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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Comparing Means Under Heteroscedasticity And Nonnormality: Further Exploring Robust Means Modeling, Alyssa Counsell, Robert Philip Chalmers, Robert A. Cribbie
Comparing Means Under Heteroscedasticity And Nonnormality: Further Exploring Robust Means Modeling, Alyssa Counsell, Robert Philip Chalmers, Robert A. Cribbie
Journal of Modern Applied Statistical Methods
Comparing the means of independent groups is a concern when the assumptions of normality and variance homogeneity are violated. Robust means modeling (RMM) was proposed as an alternative to ANOVA-type procedures when the assumptions of normality and variance homogeneity are violated. The purpose of this study is to compare the Type I error and power rates of RMM to the trimmed Welch procedure. A Monte Carlo study was used to investigate RMM and the trimmed Welch procedure under several conditions of nonnormality and variance heterogeneity. The results suggest that the trimmed Welch provides a better balance of Type I error …
The Influence Of Data Generation On Simulation Study Results: Tests Of Mean Differences, Tim Moses, Alan Klockars
The Influence Of Data Generation On Simulation Study Results: Tests Of Mean Differences, Tim Moses, Alan Klockars
Journal of Modern Applied Statistical Methods
Type I error and power of the standard independent samples t-test were compared with the trimmed and Winsorized t-test with respect to continuous distributions and various discrete distributions known to occur in applied data. The continuous and discrete distributions were generated with similar levels of skew and kurtosis but the discrete distributions had a variety of structural features not reflected in the continuous distributions. The results showed that the Type I error rates of the t-tests were not seriously affected, but the power rate of the trimmed and Winsorized t-test varied greatly across the considered distributions.
An Evaluation Of Standard, Alternative, And Robust Slope Test Strategies, Tim Moses, Alan Klockars
An Evaluation Of Standard, Alternative, And Robust Slope Test Strategies, Tim Moses, Alan Klockars
Journal of Modern Applied Statistical Methods
The robustness and power of nine strategies for testing the differences between two groups’ regression slopes under nonnormality and residual variance heterogeneity are compared. The results showed that three most robust slope test strategies were the combination of the trimmed and Winsorized slopes with the James second order test, the combination of Theil-Sen with James, and Theil-Sen with percentile bootstrapping. The slope tests based on Theil-Sen slopes were more powerful than those based on trimmed and Winsorized slopes.
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.
Multiple Comparison Procedures, Trimmed Means And Transformed Statistics, Rhonda K. Kowalchuk, H. J. Keselman, Rand R. Wilcox, James Algina, James Algina, James Algina
Multiple Comparison Procedures, Trimmed Means And Transformed Statistics, Rhonda K. Kowalchuk, H. J. Keselman, Rand R. Wilcox, James Algina, James Algina, James Algina
Journal of Modern Applied Statistical Methods
A modification to testing pairwise comparisons that may provide better control of Type I errors in the presence of non-normality is to use a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically. Several pairwise MCPs were investigated, employing a test of symmetry with a number of heteroscedastic test statistics that used trimmed means and Winsorized variances. Results showed improved Type I error control than competing robust statistics.
Jmasm24: Numerical Computing For Third-Order Power Method Polynomials (Excel), Todd C. Headrick
Jmasm24: Numerical Computing For Third-Order Power Method Polynomials (Excel), Todd C. Headrick
Journal of Modern Applied Statistical Methods
The power method polynomial transformation is a popular procedure used for simulating univariate and multivariate non-normal distributions. It requires software that solves simultaneous nonlinear equations. Potential users of the power method may not have access to commercial software packages (e.g., Mathematica, Fortran). Therefore, algorithms are presented in the more commonly available Excel 2003 spreadsheets. The algorithms solve for (1) coefficients for polynomials of order three, (2) intermediate correlations and Cholesky factorizations for multivariate data generation, and (3) the values of skew and kurtosis for determining if a transformation will produce a valid power method probability density function (pdf). The Excel …
Robust Confidence Intervals For Effect Size In The Two-Group Case, H. J. Keselman, James Algina, Katherine Fradette
Robust Confidence Intervals For Effect Size In The Two-Group Case, H. J. Keselman, James Algina, Katherine Fradette
Journal of Modern Applied Statistical Methods
The probability coverage of intervals involving robust estimates of effect size based on seven procedures was compared for asymmetrically trimming data in an independent two-groups design, and a method that symmetrically trims the data. Four conditions were varied: (a) percentage of trimming, (b) type of nonnormal population distribution, (c) population effect size, and (d) sample size. Results indicated that coverage probabilities were generally well controlled under the conditions of nonnormality. The symmetric trimming method provided excellent probability coverage. Recommendations are provided.
Testing For Aptitude-Treatment Interactions In Analysis Of Covariance And Randomized Block Designs Under Assumption Violations, Tim Moses, Alan Klockars
Testing For Aptitude-Treatment Interactions In Analysis Of Covariance And Randomized Block Designs Under Assumption Violations, Tim Moses, Alan Klockars
Journal of Modern Applied Statistical Methods
This study compared the robustness of two analysis strategies designed to detect Aptitude-Treatment Interactions to two of their similarly-held assumptions, normality and residual variance homogeneity. The analysis strategies were the test of slope differences in analysis of covariance and the test of the Block-by- Treatment interaction in randomized block analysis of variance. With equal sample sizes in the treatment groups the results showed that residual variance heterogeneity has little effect on either strategy but nonnormality makes the test of slope differences liberal and the test of the Block-by-Treatment interaction conservative. With unequal sample sizes in the treatment groups the often-reported …
A Power Comparison Of Robust Test Statistics Based On Adaptive Estimators, H. J. Keselman, Rand R. Wilcox, James Algina, Abdul R. Othman
A Power Comparison Of Robust Test Statistics Based On Adaptive Estimators, H. J. Keselman, Rand R. Wilcox, James Algina, Abdul R. Othman
Journal of Modern Applied Statistical Methods
Seven test statistics known to be robust to the combined effects of nonnormality and variance heterogeneity were compared for their sensitivity to detect treatment effects in a one-way completely randomized design containing four groups. The six Welch-James-type heteroscedastic tests adopted either symmetric or asymmetric trimmed means, were transformed for skewness, and used a bootstrap method to assess statistical significance. The remaining test, due to Wilcox and Keselman (2003), used a modification of the well-known one-step M-estimator of central tendency rather than trimmed means. The Welch-James-type test is recommended because for nonnormal data likely to be encountered in applied research settings …
On Polynomial Transformations For Simulating Multivariate Non-Normal Distributions, Todd C. Headrick
On Polynomial Transformations For Simulating Multivariate Non-Normal Distributions, Todd C. Headrick
Journal of Modern Applied Statistical Methods
Procedures are introduced and discussed for increasing the computational and statistical efficiency of polynomial transformations used in Monte Carlo or simulation studies. Comparisons are also made between polynomials of order three and five in terms of (a) computational and statistical efficiency, (b) the skew and kurtosis boundary, and (c) boundaries for Pearson correlations. It is also shown how ranked data can be simulated for specified Spearman correlations and sample sizes. Potential consequences of nonmonotonic transformations on rank correlations are also discussed.
A Longitudinal Follow-Up Of Discrete Mass At Zero With Gap, Joseph L. Musial, Patrick D. Bridge, Nicol R. Shamey
A Longitudinal Follow-Up Of Discrete Mass At Zero With Gap, Joseph L. Musial, Patrick D. Bridge, Nicol R. Shamey
Journal of Modern Applied Statistical Methods
The first part of this paper discusses a five-year systematic review of the Journal of Consulting and Clinical Psychology following the landmark power study conducted by Sawilowsky and Hillman (1992). The second part discusses a five-year longitudinal follow-up of a radically nonnormal population distribution: discrete mass at zero with gap. This distribution was based upon a real dataset.