Statistics with JMP: Hypothesis Tests, ANOVA and Regression

Peter Goos, David Meintrup

• Publisher: Wiley
• Year: 2016
• Print ISBN: 9781119097150
• eBook ISBN: 9781119097167
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Part One
Estimators and Tests

1
Estimating 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)

A major goal in statistics is to make statements about populations or processes. Often, the interest is in specific parameters of the distributions or densities of the populations or processes under study. For instance, researchers in political science want to make statements about the proportion of a population that votes for a certain political party. Industrial engineers want to make statements about the proportion of defective smartphones produced by a production process. Bioscience engineers are interested in comparing the mean amounts of growth resulting from applying two or more different fertilizers. Economists are interested in income inequality and may want to compare the variance in income across different groups.

To be able to make such statements, the proportions, means, and variances under study need to be quantified. In statistical jargon, we say that these parameters need to be estimated. It is also important to quantify how reliable each of the estimates is, in order to judge the confidence we can have in any statement we make. This chapter discusses the properties of the most important sample statistics that are used to make statements about population and process means, proportions, and variances.

1.1 Introduction: Estimators Versus Estimates

In practice, population parameters such as μ, σ², π, and λ (see our book Statistics with JMP: Graphs, Descriptive Statistics and Probability) are rarely known. For example, if we study the arrival times of the customers of a bank, we know that the number of arrivals per unit of time often follows a Poisson¹ distribution. However, we do not know the exact value of the distribution’s parameter λ. One way or another, we therefore need to estimate this parameter. This estimate will be based on a number of measurements or observations, x₁, x₂, …, x_n, that we perform in the bank; in other words, on the sample data we collect.

The estimate for the u...

Table of contents

• Cover
• Title page
• Copyright
• Dedication
• Preface
• Acknowledgments
• Part One Estimators and Tests
• Part Two One Population
• Part Three Two Populations
• Part Four More Than Two Populations
• Part Five Additional Useful Tests and Procedures
• Appendix A The Binomial Distribution
• Appendix B The Standard Normal Distribution
• Appendix C The χ2-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