Statistics with JMP E-Book

Peter Goos

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 809

Veröffentlichungsjahr: 2016

Beschreibung

Statistics with JMP: Hypothesis Tests, ANOVA and Regression Peter Goos, University of Leuven and University of Antwerp, Belgium David Meintrup, University of Applied Sciences Ingolstadt, Germany A first course on basic statistical methodology using JMP This book provides a first course on parameter estimation (point estimates and confidence interval estimates), hypothesis testing, ANOVA and simple linear regression. The authors approach combines mathematical depth with numerous examples and demonstrations using the JMP software. Key features: * Provides a comprehensive and rigorous presentation of introductory statistics that has been extensively classroom tested. * Pays attention to the usual parametric hypothesis tests as well as to non-parametric tests (including the calculation of exact p-values). * Discusses the power of various statistical tests, along with examples in JMP to enable in-sight into this difficult topic. * Promotes the use of graphs and confidence intervals in addition to p-values. * Course materials and tutorials for teaching are available on the book's companion website. Masters and advanced students in applied statistics, industrial engineering, business engineering, civil engineering and bio-science engineering will find this book beneficial. It also provides a useful resource for teachers of statistics particularly in the area of engineering.

Leseprobe

STATISTICS WITH JMP

HYPOTHESIS TESTS, ANOVA AND REGRESSION

Peter Goos

University of Leuven and University of Antwerp, Belgium

David Meintrup

University of Applied Sciences Ingolstadt, Germany

This edition first published 2016 © 2016 John Wiley & Sons, Ltd

Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

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Library of Congress Cataloging-in-Publication Data

Names: Goos, Peter. | Meintrup, David. Title: Statistics with JMP : hypothesis tests, ANOVA, and regression / Peter    Goos, David Meintrup. Description: Chichester, West Sussex : John Wiley & Sons, Inc., 2016. |    Includes index. Identifiers: LCCN 2015039990 (print) | LCCN 2015047679 (ebook) | ISBN 9781119097150 (cloth) |    ISBN 9781119097044 (Adobe PDF) | ISBN 9781119097167 (ePub) Subjects: LCSH: Probabilities--Data processing. | Mathematical statistics--Data processing. |    Regression analysis. | JMP (Computer file) Classification: LCC QA273.19.E4 G68 2016 (print) | LCC QA273.19.E4 (ebook) |    DDC 519.50285/53--dc23 LC record available at http://lccn.loc.gov/2015039990

A catalogue record for this book is available from the British Library.

To Marijke, Bas, Loes, and Mien To Béatrice and Werner

CONTENTS

Preface

Acknowledgments

Part One Estimators and Tests

1 Estimating Population Parameters

1.1 Introduction: Estimators Versus Estimates

1.2 Estimating a Mean Value

1.3 Criteria for Estimators

1.4 Methods for the Calculation of Estimators

1.5 The Sample Mean

1.6 The Sample Proportion

1.7 The Sample Variance

1.8 The Sample Standard Deviation

1.9 Applications

Notes

2 Interval Estimators

2.1 Point and Interval Estimators

2.2 Confidence Intervals for a Population Mean with Known Variance

2.3 Confidence Intervals for a Population Mean with Unknown Variance

2.4 Confidence Intervals for a Population Proportion

2.5 Confidence Intervals for a Population Variance

2.6 More Confidence Intervals in JMP

2.7 Determining the Sample Size

Notes

3 Hypothesis Tests

3.1 Key Concepts

3.2 Testing Hypotheses About a Population Mean

3.3 The Probability of a Type II Error and the Power

3.4 Determination of the Sample Size

3.5 JMP

3.6 Some Important Notes Concerning Hypothesis Testing

Notes

Part Two One Population

4 Hypothesis Tests for a Population Mean, Proportion, or Variance

4.1 Hypothesis Tests for One Population Mean

4.2 Hypothesis Tests for a Population Proportion

4.3 Hypothesis Tests for a Population Variance

4.4 The Probability of a Type II Error and the Power

Notes

5 Two Hypothesis Tests for the Median of a Population

5.1 The Sign Test

5.2 The Wilcoxon Signed-Rank Test

Notes

6 Hypothesis Tests for the Distribution of a Population

6.1 Testing Probability Distributions

6.2 Testing Probability Densities

6.3 Discussion

Notes

Part Three Two Populations

7 Independent Versus Paired Samples

8 Hypothesis Tests for the Means, Proportions, or Variances of Two Independent Samples

8.1 Tests for Two Population Means for Independent Samples

8.2 A Hypothesis Test for Two Population Proportions

8.3 A Hypothesis Test for Two Population Variances

8.4 Hypothesis Tests for Two Independent Samples in JMP

Notes

9 A Nonparametric Hypothesis Test for the Medians of Two Independent Samples

9.1 The Hypotheses Tested

9.2 Exact

p

-Values in the Absence of Ties

9.3 Exact

p

-Values in the Presence of Ties

9.4 Approximate

p

-Values

Notes

10 Hypothesis Tests for the Means of Two Paired Samples

10.1 The Hypotheses Tested

10.2 The Procedure

10.3 Examples

10.4 The Technical Background

10.5 Generalized Hypothesis Tests

10.6 A Confidence Interval for a Difference of Two Population Means

Notes

11 Two Nonparametric Hypothesis Tests for Paired Samples

11.1 The Sign Test

11.2 The Wilcoxon Signed-Rank Test

11.3 Contradictory Results

Notes

Part Four More Than Two Populations

12 Hypothesis Tests for More Than Two Population Means: One-Way Analysis of Variance

12.1 One-Way Analysis of Variance

12.2 The Test

12.3 One-Way Analysis of Variance in JMP

12.4 Pairwise Comparisons

12.5 The Relation Between a One-Way Analysis of Variance and a

t

-Test for Two Population Means

12.6 Power

12.7 Analysis of Variance for Nonnormal Distributions and Unequal Variances

Notes

13 Nonparametric Alternatives to an Analysis of Variance

13.1 The Kruskal–Wallis Test

13.2 The van der Waerden Test

13.3 The Median Test

13.4 JMP

Notes

14 Hypothesis Tests for More Than Two Population Variances

14.1 Bartlett’s Test

14.2 Levene’s Test

14.3 The Brown–Forsythe Test

14.4 O’Brien’s Test

14.5 JMP

14.6 The Welch Test

Notes

Part Five Additional Useful Tests and Procedures

15 The Design of Experiments and Data Collection

15.1 Equal Costs for All Observations

15.2 Unequal Costs for the Observations

16 Testing Equivalence

16.1 Shortcomings of Classical Hypothesis Tests

16.2 The Principles of Equivalence Tests

16.3 An Equivalence Test for Two Population Means

17 The Estimation and Testing of Correlation and Association

17.1 The Pearson Correlation Coefficient

17.2 Spearman’s Rank Correlation Coefficient

17.3 A Test for the Independence of Two Qualitative Variables

18 An Introduction to Regression Modeling

18.1 From a Theory to a Model

18.2 A Statistical Model

18.3 Causality

18.4 Linear and Nonlinear Regression Models

19 Simple Linear Regression

19.1 The Simple Linear Regression Model

19.2 Estimation of the Model

19.3 The Properties of Least Squares Estimators

19.4 The Estimation of σ

2

19.5 Statistical Inference for β

0

and β

1

19.6 The Quality of the Simple Linear Regression Model

19.7 Predictions

19.8 Regression Diagnostics

Notes

Appendix A The Binomial Distribution

Appendix B The Standard Normal Distribution

Appendix C The χ

2

-Distribution

Appendix D Student’s

t

-Distribution

Appendix E The Wilcoxon Signed-Rank Test

Appendix F The Shapiro–Wilk Test

Appendix G Fisher’s

F

-Distribution

Appendix H The Wilcoxon Rank-Sum Test

Appendix I The Studentized Range or

Q

-Distribution

Appendix J The Two-Tailed Dunnett Test

Appendix K The One-Tailed Dunnett Test

Appendix L The Kruskal–Wallis Test

Appendix M The Rank Correlation Test

Index

EULA

List of Tables

Chapter 1

Table 1.1

Chapter 2

Table 2.1

Chapter 3

Table 3.1

Chapter 5

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Chapter 6

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Chapter 7

Table 7.1

Chapter 9

Table 9.1

Table 9.2

Table 9.3

Table 9.4

Table 9.5

Table 9.6

Table 9.7

Chapter 10

Table 10.1

Table 10.2

Chapter 11

Table 11.1

Table 11.2

Table 11.3

Table 11.4

Table 11.5

Table 11.6

Chapter 12

Table 12.1

Table 12.2

Table 12.3

Table 12.4

Chapter 13

Table 13.1

Table 13.2

Table 13.3

Table 13.4

Table 13.5

Table 13.6

Table 13.7

Table 13.8

Table 13.9

Chapter 14

Table 14.1

Table 14.2

Table 14.3

Table 14.4

Chapter 15

Table 15.1

Table 15.2

Table 15.3

Chapter 16

Table 16.1

Table 16.2

Chapter 17

Table 17.1

Table 17.2

Table 17.3

Table 17.4

Table 17.5

Chapter 18

Table 18.1

Chapter 19

Table 19.1

Table 19.2

Table 19.3

Table 19.4

Table 19.5

Appendix E

Table 5.1

Guide

Cover

Table of Contents

Preface

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Preface

This book is the result of a thorough revision of the lecture notes for the course “Statistics for Business and Economics 2” that were developed by Peter Goos at the Faculty of Applied Economics of the University of Antwerp in Belgium. Encouraged by the success of the Dutch version of this book (entitled Verklarende Statistiek: Schatten and Toetsen, published in 2014 by Acco Leuven/Den Haag), we joined forces to create an English version. The new book builds on our first joint work, Statistics with JMP: Graphs, Descriptive Statistics and Probability (Wiley, 2015), which adopts the same philosophy, and uses the same software package, JMP. Hence, it can be regarded as a sequel, but it can also be read as a stand-alone book.

In this book, we give a detailed introduction to point estimators, interval estimators, hypo-thesis tests, analysis of variance, and simple linear regression. Compared with other introductory textbooks on inferential statistics, we cover several additional topics. For example, considerable attention is paid to nonparametric tests, such as the sign test, the signed-rank test, and the Kruskal–Wallis test. In addition, we discuss tests and confidence intervals for the Pearson and Spearman correlation coefficients, introduce the concept of equivalence tests, and include a chapter on the principles of optimal design of experiments. For nonparametric tests, exact p-values are discussed in detail, alongside the better-known approximate p-values. Throughout the book, we discuss different versions of tests and confidence intervals, which includes the construction of confidence intervals for a proportion and approximate p-values for certain tests. The book also incorporates recent insights from the literature, such as a more detailed table with critical values for the Shapiro–Wilk test and a recent table with critical values for the Kruskal–Wallis test.

As in our first book, we pay equal attention to mathematical aspects, the interpretation of all the statistical concepts that are introduced, and their practical application. In order to facilitate the understanding of the methods and to appreciate their usefulness, the book contains many examples involving real-life data. To demonstrate the broad applicability of statistics and probability, these examples have been taken from various fields of application, including business, economics, sports, engineering, and the natural sciences.

Our motivation in writing this book was twofold. First, we wanted to provide students and teachers with a resource that goes beyond other textbooks of similar scope in its technical and mathematical content. It has become increasingly fashionable for authors and statistics teachers to sweep technicalities and mathematical derivations under the carpet. We decided against this, because we feel that students should be encouraged to apply their mathematical knowledge, and that doing so deepens their understanding of statistical methods. Reading this book obviously requires some knowledge of mathematics. In most countries, students are taught mathematics in secondary or high school and the required mathematical concepts are revisited in introductory mathematics courses at university. Therefore, we are convinced that many university students have a sufficiently strong mathematical background to appreciate and benefit from the more thorough nature of this book. In the various derivations, we have tried to include all the intermediate steps, in order to keep the book readable.

Our second motivation was to ensure that the concepts introduced in the book can be successfully put into practice. To this end, we show how to generate estimates, carry out hypothesis tests, and perform regression analyses using the statistical software package JMP (pronounced “jump”). We chose JMP as supporting software because it is powerful yet easy to use, and suitable for a wide range of statistically oriented courses (including descriptive statistics, hypothesis testing, regression, analysis of variance, design of experiments, reliability, multivariate methods, and statistical and predictive modeling). We believe that introductory courses in statistics should use such software wherever possible. Indeed, we find that, because of the way in which students can easily interact with JMP, it can actually spark enthusiasm for statistics in class. The probability that a student will use statistics in his or her future professional career is far greater if the statistics classes were more pleasurable than painful.

In summary, our approach to teaching statistics combines theoretical and mathematical depth, detailed and clear explanations, numerous practical examples, and the use of a user-friendly and yet very powerful statistical package.

Software

As mentioned, we use JMP as enabling software. With the purchase of a hard copy of this book, you receive a one-year license for JMP’s Student Edition. The license period starts when you activate your copy of the software using the code included with this book (to receive an access code, please visit www.wiley.com/go/statsjmp). To download JMP’s Student Edition, visit http://www.jmp.com/wiley. For students accessing a digital version of the book, your lecturer may contact Wiley in order to procure unique codes with which to download the free software. For more information about JMP, go to http://www.jmp.com. JMP is available for the Windows and Mac operating systems. This book is based on JMP version 12 for Windows.

In our examples, we do not assume any familiarity with JMP: the step-by-step instructions are detailed and accompanied by screenshots. For more explanations and descriptions, www.jmp.com offers a substantial amount of free material, including many video demonstrations. In addition, there is a JMP Academic User Community where you can access content, discuss questions, and collaborate with other JMP users worldwide: instructors can share teaching resources and best practices, students can ask questions, and everyone can access the latest resources provided by the JMP Academic Team. To join the community, go to http://community.jmp.com/academic.

Data Files

Throughout the book, various data sets are used. We strongly encourage everyone who wants to learn statistics to actively try things out using data. JMP files containing the data sets as well as JMP scripts to reproduce figures, tables, and analyses can be downloaded from the publisher’s companion web site to this book:

www.wiley.com/go/goosandmeintrup/JMP

There, we also provide some additional supporting files.

Peter Goos David Meintrup

Acknowledgments

We consulted plenty of sources during the preparation of this book, and we would like to acknowledge at least the most important ones. A source on nonparametric techniques that we found extremely valuable, given its depth and comprehensive explanations, is the book Nonparametric Statistical Methods by M. Hollander, D.A. Wolfe, and E. Chicken. A more general book that we found very helpful is the Handbook of Parametric and Nonparametric Statistical Procedures by David J. Sheskin. The same applies to Biostatistical Analysis by J.H. Zar.

We would like to thank numerous people who have made the publication of this book possible. The first author, Peter Goos, is very grateful to Professor Willy Gochet of the University of Leuven, who introduced him to the topics of statistics and probability. Professor Gochet allowed Peter to use his lecture notes as a backbone for his own course material, which later developed into this book.

The authors are very grateful for the support and advice offered by several people from the JMP Division of SAS: Brady Brady, Ian Cox, Bradley Jones, Volker Kraft, John Sall, and Mia Stephens. It is Volker who brought the two authors together and encouraged them to work on a series of English books on statistics with JMP (the first book is entitled Statistics with JMP: Graphs, Descriptive Statistics and Probability). A very special word of thanks goes to Ian, whose suggestions substantially improved this book, and to José Ramirez for generously sharing an example and a data set. The authors would also like to thank Eva Angels, Kris Annaert, Stefan Becuwe, Hilde Bemelmans, Marco Castro, Filip De Baerdemaeker, Hajar Hamidouche, Jérémie Haumont, Roselinde Kessels, Ida Ruts, Bagus Sartono, Daniel Palhazi Cuervo, Evelien Stoffels, Anja Struyf, Utami Syafitri, Yahri Tillmans, Ellen Vandervieren, Katrien Van Driessen, Kristel Van Rompay, Alan Vazquez Alcocer, Diane Verbiest, Tom Vermeire, Nha Vo-Thanh, Sara Weyns, Peter Willemé, and Simone Willis for their detailed comments and constructive suggestions, and for their technical assistance in creating figures and tables.

Finally, we thank Liz Wingett, Baljinder Kaur, Heather Kay, Audrey Koh, and Geoffrey D. Palmer at John Wiley & Sons.

Part OneEstimators and Tests

1Estimating Population Parameters

I don’t know how long I stand there. I don’t believe I’ve ever stood there mourning faithfully in a downpour, but statistically speaking it must have been spitting now and then, there must have been a bit of a drizzle once or twice.

(from The Misfortunates, Dimitri Verhulst, pp. 125–126)