Table Of Content

Springer Texts in Statistics Advisors: Stephen Fienberg Ingram Olkin Springer Texts in Statistics Alfred Elements of Statistics for the Life and Social Sciences Blom Probability and Statistics: Theory and Applications Chow and Teicher Probability Theory: Independence, Interchangeability, Martingales. Second Edition Christensen Plane Answers to Complex Questions: The Theory of Linear Models Christensen Linear Models for Multivariate, Time Series, and Spatial Data Christensen Log-Linear Models du Toit, Steyn and Graphical Exploratory Data Analysis Stumpf Finkelstein and Levin Statistics for Lawyers Kalbfleisch Probability and Statistical Inference: Volume 1: Probability. Second Edition Kalbfleisch Probability and Statistical Inference: Volume 2: Statistical Inference. Second Edition Keyfitz Applied Mathematical Demography. Second Edition [(jefer Introduction to Statistical Inference Kokoska and Nevison Statistical Tables and Formulae Madansky Prescriptions for Working Statisticians McPherson Statistics in Scientific Investigation: Its Basis, Application, and Interpretation (continued after index) Gottfried E. Noether Introduction to StatistÎcs The Nonparametric Way With the Assistance of Marilynn Dueker With 42 IIlustrations Springer Science+Business Media, LLC Gottfried E. Noether Professor Emeritus Department of Statistics University of Connecticut Storrs, CT 06269 USA Editorial Board Stephen Fienberg lngram Olkin Department of Statistics Department of Statistics Carnegie-Mellon University Stanford University Pittsburgh, PA 15213 Stanford, CA 94305 USA USA Mathematical Subject Classifications: 62-01, 62Gxx. Library of Congress Cataloging-in-Publication Data Noether, Gottfried E. (Gottfried Emanuel) Introduction to statistics : the nonparametrie way 1 Gottfried E. Noether. p. cm. - (Springer series in statistics) Includes index. ISBN 978-1-4612-6955-7 ISBN 978-1-4612-0943-0 (eBook) DOI 10.1007/978-1-4612-0943-0 1. Statistics. I. Title. 11. Series. HA29.N77S 1990 SI9.S -dc20 90-9791 CIP Printed on acid-free paper. © 1991 Springer Science+Business Media New York Originally published by Springer-Verlag New York in 1991 Softcover reprint ofthe hardcover 1st edition 1991 All rights reserved . This work may not be translated or copied in whole or in part without the written permission of the Springer Science+Business Media, LLC, except for brief ex cerpts in connection with reviews or scholarly analysis. Use in connection with any form ofinformation storage and retrieval, electronic adaptation, computer software, or by simi lar or dissimilar methodology now known or hereafter developed is forbidden . Tbe use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Photocomposed from a laTeX file. 9 8 7 6 S 4 321 ISBN 978-1-4612-6955-7 ToL. Preface The introductory statistics course presents serious pedagogical problems to the instructor. For the great majority of students, the course represents the only formal contact with statistical thinking that he or she will have in college. Students come from many different fields of study, and a large number suffer from math anxiety. Thus, an instructor who is willing to settle for some limited objectives will have a much better chance of success than an instructor who aims for a broad exposure to statistics. Many statisticians agree that the primary objective of the introductory statistics course is to introduce students to variability and uncertainty and how to cope with them when drawing inferences from observed data. Addi tionally, the introductory COurse should enable students to handle a limited number of useful statistical techniques. The present text, which is the successor to the author's Introduction to Statistics: A Nonparametric Approach (Houghton Mifflin Company, Boston, 1976), tries to meet these objectives by introducing the student to the ba sic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem, which is both conceptually simpler and more realistic than the one-sample problem that customarily serves as the basis for the discussion of statistical inference. Instead of the theoretically and computa tionally awkward two-sample t-statistic, the book exploits nonparametric ideas that rely on nothing more complicated than sample differences Y - X, referred to as elementary estimates, to define the Wilcoxon-Mann-Whitney test statistics and the related point and interval estimates. The ideas behind elementary estimates are then applied to the one sample problem and to linear regression and rank correlation. Discussion of the Kruskal-Wallis and Friedman procedures for the k-sample problem rounds out the nonparametric coverage. After each nonparametric treat ment, the corresponding classical normal-theory solution is presented. The concluding chapters provide a discussion of chi-square tests for the analysis of categorical data and introduce the student to the analysis of binomial data including the computation of power and sample size. Sufficient material has been presented for a two-semester course meeting three hours a week. For a self-contained one-semester course, the author has covered the non parametric material through rank correlation, leaving out viii Preface material has a basic understanding of statistical inference and is familiar with a number of useful practical techniques. A few sections and problems * are marked with an to indicate that they are of a somewhat mathematical or technical nature. They can be omitted without loss of continuity. Most problems in the book can be solved with nothing more than a basic calculator. But access to statistical software greatly reduces computational drudgery. The author has found MINITABl to be most helpful in accom plishing the demands of the course. Most chapters in the book have an appendix discussing relevant Minitab commands. The commands are those in Minitab Release 6.1 for MS-DOS microcomputers. A short laboratory session centered around the Appendix for Chapter 1 should be sufficient to prepare students for subsequent work with Minitab. Acknowledgments. The author is deeply greatful to Marilynn Dueker of the University of Connecticut at Stamford for her willingness to prepare the extensive problem sets at the end of chapters and to write the Minitab appendices. Without her help, publication of the book would have been delayed substantially. Tables K, U, and W are based on new computations of the distribu tions of Kendall C, Mann-Whitney U, and Wilcoxon one-sample W by Mr. Constantin Yiannoutsos. The author acknowledges the support of MINITAB, Inc., (3081 En terprise Drive, State College, PA 16801; telephone: 814-238-3280; telex: 881612) through their Author Assistance Program. IMINITAB is a registered trademark. Contents Preface vii 1 Introduction: Why Study Statistics? 1 1.1 Minitab Appendix 2 2 Organizing and Summarizing Data 5 2.1 Stem-and-Leaf Diagrams 5 2.2 Histograms 9 2.3 Five-Number Summaries 13 2.4 Boxplots 17 2.5 Minitab Appendix 18 Problem Set for Chapter 2 19 3 Intuitive Inference 29 3.1 Opinion Polls 29 3.2 Capture-Recapture 30 3.3 The Taxi Number Problem 33 3.4 Hypothesis Testing 37 3.5 Categorical and Measurement Data 39 3.6 Minitab Appendix 39 Problem Set for Chapter 3 39 4 Probability 45 4.1 The Frequency Interpretation of Probability 45 4.2 Random Numbers 48 4.3 Independence 49 4.4 The Taxi Number Problem Revisited 54 4.5 Minitab Appendix 56 Problem Set for Chapter 4 57 5 The Normal Distribution 65 5.1 Distributions as Probability Models 65 5.2 Areas Under the Normal Curve 67 5.3 Minitab Appendix 76 Problem Set for Chapter 5 77 x Contents 6 Hypothesis Testing 81 6.1 The Two-Sample Problem 87 6.2 P-Values 90 6.3 Tests of Significance 92 6.4 Making Decisions 93 Problem Set for Chapter 6 97 1 The Wilcoxon Two-Sample Test 103 7.1 Test Statistics for the Wilcoxon Two-Sample Test 103 7.2 The Rank Form of the Wilcoxon Two-Sample Test 110 7.3 The Wilcoxon Two-Sample Test with Tied Observations 112 7.4 Minitab Appendix 113 Problem Set for Chapter 7 115 8 Nonparametric and Parametric Tests 129 8.1 The Two-Sample t-Test 129 8.2 Wilcoxon Versus t-Tests 133 8.3 Minitab Appendix 135 Problem Set for Chapter 8 136 9 Estimation: The Two-Sample Shift Model 143 9.1 Elementary Estimates for 0 144 9.2 Point Estimates for the Shift Parameter 0 144 9.3 Confidence Intervals for the Parameter 0 145 9.4 t-Intervals 151 9.5 Choosing an Estimate 152 9.6 Minitab Appendix 152 Problem Set for Chapter 9 154 10 Point Estimates, Confidence Intervals, and Tests of Hypotheses 165 10.1 The Wilcoxon Two-Sample Test and the Id-Interval 165 10.2 Elementary Estimates 168 10.3 Minitab Appendix 168 Problem Set for Chapter 10 169 11 The One-Sample Problem 113 11.1 General Populations: Sign-Test Procedures 174 11.2 Symmetric Populations: Wilcoxon Procedures 178 11.3 Normal Populations: t-Tests and t-Intervals 184 11.4 Minitab Appendix 187 Problem Set for Chapter 11 190 12 The Two-Sample Problem: Paired Observations 201 12.1 Lotion Y Versus Lotion X 201