Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists (Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences
By: Herbert Hoijtink (author)Hardback
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When scientists formulate their theories, expectations, and hypotheses, they often use statements like: "I expect mean A to be bigger than means B and C"; "I expect that the relation between Y and both X1 and X2 is positive"; and "I expect the relation between Y and X1 to be stronger than the relation between Y and X2". Stated otherwise, they formulate their expectations in terms of inequality constraints among the parameters in which they are interested, that is, they formulate Informative Hypotheses. There is currently a sound theoretical foundation for the evaluation of informative hypotheses using Bayes factors, p-values and the generalized order restricted information criterion. Furthermore, software that is often free is available to enable researchers to evaluate the informative hypotheses using their own data. The road is open to challenge the dominance of the null hypothesis for contemporary research in behavioral, social, and other sciences.
Since 2003, Herbert Hoijtink has been Professor of Applied Bayesian Statistics at Utrecht University. He works in the Faculty of Social Sciences where he does research, teaches and provides statistical advice to behavioral (US spelling)and social scientists. In 2005, he received the prestigious VICI grant from the Netherlands Organisation for Scientific Research. This grant enabled him to establish a research group with the purpose to develop the statistical theory and corresponding software such that behavioral and social scientists will be able to evaluate informative hypotheses. The achievements of this group are presented in this book. Further information about the author can be found at http://tinyurl.com/hoijtink.
INTRODUCTION An Introduction to Informative Hypotheses Introduction Analysis of Variance Analysis of Covariance . Multiple Regression Epistemology and Overview of the Book Appendix A: Effect Size Determination for Multiple Regression The Multivariate Normal Linear Model Introduction The Multivariate Normal Linear Model Multivariate One Sided Testing Multivariate Treatment Evaluation Multivariate Regression Repeated Measures Analysis Other Options Appendix A: Example Data for Multivariate Regression BAYESIAN EVALUATION OF INFORMATIVE HYPOTHESES An Introduction to Bayesian Evaluation of Informative Hypotheses Introduction . Density of the Data, Prior and Posterior . Bayesian Evaluation of Informative Hypotheses Specifying the Parameters of Prior Distributions Discussion . Appendix A: Density of the Data, Prior and Posterior Distribution Appendix B: Derivation of the Bayes Factor and Prior Sensitivity . Appendix C: Using BIEMS for a two group ANOVA The J Group ANOVA Model Introduction Simple Constraints One Informative Hypothesis Constraints on Combinations of Means . Ordered Means with Effect Sizes About Equality Constraints Discussion Sample Size Determination: AN(C)OVA and Multiple Regression Introduction Sample Size Determination ANOVA: Comparison of an Informative with the Null Hypothesis ANOVA: Comparison of an Informative Hypothesis with its Complement ANCOVA Signed Regression Coecients: Informative versus Null Hypothesis Signed Regression Coecients: Informative Hypothesis versus Complement Signed Regression Coecients: Including Effect Sizes Comparing Regression Coecients Discussion . Appendix A: Bayes Factors for Parameters on the Boundary of H1 and H1c Appendix B: Command Files for GenMVLData Sample Size Determination: The Multivariate Normal Linear Model Introduction Sample Size Determination: Error Probabilities Multivariate One Sided Testing Multivariate Treatment Evaluation Multivariate Regression . Repeated Measures Analysis Discussion . Appendix A: GenMVLData and BIEMS: Multivariate One Sided Testing Appendix B: GenMVLData and BIEMS: Multivariate Treatment Evaluation Appendix C: GenMVLData and BIEMS: Multivariate Regression Appendix D: GenMVLData and BIEMS: Repeated Measures Analysis OTHER MODELS, OTHER APPROACHES AND SOFTWARE Beyond the Multivariate Normal Linear Model Introduction Contingency Tables Multilevel Models Latent Class Analysis A General Frame Work Appendices: Sampling Using Winbugs Other Approaches Introduction Resume: Bayesian Evaluation of Informative Hypotheses Null Hypothesis Signi cance Testing The Order Restricted Information Criterion Discussion Appendix A: Data and Command File for Confirmatory ANOVA Software Introduction Software Packages New Developments STATISTICAL FOUNDATIONS Foundations of Bayesian Evaluation of Informative Hypotheses Introduction The Bayes Factor The Prior Distribution The Posterior Distribution Estimation of the Bayes Factor Discussion Appendix A: Density of the Data of Various Statistical Models Appendix B: Unconstrained Prior Distributions Used in Book and Software Appendix C: Probability Distributions Used in Appendices A and B References Index
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