Hoijtink Informative Hypotheses

Theory and Practice for Behavioral and Social Scientists
1. Auflage 2011
ISBN: 978-1-4398-8052-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 241 Seiten

Reihe: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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.

Zielgruppe

Practitioners and statisticians in the social sciences.

Autoren/Hrsg.

Hoijtink, Herbert

Fachgebiete

• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Empirische Sozialforschung, Statistik

Inhaltsverzeichnis

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

Über Autor(innen)

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.