Informative Hypotheses ─ Theory and Practice for Behavioral and Social Scientists

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.

INTRODUCTIONAn Introduction to Informative HypothesesIntroductionAnalysis of VarianceAnalysis of Covariance .Multiple Regression Epistemology and Overview of the Book Appendix A: Effect Size Determination for Multiple RegressionThe Multivariate Normal Linear ModelIntroduction The Multivariate Normal Linear Model Multivariate One Sided Testing Multivariate Treatment Evaluation Multivariate RegressionRepeated Measures Analysis Other Options Appendix A: Example Data for Multivariate RegressionBAYESIAN EVALUATION OF INFORMATIVE HYPOTHESESAn Introduction to Bayesian Evaluation of Informative HypothesesIntroduction .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 IntroductionSimple Constraints One Informative Hypothesis Constraints on Combinations of Means .Ordered Means with Effect Sizes About Equality Constraints DiscussionSample Size Determination: AN(C)OVA and Multiple Regression IntroductionSample Size DeterminationANOVA: Comparison of an Informative with the Null Hypothesis ANOVA: Comparison of an Informative Hypothesis with its ComplementANCOVASigned Regression Coe□cients: Informative versus Null Hypothesis Signed Regression Coe□cients: Informative Hypothesis versus Complement Signed Regression Coe□cients: Including Effect SizesComparing Regression Coe□cientsDiscussion .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 TestingMultivariate 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 SOFTWAREBeyond the Multivariate Normal Linear Model Introduction Contingency TablesMultilevel ModelsLatent Class Analysis A General Frame WorkAppendices: Sampling Using Winbugs Other ApproachesIntroduction 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 ANOVASoftwareIntroduction Software Packages New DevelopmentsSTATISTICAL FOUNDATIONSFoundations of Bayesian Evaluation of Informative HypothesesIntroduction The Bayes Factor The Prior Distribution The Posterior DistributionEstimation of the Bayes Factor Discussion Appendix A: Density of the Data of Various Statistical ModelsAppendix B: Unconstrained Prior Distributions Used in Book and Software Appendix C: Probability Distributions Used in Appendices A and B References Index