Table Of ContentSpringer 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
