Open Access. Powered by Scholars. Published by Universities.®

Statistical Theory Commons™

Open Access. Powered by Scholars. Published by Universities.®

Social and Behavioral Sciences

Institution
Keyword
Publication Year
Publication
Publication Type

Articles 1081 - 1110 of 1133

Full-Text Articles in Statistical Theory

A Test Of Symmetry, Abdul R. Othman, H. J. Keselman, Rand R. Wilcox, Katherine Fradette, A. R. Padmanabhan Nov 2002

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, …

Go to article

Best Regression Model Using Information Criteria, Phill Gagné, C. Mitchell Dayton Nov 2002

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.

Go to article

The Statistical Modeling Of The Fertility Of Chinese Women, Dudley L. Poston Jr. Nov 2002

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 …

Go to article

Fermat, Schubert, Einstein, And Behrens-Fisher: The Probable Difference Between Two Means When Σ_1^2≠Σ_2^2, Shlomo S. Sawilowsky Nov 2002

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.

Go to article

Double Median Ranked Set Sample: Comparing To Other Double Ranked Samples For Mean And Ratio Estimators, Hani M. Samawi, Eman M. Tawalbeh Nov 2002

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 …

Go to article

Robust Estimation Of Multivariate Failure Data With Time-Modulated Frailty, Pingfu Fu, J. Sunil Rao, Jiming Jiang Nov 2002

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 …

Go to article

Some Reflections On Significance Testing, Thomas R. Knapp Nov 2002

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.

Go to article

Null Distribution Of The Likelihood Ratio Statistic For Feed-Forward Neural Networks, Douglas Landsittel, Harshinder Singh, Vincent C. Arena, Stewart J. Anderson Nov 2002

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.

Go to article

Combining Quantum Mechanical Calculations And A Χ^2 Fit In A Potential Energy Function For The Co_2 + O^+ Reaction, Ellen F. Sawilowsky Nov 2002

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 …

Go to article

Type I Error Rates For Rank-Based Tests Of Homogeneity Of Slopes, Alan J. Klockars, Tim P. Moses Nov 2002

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.

Go to article

Exploration Of Distributions Of Ratio Of Partial Sum Of Sample Eigenvalues When All Population Eigenvalues Are The Same, Moonseong Heo Nov 2002

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 …

Go to article

Chronic Disease Data And Analysis: Current State Of The Field, Ralph D'Agostino Sr., Lisa M. Sullivan Nov 2002

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 …

Go to article

Twenty Nonparametric Statistics And Their Large Sample Approximations, Gail F. Fahoome Nov 2002

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 …

Go to article

Trimming, Transforming Statistics, And Bootstrapping: Circumventing The Biasing Effects Of Heterescedasticity And Nonnormality, H. J. Keselman, Rand R. Wilcox, Abdul R. Othman, Katherine Fradette Nov 2002

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 …

Go to article

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 Nov 2002

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.

Go to article

Determining Predictor Importance In Multiple Regression Under Varied Correlational And Distributional Conditions, Tiffany A. Whittaker, Rachel T. Fouladi, Natasha J. Williams Nov 2002

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.

Go to article

A Program For Generating All Permutations Of {1, 2, ..., N}, Robert Disario Nov 2002

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.

Go to article

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 Nov 2002

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 SU 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.

Go to article

Within Groups Multiple Comparisons Based On Robust Measures Of Location, Rand R. Wilcox, H. J. Keselman Nov 2002

Within Groups Multiple Comparisons Based On Robust Measures Of Location, Rand R. Wilcox, H. J. Keselman

Journal of Modern Applied Statistical Methods

Consider the problem of performing all pair-wise comparisons among J dependent groups based on measures of location associated with the marginal distributions. It is well known that the standard error of the sample mean can be large relative to other estimators when outliers are common. Two general strategies for addressing this problem are to trim a fixed proportion of observations or empirically check for outliers and remove (or down-weight) any that are found. However, simply applying conventional methods for means to the data that remain results in using the wrong standard error. Methods that address this problem have been proposed, …

Go to article

Adaptive Tests For Ordered Categorical Data, Vance W. Berger, Anastasia Ivanova Nov 2002

Adaptive Tests For Ordered Categorical Data, Vance W. Berger, Anastasia Ivanova

Journal of Modern Applied Statistical Methods

Consider testing for independence against stochastic order in an ordered 2xJ contingency table, under product multinomial sampling. In applications one may wish to exploit prior information concerning the direction of the treatment effect, yet ultimately end up with a testing procedure with good frequentist properties. As such, a reasonable objective may be to simultaneously maximize power at a specified alternative and ensure reasonable power for all other alternatives of interest. For this objective, none of the available testing approaches are completely satisfactory. A new class of admissible adaptive tests is derived. Each test in this class strictly preserves the Type …

Go to article

Accounting For Non-Independent Observations In 2×2 Tables, With Application To Correcting For Family Clustering In Exposure-Risk Relationship Studies, Leslie A. Kalsih, Katherine A. Riester, Stuart J. Pocock Nov 2002

Accounting For Non-Independent Observations In 2×2 Tables, With Application To Correcting For Family Clustering In Exposure-Risk Relationship Studies, Leslie A. Kalsih, Katherine A. Riester, Stuart J. Pocock

Journal of Modern Applied Statistical Methods

Participants in epidemiologic studies may not represent statistically independent observations. We consider modifications to conventional analyses of 2×2 tables, including Fisher’s exact test and confidence intervals, to account for correlated observations in this setting. An example is provided, assessing the robustness of conclusions from a published analysis.

Go to article

Simulation Study Of Chemical Inhibition Modeling, Pali Sen, Mary Anderson Nov 2002

Simulation Study Of Chemical Inhibition Modeling, Pali Sen, Mary Anderson

Journal of Modern Applied Statistical Methods

The combined effects of the activities of different chemicals are of interest of this study. We simulate for the synthetic data, and fit experimental data for three models and estimate the parameters. We assess the fit of the synthetic data and the experimental data by comparing the coefficients of variation for the parameter estimates and identify the best model for the inhibition process.

Go to article

On Distribution Function Estimation Using Double Ranked Set Samples With Application, Walid A. Abu-Dayyeh, Hani M. Samawi, Lara A. Bani-Hani Nov 2002

On Distribution Function Estimation Using Double Ranked Set Samples With Application, Walid A. Abu-Dayyeh, Hani M. Samawi, Lara A. Bani-Hani

Journal of Modern Applied Statistical Methods

As a variation of ranked set sampling (RSS); double ranked set sampling (DRSS) was introduced by Al-Saleh and Al-Kadiri (2000), and it has been used only for estimating the mean of the population. In this paper DRSS will be used for estimating the distribution function (cdf). The efficiency of the proposed estimators will be obtained when ranking is perfect. Some inference on the distribution function will be drawn based on Kolomgrov-Smirnov statistic. It will be shown that using DRSS will increase the efficiency in this case.

Go to article

On The Estimation Of Binomial Success Probability With Zero Occurrence In Sample, Mehdi Razzaghi Nov 2002

On The Estimation Of Binomial Success Probability With Zero Occurrence In Sample, Mehdi Razzaghi

Journal of Modern Applied Statistical Methods

The problem of estimating the probability of a rare event when the sample shows no incidence of the event is considered. Several methodologies based on various statistical techniques are described and their relative performances are investigated. A decision theoretic approach for estimation of response probability when the sample contains zero responses is examined in depth. The properties of each method are discussed and an example from teratology is used to provide illustration and to demonstrate the results.

Go to article

A Longitudinal Follow-Up Of Discrete Mass At Zero With Gap, Joseph L. Musial, Patrick D. Bridge, Nicol R. Shamey Nov 2002

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.

Go to article

Jmasm4: Critical Values For Four Nonparametric And/Or Distribution-Free Tests Of Location For Two Independent Samples, Bruce R. Fay Nov 2002

Jmasm4: Critical Values For Four Nonparametric And/Or Distribution-Free Tests Of Location For Two Independent Samples, Bruce R. Fay

Journal of Modern Applied Statistical Methods

Researchers engaged in computer-intensive studies may need exact critical values, especially for sample sizes and alpha levels not normally found in published tables, as well as the ability to control ‘best-fit’ criteria. They may also benefit from the ability to directly generate these values rather than having to create lookup tables. Fortran 90 programs generate ‘best-conservative’ (bc) and ‘best-fit’ (bf) critical values with associated probabilities for the Kolmogorov-Smirnov test of general differences (bc), Rosenbaum’s test of location (bc), Tukey’s quick test (bc and bf)) and the Wilcoxon rank-sum test (bc).

Go to article

Power Analyses When Comparing Trimmed Means, Rand R. Wilcox, H. J. Keselman May 2002

Power Analyses When Comparing Trimmed Means, Rand R. Wilcox, H. J. Keselman

Journal of Modern Applied Statistical Methods

Given a random sample from each of two independent groups, this article takes up the problem of estimating power, as well as a power curve, when comparing 20% trimmed means with a percentile bootstrap method. Many methods were considered, but only one was found to be satisfactory in terms of obtaining both a point estimate of power as well as a (one-sided) confidence interval. The method is illustrated with data from a reading study where theory suggests two groups should differ but nonsignificant results were obtained.

Go to article

Some Locally Most Powerful Rank Tests For Correlation, W. J. Conover May 2002

Some Locally Most Powerful Rank Tests For Correlation, W. J. Conover

Journal of Modern Applied Statistical Methods

Four examples are given to illustrate the ease and practicality of the procedure for finding locally most powerful rank tests for correlation. The first two examples deal with bivariate exponential models. The third example uses the bivariate normal distribution, and the fourth example analyzes the Morgenstem’s general correlation model.

Go to article

Exact Level And Power Of Permutation, Bootstrap, And Asymptotic Tests Of Trend, Christopher D. Corcoran, Cyrus R. Mehta May 2002

Exact Level And Power Of Permutation, Bootstrap, And Asymptotic Tests Of Trend, Christopher D. Corcoran, Cyrus R. Mehta

Journal of Modern Applied Statistical Methods

We develop computational tools that can evaluate the exact size and power of three tests of trend (e.g., permutation, bootstrap and asymptotic) without resorting to large-sample theory or simulations. We then use these tools to compare the operating characteristics of the three tests. It is seen that the bootstrap test is ultra-conservative relative to the other two tests and as a result suffers from a severe deterioration in power. The power of the asymptotic test is uniformly larger than that of the other two tests, but it fails to preserve the Type I error for most of the range of …

Go to article

Six Modifications Of The Aligned Rank Transform Test For Interaction, Kathleen Peterson May 2002

Six Modifications Of The Aligned Rank Transform Test For Interaction, Kathleen Peterson

Journal of Modern Applied Statistical Methods

Testing for interactions in multivariate experiments is an important function. Studies indicate that much data from social studies research is not normally distributed, thus violating that assumption of the AN OVA procedure. The aligned rank transformation test (ART), aligning using the means of columns and rows, has been found, in limited situations, to be robust to Type I error rates and to have greater power than the ANOVA. This study explored a variety of alignments, including the median, Winsorized trimmed means (10%) and (20%), the Huber1.28 M-estimator, and the Harrell-Davis estimator of the median. Results are reported for Type …

Go to article

First Prev Next Last