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.

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 Coe□cients: Informative versus Null Hypothesis

Signed Regression Coe□cients: Informative Hypothesis versus Complement

Signed Regression Coe□cients: Including Effect Sizes

Comparing Regression Coe□cients

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

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.

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