The Foundations of Statistics: A Simulation-based Approach
Statistics and hypothesis testing are routinely used in areas (such as linguistics) that are traditionally not mathematically intensive. In such fields, when faced with experimental data, many students and researchers tend to rely on commercial packages t
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Shravan Vasishth · Michael Broe
The Foundations of Statistics: A Simulation-based Approach
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Shravan Vasishth Department of Linguistics University of Potsdam Karl-Liebknecht-Str. 24-25 14476 Potsdam Germany [email protected]
Michael Broe Department of Evolution, Ecology & Organismal Biology Ohio State University 1304 Museum of Biological Diversity Kinnear Road 1315 OH 43212 Columbus USA [email protected]
ISBN 978-3-642-16312-8 e-ISBN 978-3-642-16313-5 DOI 10.1007/978-3-642-16313-5 Springer Heidelberg Dordrecht London New York c Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Cover image: Daniel A. Becker Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
SV dedicates this book to his son, Atri; MB dedicates this book to his parents.
Foreword
Teaching the fundamental concepts and ideas of statistics is a relatively easy task when students have already completed courses in probability theory and calculus. Such students not only come well-prepared to an introductory statistics course, they are likely to follow additional, more advanced courses in mathematics and related areas. If so, many of the statistical techniques acquired remain relevant and are developed by further training. For students without much of a background in probability or calculus, the situation is quite different. For many of us, just about everything is new, from integration to probability density functions, and from slopes of regression lines to random variables. Traditionally, introductory statistics courses targeting students from the arts and social sciences seek to explain the basic concepts and results of mathematical statistics, while omitting proofs. To survive such a course, one typically dutifully memorizes the equation for the density of the normal curve, the definition of the central limit theorem, and the sums of squares of a one-way analysis of variance. Once through this bottleneck, there is the safe haven of menu-driven software packages that will calculate everything one needs (and more). Sadly enough, many students will not come to appreciate the beauty of the fundamentals of statistics, and they will also remain
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