MINITAB Manual For Introduction ToThe Practice of Statistics

[Pages:256]MINITAB Manual For

David Moore and George McCabe's

Introduction To The Practice of Statistics

Michael Evans

University of Toronto

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Contents

Preface

vii

I Minitab for Data Management

1

1 Manual Overview and Conventions . . . . . . . . . . . . . . . . . 3

2 Accessing and Exiting Minitab . . . . . . . . . . . . . . . . . . . . 4

3 Files Used by Minitab . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 The Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

6 Minitab Commands . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7 Entering Data into a Worksheet . . . . . . . . . . . . . . . . . . . 12

7.1 Importing Data . . . . . . . . . . . . . . . . . . . . . . . . 13

7.2 Patterned Data . . . . . . . . . . . . . . . . . . . . . . . . 17

7.3 Printing Data in the Session Window . . . . . . . . . . . . 18

7.4 Assigning Constants . . . . . . . . . . . . . . . . . . . . . . 19

7.5 Naming Variables and Constants . . . . . . . . . . . . . . . 20

7.6 Information about a Worksheet . . . . . . . . . . . . . . . 21

7.7 Editing a Worksheet . . . . . . . . . . . . . . . . . . . . . . 21

8 Saving, Retrieving, and Printing . . . . . . . . . . . . . . . . . . . 24

9 Mathematical Operations . . . . . . . . . . . . . . . . . . . . . . . 27

9.1 Arithmetical Operations . . . . . . . . . . . . . . . . . . . . 27

9.2 Mathematical Functions . . . . . . . . . . . . . . . . . . . . 28

9.3 Comparisons and Logical Operations . . . . . . . . . . . . . 29

9.4 Column and Row Statistics . . . . . . . . . . . . . . . . . . 31

9.5 Sorting Data . . . . . . . . . . . . . . . . . . . . . . . . . . 33

9.6 Computing Ranks . . . . . . . . . . . . . . . . . . . . . . . 34

10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

II Minitab for Data Analysis

37

1 Looking at Data?Distributions

39

1.1 Tabulating and Summarizing Data . . . . . . . . . . . . . . . . . 40

1.1.1 Tallying Data . . . . . . . . . . . . . . . . . . . . . . . . . 41

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CONTENTS

1.1.2 Describing Data . . . . . . . . . . . . . . . . . . . . . . . 43 1.2 Plotting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1.2.1 Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . 45 1.2.2 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.2.3 Boxplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 1.2.4 Bar Charts . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.2.5 Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.2.6 Time Series Plots . . . . . . . . . . . . . . . . . . . . . . . 56 1.3 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . 58 1.3.1 Calculating the Density . . . . . . . . . . . . . . . . . . . 58 1.3.2 Calculating the Distribution Function . . . . . . . . . . . 59 1.3.3 Calculating the Inverse Distribution Function . . . . . . . 60 1.3.4 Normal Probability Plots . . . . . . . . . . . . . . . . . . 60 1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2 Looking at Data?Relationships

65

2.1 Scatterplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.2 Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

2.3 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

2.4 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3 Producing Data

77

3.1 Generating a Random Sample . . . . . . . . . . . . . . . . . . . . 78

3.2 Sampling from Distributions . . . . . . . . . . . . . . . . . . . . . 80

3.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4 Probability: The Study of Randomness

85

4.1 Basic Probability Calculations . . . . . . . . . . . . . . . . . . . . 85

4.2 More on Sampling from Distributions . . . . . . . . . . . . . . . 87

4.3 Simulation for Approximating Probabilities . . . . . . . . . . . . 90

4.4 Simulation for Approximating Means . . . . . . . . . . . . . . . . 91

4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5 Sampling Distributions

95

5.1 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . 95

5.2 Simulating Sampling Distributions . . . . . . . . . . . . . . . . . 98

5.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 Introduction to Inference

105

6.1 z Con?dence Intervals . . . . . . . . . . . . . . . . . . . . . . . . 105

6.2 z Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.3 Simulations for Con?dence Intervals . . . . . . . . . . . . . . . . 108

6.4 Power Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.5 The Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . 112

6.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

CONTENTS

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7 Inference for Distributions

115

7.1 The Student Distribution . . . . . . . . . . . . . . . . . . . . . . 115

7.2 t Con?dence Intervals . . . . . . . . . . . . . . . . . . . . . . . . 116

7.3 t Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.4 The Sign Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.5 Comparing Two Samples . . . . . . . . . . . . . . . . . . . . . . 120

7.6 The F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

8 Inference for Proportions

127

8.1 Inference for a Single Proportion . . . . . . . . . . . . . . . . . . 127

8.2 Inference for Two Proportions . . . . . . . . . . . . . . . . . . . . 130

8.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

9 Inference for Two-Way Tables

133

9.1 Tabulating and Plotting . . . . . . . . . . . . . . . . . . . . . . . 133

9.2 The Chi-square Test . . . . . . . . . . . . . . . . . . . . . . . . . 138

9.3 Analyzing Tables of Counts . . . . . . . . . . . . . . . . . . . . . 140

9.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

10 Inference for Regression

145

10.1 Simple Regression Analysis . . . . . . . . . . . . . . . . . . . . . 145

10.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

11 Multiple Regression

155

11.1 Example of a Multiple Regression . . . . . . . . . . . . . . . . . . 155

11.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

12 One-Way Analysis of Variance

163

12.1 A Categorical Variable and a Quantitative Variable . . . . . . . . 163

12.2 One-Way Analysis of Variance . . . . . . . . . . . . . . . . . . . 167

12.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

13 Two-Way Analysis of Variance

175

13.1 The Two-Way ANOVA Command . . . . . . . . . . . . . . . . . 175

13.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

14 Bootstrap Methods and Permutation Tests

181

14.1 Bootstrap Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 182

14.2 Permutation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 185

14.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

15 Nonparametric Tests

191

15.1 The Wilcoxon Rank Sum Procedures . . . . . . . . . . . . . . . . 191

15.2 The Wilcoxon Signed Rank Procedures . . . . . . . . . . . . . . . 193

15.3 The Kruskal-Wallis Test . . . . . . . . . . . . . . . . . . . . . . . 194

15.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

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CONTENTS

16 Logistic Regression

197

16.1 The Logistic Regression Model . . . . . . . . . . . . . . . . . . . 197

16.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

16.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

17 Statistics for Quality: Control and Capability

203

17.1 Producing x? Charts . . . . . . . . . . . . . . . . . . . . . . . . . 203

17.2 Producing S Charts . . . . . . . . . . . . . . . . . . . . . . . . . 207

17.3 Producing p Charts . . . . . . . . . . . . . . . . . . . . . . . . . . 208

17.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

A Projects

213

B Functions in Minitab

215

B.1 Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . 215

B.2 Column Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

B.3 Row Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

C More Minitab Commands

219

C.1 Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

C.2 Concatenating Columns . . . . . . . . . . . . . . . . . . . . . . . 220

C.3 Converting Data Types . . . . . . . . . . . . . . . . . . . . . . . 221

C.4 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

C.5 Stacking and Unstacking Columns . . . . . . . . . . . . . . . . . 223

D Programming in Minitab

225

D.1 Global Macros . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

D.2 Control Statements . . . . . . . . . . . . . . . . . . . . . . . . . . 226

D.3 Startup Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

D.4 Interactive Macros . . . . . . . . . . . . . . . . . . . . . . . . . . 230

D.5 Local Macros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

E Matrix Algebra in Minitab

233

E.1 Creating Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 234

E.2 Commands for Matrix Operations . . . . . . . . . . . . . . . . . 238

Index

243

Preface

This Minitab manual is to be used as an accompaniment to Introduction to the Practice of Statistics, Fifth Edition, by David S. Moore and George P. McCabe, and to the CD-ROM that accompanies this text. We abbreviate the textbook title as IPS. It can be used with either Minitab Student Version 14, Minitab Version 14 or Minitab Version 13 running under Windows. The text is based on Minitab Student Version 14 and Minitab Version 14, but we have also indicated in the manual wherever there are differences with Minitab Version 13, in the way these versions work. The core of the manual is a discussion of the menu commands while not neglecting to refer to the session commands, as these are needed for certain problems. The material on session commands is always at the end of each section and can be skipped if the reader will de?nitely not be using them. We have provided some Exercises for each chapter.

Minitab is a statistical software package that was designed especially for the teaching of introductory statistics courses. It is our view that an easy-to-use statistical software package is a vital and signi?cant component of such a course. This permits the student to focus on statistical concepts and thinking rather than computations or the learning of a statistical package. The main aim of any introductory statistics course should always be the "why" of statistics rather than technical details that do little to stimulate the majority of students or, in our opinion, do little to reinforce the key concepts. IPS succeeds admirably in communicating the important basic foundations of statistical thinking, and it is hoped that this manual serves as a useful adjunct to the text.

It is natural to ask why Minitab is advocated for the course. In the author's experience, ease of learning and use are the salient features of the package, with obvious bene?ts to the student and to the instructor, who can relegate many details to the software. While more sophisticated packages are necessary for higher-level professional work, it is our experience that attempting to teach one of these in a course forces too much attention on technical aspects. The time students need to spend to learn Minitab is relatively small and it is a great virtue. Further Minitab will serve as a perfectly adequate tool for many of the statistical problems students will encounter in their undergraduate education.

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This manual is divided into two parts. Part I is an introduction that provides the necessary details to start using Minitab and, in particular, how to use worksheets. We recommend reading Part I before starting to use Minitab. Overall, the introductory Part I serves as a reference for most of the nonstatistical commands in Minitab.

Part II follows the structure of the textbook. Each chapter is titled and numbered as in IPS. The last two chapters are not in IPS but correspond to optional material included on the CD-ROM. The Minitab commands relevant to doing the problems in each IPS chapter are introduced and their use illustrated. Each chapter concludes with a set of exercises, some of which are modi?cations of or related to problems in IPS and many of which are new and speci?cally designed to ensure that the relevant Minitab material has been understood. There are also appendices dealing with some more advanced features of Minitab, such as programming in Minitab and matrix algebra.

This manual does not attempt a complete coverage of Minitab. Rather, we introduce and discuss those concepts in Minitab that we feel are most relevant for a student studying introductory statistics with IPS. We do introduce some concepts that are, strictly speaking, not necessary for solving the problems in IPS where we feel that they were likely to prove useful in a large number of data analysis problems encountered outside the classroom. While the manual's primary goal is to teach Minitab, generally we want to help develop strong data analytic skills in conjunction with the text and the CD-ROM.

Thanks to W. H. Freeman and Company for their help and consideration. Also thanks to Rosemary and Heather.

For further information on Minitab software, contact:

Minitab Inc. 3081 Enterprise Drive State College, PA 16801 USA

ph: 814.328.3280 fax: 814.238.4383 email: Info@ URL:

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