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Researchers are often concerned with what sample sizes are necessary to achieve sufficient statistical power when designing their research studies. Sample sizes in such studies are often based on the omnibus test and do not necessarily provide sufficient statistical power for pairwise multiple comparisons commonly used to investigate statistically significant main effects. The purpose of this study was to conduct Monte Carlo simulations in order to investigate the appropriate sample sizes needed to achieve sufficient statistical power for numerous multiple comparison procedures (MCPs). An effect-of-most-interest approach was employed. Numerous test conditions for 3-, 4-, and 5-group one-way ANOVA designs were examined. Results show clear and consistent differences between sample sizes estimated based on the omnibus F test, t-tests, and MCPs. Comprehensive sample size tables are provided in the Appendix to this study. Analyses tables containing recommendations for sample size estimates are also provided in the results and discussion sections.
A study was conducted on the multiple comparison methods presented by Scheffe, Tukey, Student-Newman-Keuls, and Duncan under the experimental situation in which all populations were normal with equal variances and all means but one were equal. The characteristics of all four test procedures were compared for the case of multiple comparisons of pairs of means. These tests were conducted both with and without the prior performance of an analysis of variance. The Tukey and Scheffe procedures were compared in tests of linear combinations of three means. Estimates were made of the power of the tests and of Type I error rates under both the null and alternate hypotheses. Scheffe's method was found to be too conservative for pairwise comparisons of means, but it was to be preferred over Tukey's method for combinations of more than two means. Duncan's method was the most powerful test of pairwise comparisons, but it maintained little control over one kind of Type I error. The S-N-K procedure showed a good balance between power and control of Type I errors. (Author).
A study was conducted on the multiple comparison methods presented by Scheffe, Tukey, Student-Newman-Keuls, and Duncan under the experimental situation in which all populations were normal with equal variances and all means but one were equal. The characteristics of all four test procedures were compared for the case of multiple comparisons of pairs of means. These tests were conducted both with and without the prior performance of an analysis of variance. The Tukey and Scheffe procedures were compared in tests of linear combinations of three means. Estimates were made of the power of the tests and of Type I error rates under both the null and alternate hypotheses. Scheffe's method was found to be too conservative for pairwise comparisons of means, but it was to be preferred over Tukey's method for combinations of more than two means. Duncan's method was the most powerful test of pairwise comparisons, but it maintained little control over one kind of Type I error. The S-N-K procedure showed a good balance between power and control of Type I errors. (Author).
"Comprising more than 500 entries, the Encyclopedia of Research Design explains how to make decisions about research design, undertake research projects in an ethical manner, interpret and draw valid inferences from data, and evaluate experiment design strategies and results. Two additional features carry this encyclopedia far above other works in the field: bibliographic entries devoted to significant articles in the history of research design and reviews of contemporary tools, such as software and statistical procedures, used to analyze results. It covers the spectrum of research design strategies, from material presented in introductory classes to topics necessary in graduate research; it addresses cross- and multidisciplinary research needs, with many examples drawn from the social and behavioral sciences, neurosciences, and biomedical and life sciences; it provides summaries of advantages and disadvantages of often-used strategies; and it uses hundreds of sample tables, figures, and equations based on real-life cases."--Publisher's description.
A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. When there are no nuisance parameters to be estimated, the nonparametric Monte Carlo test can exactly maintain the significance level, and when nuisance parameters exist, this method can allow the test to asymptotically maintain the level. The author addresses both applied and theoretical aspects of nonparametric Monte Carlo tests. The new methodology has been used for model checking in many fields of statistics, such as multivariate distribution theory, parametric and semiparametric regression models, multivariate regression models, varying-coefficient models with longitudinal data, heteroscedasticity, and homogeneity of covariance matrices. This book will be of interest to both practitioners and researchers investigating goodness-of-fit tests and resampling approximations. Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability/empirical process theory. The less mathematically sophisticated reader will find Chapters 1, 2 and 6 to be a comprehensible introduction on how and where the new method can apply and the rest of the book to be a valuable reference for Monte Carlo test approximation and goodness-of-fit tests. Lixing Zhu is Associate Professor of Statistics at the University of Hong Kong. He is a winner of the Humboldt Research Award at Alexander-von Humboldt Foundation of Germany and an elected Fellow of the Institute of Mathematical Statistics. From the reviews: "These lecture notes discuss several topics in goodness-of-fit testing, a classical area in statistical analysis. ... The mathematical part contains detailed proofs of the theoretical results. Simulation studies illustrate the quality of the Monte Carlo approximation. ... this book constitutes a recommendable contribution to an active area of current research." Winfried Stute for Mathematical Reviews, Issue 2006 "...Overall, this is an interesting book, which gives a nice introduction to this new and specific field of resampling methods." Dongsheng Tu for Biometrics, September 2006