Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists

✍ Scribed by Herbert Hoijtink

• Publisher: Chapman and Hall/CRC
• Year: 2011
• Tongue: English
• Leaves: 240
• Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Dedication......Page 6
Contents......Page 8
Preface......Page 14
I. Introduction......Page 16
Symbol Description......Page 19
1. An Introduction to Informative Hypotheses......Page 20
2. Multivariate Normal Linear Model......Page 36
II. Bayesian Evaluation of Informative Hypotheses......Page 54
Symbol Description......Page 57
3. An Introduction to Bayesian Evaluation of Informative Hypotheses......Page 58
4. The J Group ANOVA Model......Page 78
5. Sample Size Determination: AN(C)OVA and Multiple Regression......Page 92
6. Sample Size Determination: The Multivariate Normal Linear Model......Page 124
III. Other Models, Other Approaches, and Software......Page 152
Symbol Description......Page 155
7. Beyond the Multivariate Normal Linear Model......Page 156
8. Other Approaches......Page 180
9. Software......Page 194
IV. Statistical Foundations......Page 202
10. Foundations of Bayesian Evaluation of Informative Hypotheses......Page 206
References......Page 232