Physical Sciences and Mathematics Commons^™

Jmasm 53: Miccerird, Michael Lance

Journal of Modern Applied Statistical Methods

Fortran 77 and 90 modules (REALPOPS.lib) exist for invoking the 8 distributions estimated by Micceri (1989). These respective modules were created by Sawilowsky et al. (1990) and Sawilowsky and Fahoome (2003). The MicceriRD (Micceri’s Real Distributions) Python package was created because Python is increasingly used for data analysis and, in some cases, Monte Carlo simulations.

An Empirical Demonstration Of The Need For Exact Tests, Vance W. Berger

Journal of Modern Applied Statistical Methods

The robustness of parametric analyses is rarely questioned or qualified. Robustness, generally understood, means the exact and approximate p-values will lie on the same side of alpha for any reasonable data set; and 1) any data set would qualify as reasonable and 2) robustness holds universally, for all alpha levels and approximations. For this to be true, the approximation would need to be perfect all of the time. Any discrepancy between the approximation and the exact p-value, for any combination of alpha level and data set, would constitute a violation. Clearly, this is not true, and when confronted with this …

Robustness And Power Of The Student T, Welch-Aspin, Yuen, Tukey Quick, And Haga Tests, Dong Li

Wayne State University Dissertations

Classical parametric statistic procedures are widely used in the research community. However, for classical tests to produce accurate results, the assumptions underlying them must be sufficiently satisfied. When the assumptions are not met, the results of the analysis may be due to the violation of the assumptions, instead of the true pattern of the data. The assumptions are rarely met when analyzing real data. The use of classic parametric methods with violated assumptions may lead to substantive errors in the interpretation of data. As an alternative to normal theory statistics, nonparametric statistical procedures do not make assumptions about the underlying …

A Monte Carlo Simulation Of The Robust Rank-Order Test Under Various Population Symmetry Conditions, William T. Mickelson

Journal of Modern Applied Statistical Methods

The Type I Error Rate of the Robust Rank Order test under various population symmetry conditions is explored through Monte Carlo simulation. Findings indicate the test has difficulty controlling Type I error under generalized Behrens-Fisher conditions for moderately sized samples.

Robustness Of Dewma Versus Ewma Control Charts To Non-Normal Processes, Saad Saeed Alkahtani

Journal of Modern Applied Statistical Methods

Exponentially weighted moving average (EWMA) and double EWMA (DEWMA) control charts were designed under the normality assumption. This study considers various skewed (Gamma) and symmetric non-normal (t) distributions to examine the effect of non-normality on the average run length (ARL) performance of EWMA and DEWMA. ARL performances were investigated and compared using Monte Carlo simulations. Results show that DEWMA charts can be designed to be robust to non-normality, that the ARL performances of EWMA and DEWMA charts were more robust to t distributions and DEWMA was more robust to non-normality for larger values of the smoothing parameter.

Approximate Vs. Monte Carlo Critical Values For The Winsorized T-Test, Michael Lance

Wayne State University Dissertations

Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.

Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per …

Type Ii Robustness Of The Null Hypothesis Rho = 0 For Non-Normal Distributions, Stephanie Wren

Wayne State University Dissertations

Is the t test statistic for the Pearson Product Moment Correlation Coefficient robust to errors of the second kind? This investigation indirectly measured the effects of power through a type 2 error rate robustness study. The results were revealing.

Robustness To Non-Independence And Power Of The I Test For Trend In Construct Validity, John Cuzzocrea, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

The Multitrait-Multimethod Matrix is used to evaluate construct validity; Sawilowsky (2002) created the I test to analyze the matrix. This article examined the robustness and power of the Sawilowsky I test. Ad hoc critical values were determined to improve the statistical power of the technique for analyzing the Multitrait-Multimethod Matrix.

Robustness To Non-Independence And Power Of The I Test For Trend In Construct Validity, John L. Cuzzocrea, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The Multitrait-Multimethod Matrix is used to evaluate construct validity; Sawilowsky (2002) created the I test to analyze the matrix. This article examined the robustness and power of the Sawilowsky I test. Ad hoc critical values were determined to improve the statistical power of the technique for analyzing the Multitrait-Multimethod Matrix.

Type I Error Rates Of The Kenward-Roger F-Test For A Split-Plot Design With Missing Values And Non-Normal Data, Miguel A. Padilla, Youngkyoung Min, Guili Zhang

Journal of Modern Applied Statistical Methods

The Type I error of the Kenward-Roger (KR) F-test was assessed through a simulation study for a between- by within-subjects split-plot design with non-normal ignorable missing data. The KR-test for the between- and within-subjects main effect was robust under all simulation variables investigated and when the data were missing completely at random (MCAR). This continued to hold for the between-subjects main effect when data were missing at random (MAR). For the interaction, the KR F-test performed fairly well at controlling Type I under MCAR and the simulation variables investigated. However, under MAR, the KR F-test for the …

Robust Predictive Inference For Multivariate Linear Models With Elliptically Contoured Distribution Using Bayesian, Classical And Structural Approaches, B. M. Golam Kibria

Journal of Modern Applied Statistical Methods

Predictive distributions of future response and future regression matrices under multivariate elliptically contoured distributions are discussed. Under the elliptically contoured response assumptions, these are identical to those obtained under matric normal or matric-t errors using structural, Bayesian with improper prior, or classical approaches. This gives inference robustness with respect to departure from the reference case of independent sampling from the matric normal or matric t to multivariate elliptically contoured distributions. The importance of the predictive distribution for skewed elliptical models is indicated; the elliptically contoured distribution, as well as matric t distribution, have significant applications in statistical practices.

Robustness Of Some Estimators Of Linear Model With Autocorrelated Error Terms When Stochastic Regressors Are Normally Distributed, Kayode Ayinde, J. O. Olaomi

Journal of Modern Applied Statistical Methods

Performances of estimators of the linear model under different level of autocorrelation (ρ) are known to be affected by different specifications of regressors. The robustness of some methods of parameter estimation of linear model to autocorrelation are examined when stochastic regressors are normally distributed. Monte Carlo experiments were conducted at both low and high replications. Comparison and preference of estimator(s) are based on their performances via bias, absolute bias, variance and more importantly the mean squared error of the estimated parameters of the model. Results show that the performances of the estimators improve with increased replication. In estimating …

A Comparison Of Procedures For The Analysis Of Multivariate Repeated Measurements, Lisa M. Lix, Anita M. Lloyd

Journal of Modern Applied Statistical Methods

Three procedures for analyzing within-subjects effects in multivariate repeated measures designs are compared when group covariances are heterogeneous: the multiple regression model (MRM) with a structured covariance, Johansen’s (1980) procedure, and the multivariate Brown and Forsythe (1974) procedure. A preliminary likelihood ratio test of a Kronecker product covariance structure is sensitive to sample size and derivational assumption violations. Error rates of the procedures are generally well-controlled except when the distribution is skewed. The MRM procedure displayed few power advantages over the other procedures.

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 …

Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test.

Simulation Of Non-Normal Autocorrelated Variables, H.E.T. Holgersson

Journal of Modern Applied Statistical Methods

All statistical methods rely on assumptions to some extent. Two assumptions frequently met in statistical analyses are those of normal distribution and independence. When examining robustness properties of such assumptions by Monte Carlo simulations it is therefore crucial that the possible effects of autocorrelation and non-normality are not confounded so that their separate effects may be investigated. This article presents a number of non-normal variables with non-confounded autocorrelation, thus allowing the analyst to specify autocorrelation or shape properties while keeping the other effect fixed.

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 …

Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test.

Type I Error Rates For A One Factor Within-Subjects Design With Missing Values, Miguel A. Padilla, James Algina

Journal of Modern Applied Statistical Methods

Missing data are a common problem in educational research. A promising technique, that can be implemented in SAS PROC MIXED and is therefore widely available, is to use maximum likelihood to estimate model parameters and base hypothesis tests on these estimates. However, it is not clear which test statistic in PROC MIXED performs better with missing data. The performance of the Hotelling- Lawley-McKeon and Kenward-Roger omnibus test statistics on the means for a single factor withinsubject ANOVA are compared. The results indicate that the Kenward-Roger statistic performed better in terms of keeping the Type I error close to the nominal …

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.

An Adaptive Inference Strategy: The Case Of Auditory Data, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

By way of an example some of the basic features in the derivation and use of adaptive inferential methods are demonstrated. The focus of this paper is dyadic (coupled) data in auditory and perceptual research. We present: (a) why one should not use the conventional methods, (b) a derivation of an adaptive method, and (c) how the new adaptive method works with the example data. In the concluding remarks we draw attention to the work of Professor George Barnard who provided the adaptive inference strategy in the context of the Behrens-Fisher problem -- testing the equality of means when one …

Hotelling's T2 Vs. The Rank Transform With Real Likert Data, Michael J. Nanna

Journal of Modern Applied Statistical Methods

Monte Carlo research has demonstrated that there are many applications of the rank transformation that result in an invalid procedure. Examples include the two dependent samples, the factorial analysis of variance, and the factorial analysis of covariance layouts. However, the rank transformation has been shown to be a valid and powerful test in the two independent samples layout. This study demonstrates that the rank transformation is also a robust and powerful alternative to the Hotellings T² test when the data are on a Likert scale.

Parametric Analyses In Randomized Clinical Trials, Vance W. Berger, Clifford E. Lunneborg, Michael D. Ernst, Jonathan G. Levine

Journal of Modern Applied Statistical Methods

One salient feature of randomized clinical trials is that patients are randomly allocated to treatment groups, but not randomly sampled from any target population. Without random sampling parametric analyses are inexact, yet they are still often used in clinical trials. Given the availability of an exact test, it would still be conceivable to argue convincingly that for technical reasons (upon which we elaborate) a parametric test might be preferable in some situations. Having acknowledged this possibility, we point out that such an argument cannot be convincing without supporting facts concerning the specifics of the problem at hand. Moreover, we have …