and univariate noncentrality parameters in repeated measures designs was developed for the purpose of assessing the relative power of the univariate and multivariate approaches. An application is provided examining the use of repeated measures designs to evaluate student achievement in a K-12 school system
Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning
Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning
Journal of Modern Applied Statistical Methods
The one sample t-test is compared with the Wilcoxon Signed-Rank test for identical data sets representing various Likert scales. An empirical approach is used with simulated data. Comparisons are based on observed error rates for 27,850 data sets. Recommendations are provided.
Another Look At The Confidence Intervals For The Noncentral T Distribution, Bruno Lecoutre
Another Look At The Confidence Intervals For The Noncentral T Distribution, Bruno Lecoutre
Journal of Modern Applied Statistical Methods
An alternative approach to the computation of confidence intervals for the noncentrality parameter of the Noncentral t distribution is proposed. It involves the percent points of a statistical distribution. This conceptual improvement renders the technical process for deriving the limits more comprehensible. Accurate approximations can be derived and easily used.
The Effects Of Heteroscedasticity On Tests Of Equivalence, Jamie A. Gruman, Robert A. Cribbie, Chantal A. Arpin-Cribbie
The Effects Of Heteroscedasticity On Tests Of Equivalence, Jamie A. Gruman, Robert A. Cribbie, Chantal A. Arpin-Cribbie
Journal of Modern Applied Statistical Methods
Tests of equivalence, which are designed to assess the similarity of group means, are becoming more popular, yet very little is known about the statistical properties of these tests. Monte Carlo methods are used to compare the test of equivalence proposed by Schuirmann with modified tests of equivalence that incorporate a heteroscedastic error term. It was found that the latter were more accurate than the Schuirmann test in detecting equivalence when sample sizes and variances were unequal.
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.
A Comparison Of Eight Shrinkage Formulas Under Extreme Conditions, David A. Walker
A Comparison Of Eight Shrinkage Formulas Under Extreme Conditions, David A. Walker
Journal of Modern Applied Statistical Methods
The performance of various shrinkage formulas for estimating the population squared multiple correlation coefficient (ρ2) were compared under extreme conditions often found in educational research with small sample sizes of 10, 15, 20, 25, 30 and regressor variates ranging from 2 to 4. A new formula for estimating ρ2, Adj R2 DW, was examined in terms of its performance under various conditions of N, p, ρ2, along with its bias properties and standard error estimates. The two shrinkage formulas that performed most consistently were the Claudy (Adj R2 C) and Walker (Adj R2 DW)
Better Binomial Confidence Intervals, James F. Reed Iii
Better Binomial Confidence Intervals, James F. Reed Iii
Journal of Modern Applied Statistical Methods
The construction of a confidence interval for a binomial parameter is a basic analysis in statistical inference. Most introductory statistics textbook authors present the binomial confidence interval based on the asymptotic normality of the sample proportion and estimating the standard error - the Wald method. For the one sample binomial confidence interval the Clopper-Pearson exact method has been regarded as definitive as it eliminates both overshoot and zero width intervals. The Clopper-Pearson exact method is the most conservative and is unquestionably a better alternative to the Wald method. Other viable alternatives include Wilson's Score, the Agresti-Coull method, and the Borkowf …
Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade
Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade
Journal of Modern Applied Statistical Methods
Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-and-neck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution.
On The Product Of Maxwell And Rice Random Variables, M. Shakil, B. M. Golam Kibria
On The Product Of Maxwell And Rice Random Variables, M. Shakil, B. M. Golam Kibria
Journal of Modern Applied Statistical Methods
The distributions of the product of independent random variables arise in many applied problems. These have been extensively studied by many researchers. In this paper, the exact distributions of the product |XY| have been derived when X and Y are Maxwell and Rice random variables respectively, and are distributed independently of each other. The associated cdfs, pdfs, and kth moments have been given.
Optimal Lp-Metric For Minimizing Powered Deviations In Regression, Stan Lipovetsky
Optimal Lp-Metric For Minimizing Powered Deviations In Regression, Stan Lipovetsky
Journal of Modern Applied Statistical Methods
Minimizations by least squares or by least absolute deviations are well known criteria in regression modeling. In this work the criterion of generalized mean by powered deviations is suggested. If the parameter of the generalized mean equals one or two, the fitting corresponds to the least absolute or the least squared deviations, respectively. Varying the power parameter yields an optimum value for the objective with a minimum possible residual error. Estimation of a most favorable value of the generalized mean parameter shows that it almost does not depend on data. The optimal power always occurs to be close to 1.7, …
A Spline-Based Lack-Of-Fit Test For Independent Variable Effect, Chin-Shang Li, Wanzhu Tu
A Spline-Based Lack-Of-Fit Test For Independent Variable Effect, Chin-Shang Li, Wanzhu Tu
Journal of Modern Applied Statistical Methods
In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the …
Practical Unit-Root Analysis Using Information Criteria: Simulation Evidence, Kosei Fukuda
Practical Unit-Root Analysis Using Information Criteria: Simulation Evidence, Kosei Fukuda
Journal of Modern Applied Statistical Methods
The information-criterion-based model selection method for detecting a unit root is proposed. The simulation results suggest that the performances of the proposed method are usually comparable to and sometimes better than those of the conventional unit-root tests. The advantages of the proposed method in practical applications are also discussed.
A Comparison Of One-High-Threshold And Two-High-Threshold Multinomial Models Of Source Monitoring, Mahesh Menon, Todd S. Woodward
A Comparison Of One-High-Threshold And Two-High-Threshold Multinomial Models Of Source Monitoring, Mahesh Menon, Todd S. Woodward
Journal of Modern Applied Statistical Methods
A data simulation study comparing the one-high-threshold (1HT) and two-high-threshold (2HT) multinomial models suggested that 2HT models are more likely to misestimate the underlying parameter values, due to inflation of some parameters (b and d), and deflation of others (D).
Examining Cronbach Alpha, Theta, Omega Reliability Coefficients According To Sample Size, Ilker Ercan, Berna Yazici, Deniz Sigirli, Bulent Ediz, Ismet Kan
Examining Cronbach Alpha, Theta, Omega Reliability Coefficients According To Sample Size, Ilker Ercan, Berna Yazici, Deniz Sigirli, Bulent Ediz, Ismet Kan
Journal of Modern Applied Statistical Methods
Differentiations according to the sample size of different reliability coefficients are examined. It is concluded that the estimates obtained by Cronbach alpha and teta coefficients are not related with the sample size, even the estimates obtained from the small samples can represent the population parameter. However, the Omega coefficient requires large sample sizes.
Estimation Of Risk For Developing Cardiac Problem In Patients Of Type 2 Diabetes As Obtained By The Technique Of Density Estimation, Ajit Mukherjee, Ajit Mathur, Rakesh Mittal
Estimation Of Risk For Developing Cardiac Problem In Patients Of Type 2 Diabetes As Obtained By The Technique Of Density Estimation, Ajit Mukherjee, Ajit Mathur, Rakesh Mittal
Journal of Modern Applied Statistical Methods
High levels of cholesterol and triglyceride are known to be strongly associated with development of cardiac problem in patients of type 2 diabetes. In a hospital-based study, patients showing ECG positive were compared with those who were not. The observations on cholesterol and triglyceride were considered for estimation of risk for developing the cardiac problem. The technique of density estimation employing Epanechnikov kernel was used for estimating bivariate probability density functions with respect to observations on cholesterol and triglyceride of the two groups. Using the odds form of Bayes’ rule, the estimates of posterior odds were computed.
Multinomial Logistic Regression Model For The Inferential Risk Age Groups For Infection Caused By Vibrio Cholerae In Kolkata, India, Krishnan Rajendran, Thandavarayan Ramamurthy, Dipika Sur
Multinomial Logistic Regression Model For The Inferential Risk Age Groups For Infection Caused By Vibrio Cholerae In Kolkata, India, Krishnan Rajendran, Thandavarayan Ramamurthy, Dipika Sur
Journal of Modern Applied Statistical Methods
Multinomial Logistic Regression (MLR) modeling is an effective approach for categorical outcomes, as compared with discriminant function analysis and log-linear models for profiling individual category of dependent variable. To explore the yearly change of inferential age groups of acute diarrhoeal patients infected with Vibrio cholerae during 1996-2000 by MLR, systematic sampling data were generated from an active surveillance study. Among 1330 V.cholerae infected cases, the predominant age category was up to 5 years accounting for 478 (30.5%) cases. The independent variables V.cholerae O1 (p<0.001) and non-O1 and non-O139 (p < 0.001) were significantly associated with children under 5 years age group. V.cholerae O139 inferential age group was > 40 years. The infection mediated by V.cholerae O1 had significantly decreasing trend Exp(B) year wise from …
Jmasm27: An Algorithm For Implementing Gibbs Sampling For 2pno Irt Models (Fortran), Yanyan Sheng, Todd C. Headrick
Jmasm27: An Algorithm For Implementing Gibbs Sampling For 2pno Irt Models (Fortran), Yanyan Sheng, Todd C. Headrick
Journal of Modern Applied Statistical Methods
A Fortran 77 subroutine is provided for implementing the Gibbs sampling procedure to a normal ogive IRT model for binary item response data with the choice of uniform and normal prior distributions for item parameters. The subroutine requires the user to have access to the IMSL library. The source code is available at http://www.siu.edu/~epse1/sheng/Fortran/, along with a stand alone executable file.
Mathmatics In Volume I Of Scripta Universitatis, Shlomo S. Sawilowsky
Mathmatics In Volume I Of Scripta Universitatis, Shlomo S. Sawilowsky
Journal of Modern Applied Statistical Methods
Immanuel Velikovsky’s journal, Scripta Universitatis, edited by Albert Einstein and first published in 1923, played a significant role in the establishment of the library, and hence, Hebrew University in Jerusalem. The inaugural issue contained an article by the French mathematician Jacques Hadamard. Excerpts from Velikovsky’s diary pertaining to the rationale for the creation of the journal, and the interest in Jewish scholars such as Hadamard, are translated here.
Bimodality Revisited, Thomas R. Knapp
Bimodality Revisited, Thomas R. Knapp
Journal of Modern Applied Statistical Methods
Degree of bimodality is an important feature of a frequency distribution, because it could suggest heterogeneity, such as polarization or two underlying distributions combined into one. The literature contains several measures of bimodality. This article attempts to summarize most of those measures, with their attendant advantages and disadvantages.
Ordinal Versions Of Coefficients Alpha And Theta For Likert Rating Scales, Bruno D. Zumbo, Anne M. Gadermann, Cornelia Zeisser
Ordinal Versions Of Coefficients Alpha And Theta For Likert Rating Scales, Bruno D. Zumbo, Anne M. Gadermann, Cornelia Zeisser
Journal of Modern Applied Statistical Methods
Two new reliability indices, ordinal coefficient alpha and ordinal coefficient theta, are introduced. A simulation study was conducted in order to compare the new ordinal reliability estimates to each other and to coefficient alpha with Likert data. Results indicate that ordinal coefficients alpha and theta are consistently suitable estimates of the theoretical reliability, regardless of the magnitude of the theoretical reliability, the number of scale points, and the skewness of the scale point distributions. In contrast, coefficient alpha is in general a negatively biased estimate of reliability. The use of ordinal coefficients alpha and theta as alternatives to coefficient alpha …
Tests For Treatment Group Equality When Data Are Nonnormal And Heteroscedastic, Robert A. Cribbie, Rand R. Wilcox, Carmen Bewell, H. J. Keselman
Tests For Treatment Group Equality When Data Are Nonnormal And Heteroscedastic, Robert A. Cribbie, Rand R. Wilcox, Carmen Bewell, H. J. Keselman
Journal of Modern Applied Statistical Methods
Several tests for group mean equality have been suggested for analyzing nonnormal and heteroscedastic data. A Monte Carlo study compared the Welch tests on ranked data and heterogeneous, nonparametric statistics with previously recommended procedures. Type I error rates for the Welch tests on ranks and the heterogeneous, nonparametric statistics were well controlled with a slight power advantage for the Welch tests on ranks.
On The Properties Of Beta-Gamma Distribution, Lingji Kong, Carl Lee, J.H. Sepanski
On The Properties Of Beta-Gamma Distribution, Lingji Kong, Carl Lee, J.H. Sepanski
Journal of Modern Applied Statistical Methods
A class of generalized gamma distribution called the beta-gamma distribution is proposed. Some of its properties are examined. Its shape can be reversed J-shaped, unimodal, or bimodal. Reliability and hazard functions are also derived, and applications are discussed.
Lq-Moments For Statistical Analysis Of Extreme Events, Ani Shabri, Abdul Aziz Jemain
Lq-Moments For Statistical Analysis Of Extreme Events, Ani Shabri, Abdul Aziz Jemain
Journal of Modern Applied Statistical Methods
Statistical analysis of extremes is conducted for predicting large return periods events. LQ-moments that are based on linear combinations are reviewed for characterizing the upper quantiles of distributions and larger events in data. The LQ-moments method is presented based on a new quick estimator using five points quantiles and the weighted kernel estimator to estimate the parameters of the generalized extreme value (GEV) distribution. Monte Carlo methods illustrate the performance of LQ-moments in fitting the GEV distribution to both GEV and non-GEV samples. The proposed estimators of the GEV distribution were compared with conventional L-moments and LQ-moments based on linear …
Modeling Longitudinal Ordinal Response Variables For Educational Data, Ann A. O'Connell, Heather Levitt Doucette
Modeling Longitudinal Ordinal Response Variables For Educational Data, Ann A. O'Connell, Heather Levitt Doucette
Journal of Modern Applied Statistical Methods
This article presents applications for the analysis of multilevel ordinal response data through the proportional odds model. Data are drawn from the public-use Early Childhood Longitudinal Study. Results showed that gender, number of family risk characteristics, and age at kindergarten entry were associated with initial reading proficiency (0 to 5 scale). The number of family risks and age were associated with time-slopes. Three issues are highlighted: building multilevel ordinal models, interpretation of multilevel effects; and determination of predicted probabilities based on results of the multilevel proportional odds models.
Jmasm 26: Hettmansperger And Mckean Linear Model Aligned Rank Test For The Single Covariate And One-Way Ancova Case (Sas), Paul A. Nakonezny, Robert D. Shull
Jmasm 26: Hettmansperger And Mckean Linear Model Aligned Rank Test For The Single Covariate And One-Way Ancova Case (Sas), Paul A. Nakonezny, Robert D. Shull
Journal of Modern Applied Statistical Methods
A SAS program (SAS 9.1.3 release, SAS Institute, Cary, N.C.) is presented to implement the Hettmansperger and McKean (1983) linear model aligned rank test (nonparametric ANCOVA) for the single covariate and one-way ANCOVA case. As part of this program, SAS code is also provided to derive the residuals from the regression of Y on X (which is step 1 in the Hettmansperger and McKean procedure) using either ordinary least squares regression (proc reg in SAS) or robust regression with MM estimation (proc robustreg in SAS).
On Flexible Tests Of Independence And Homoscedasticity, Rand R. Wilcox
On Flexible Tests Of Independence And Homoscedasticity, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Consider the nonparametric regression model Y = m(X) + τ(X)ε , where X and ε are independent random variables, ε has a mean of zero and variance σ2, τ is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated with Y, given X. Detecting dependence, by testing the hypothesis that m(X) does not vary with X, has the potential of being more sensitive to a wider range of associations compared to using Pearson's correlation. This note has two goals. The first is to point …