This book, with a foreword by the outstanding philosopher of science and mathematical psychologist Patrick Suppes of Stanford University, is the outgrowth of the work developed within the Groupe Mathematiques et Psychologie, a research unit of the University Rene Descartes and CNRS (the French National Center for Scientific Research). New ways in statistical methodology are presented, which complement the familiar significance tests by new methods better suited to the researchers’ objectives, in the first place, Bayesian methods. In mathematical statistics, Bayesian methods have made a breakthrough in the last few years, but those developments are still ignored by the current statistical methodology and practice. The present book is really the first one to fill this gap. This book is written for a large audience of researchers, statisticians and users of statistics in behavioral and social sciences, and contains both an analysis of the attitude of researchers toward statistical inference, and concrete proposals for improving statistical practice. The statistical consulting experience of the authors is centered around psychology and covers a broad range of subjects from social sciences to biostatistics. All methods developed by the authors are implemented in software.