The Significance Test Controversy Revisited : The Fiducial Bayesian Alternative The purpose of this book is not only to revisit the “significance test controversy ”but also to provide a conceptually sounder alternative. As such it presents a Bayesian framework for a new approach to analyzing and interpreting experimental data. It also prepares students and researchers for reporting on experimental results. Normative aspects: The main views of statistical tests are revisited and the philosophies of Fisher Neyman Pearson and Jeffrey are discussed in detail. Descriptive aspects: The misuses of Null Hypothesis Significance Tests are reconsidered in light of Jeffreys’ Bayesian conceptions concerning the role of statistical inference in experimental investigations. Prescriptive aspects: The current effect size and confidence interval reporting practices are presented and seriously questioned. Methodological aspects are carefully discussed and fiducial Bayesian methods are proposed as a more suitable alternative for reporting on experimental results. In closing basic routine procedures regarding the means and their generalization to the most common ANOVA applications are presented and illustrated. All the calculations discussed can be easily carried out using the freeware LePAC package Introduction Preamble Frequentist and Bayesian Inference The Fisher Neyman Pearson and Jeffreys Views of Statistical Tests GHOST: An Officially Recommended Practice The Significance Test Controversy Revisited Reporting Effect Sizes: The New Star System Reporting Confidence Intervals: A Paradoxical Situation Basic Fiducial Bayesian Procedures for Inference About Means Generalizations and Methodological Considerations for ANOVA Conclusion Index