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FOOTNOTES:
[A] Before I left Tennenji he wrote in one of my sketch-books the poem inscribed
above in Japanese characters. The reading is, “Yukuri no Omi no midzu-umi no fukaki
kokoro wa chiyomo chigiran,” and it may be roughly translated thus: Deep as the](https://image.slidesharecdn.com/95315-250416215456-0f7378c6/85/Applied-Statistical-Inference-with-MINITAB-Sally-Lesik-35-320.jpg)
![water of Lake Biwa, my heart has been ever true and changeless since chance brought
us together.
[B] “Daikon” is a large kind of white radish, which is boiled and cut in strips and
served as a savor with every meal; it is very tough, and both the smell and the flavor
are repulsive. A well-known Yokohama poet has written some verses on the subject,
which show a great knowledge of culinary French, and a rooted dislike to the
vegetable which is shared by most foreigners. It commences in this way:
Cook loquitur (gently).
Won’t daikon do
To stew
With carrots and a bean or two?
Methinks ’twould give a savor rare
To cutlets à la Financière.
Won’t daikon do?
Master (decisively).
No—daikon will not do!](https://image.slidesharecdn.com/95315-250416215456-0f7378c6/85/Applied-Statistical-Inference-with-MINITAB-Sally-Lesik-36-320.jpg)
Applied Statistical Inference with MINITAB Sally Lesik
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- 5. Applied Statistical Inference with MINITAB Sally Lesik Digital Instant Download Author(s): Sally Lesik ISBN(s): 9781420065848, 142006584X Edition: Har/Cdr File Details: PDF, 14.83 MB Year: 2009 Language: english
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- 8. STATISTICS: Textbooks and Monographs D. B. Owen Founding Editor, 1972–1991 Editors N. Balakrishnan McMaster University William R. Schucany Southern Methodist University Editorial Board Thomas B. Barker Rochester Institute of Technology Paul R. Garvey The MITRE Corporation Subir Ghosh University of California, Riverside David E. A. Giles University of Victoria Arjun K. Gupta Bowling Green State University Nicholas Jewell University of California, Berkeley Sastry G. Pantula North Carolina State University Daryl S. Paulson Biosciences Laboratories, Inc. Aman Ullah University of California, Riverside Brian E. White The MITRE Corporation C6583_C000.indd 3 11/20/09 11:11:48 AM © 2010 by Taylor & Francis Group, LLC
- 9. STATISTICS: Textbooks and Monographs Recent Titles Nonparametric Statistical Inference, Fourth Edition, Revised and Expanded, Jean Dickinson Gibbons and Subhabrata Chakraborti Computer-Aided Econometrics, edited by David E.A. Giles The EM Algorithm and Related Statistical Models, edited by Michiko Watanabe and Kazunori Yamaguchi Multivariate Statistical Analysis, Second Edition, Revised and Expanded, Narayan C. Giri Computational Methods in Statistics and Econometrics, Hisashi Tanizaki Applied Sequential Methodologies: Real-World Examples with DataAnalysis, edited by Nitis Mukhopadhyay, Sujay Datta, and Saibal Chattopadhyay Handbook of Beta Distribution and Its Applications, edited by Arjun K. Gupta and Saralees Nadarajah Item Response Theory: Parameter Estimation Techniques, Second Edition, edited by Frank B. Baker and Seock-Ho Kim Statistical Methods in Computer Security, edited by William W. S. Chen Elementary Statistical Quality Control, Second Edition, John T. Burr Data Analysis of Asymmetric Structures, Takayuki Saito and Hiroshi Yadohisa Mathematical Statistics with Applications, Asha Seth Kapadia, Wenyaw Chan, and Lemuel Moyé Advances on Models, Characterizations and Applications, N. Balakrishnan, I. G. Bairamov, and O. L. Gebizlioglu Survey Sampling: Theory and Methods, Second Edition, Arijit Chaudhuri and Horst Stenger Statistical Design of Experiments with Engineering Applications, Kamel Rekab and Muzaffar Shaikh Quality by Experimental Design, Third Edition, Thomas B. Barker Handbook of Parallel Computing and Statistics, Erricos John Kontoghiorghes Statistical Inference Based on Divergence Measures, Leandro Pardo A Kalman Filter Primer, Randy Eubank Introductory Statistical Inference, Nitis Mukhopadhyay Handbook of Statistical Distributions with Applications, K. Krishnamoorthy A Course on Queueing Models, Joti Lal Jain, Sri Gopal Mohanty, and Walter Böhm Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition, Kevin Kim and Neil Timm Randomization Tests, Fourth Edition, Eugene S. Edgington and Patrick Onghena Design and Analysis of Experiments: Classical and Regression Approaches with SAS, Leonard C. Onyiah Analytical Methods for Risk Management: A Systems Engineering Perspective, Paul R. Garvey Confidence Intervals in Generalized Regression Models, Esa Uusipaikka Introduction to Spatial Econometrics, James LeSage and R. Kelley Pace Acceptance Sampling in Quality Control, Edward G. Schilling and Dean V. Neubauer Applied Statistical Inference with MINITAB, Sally A. Lesik C6583_C000.indd 4 11/20/09 11:11:48 AM © 2010 by Taylor & Francis Group, LLC
- 10. Sally A. Lesik Central Connecticut State University New Britain, Connecticut, U.S.A. Applied Statistical Inference with MINITAB® C6583_C000.indd 5 11/20/09 11:11:48 AM © 2010 by Taylor & Francis Group, LLC
- 11. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20110725 International Standard Book Number-13: 978-1-4200-6584-8 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com © 2010 by Taylor & Francis Group, LLC
- 12. Dedication To DHK … for all the laughter and the joy. To NNK … for believing. C6583_C000e.indd 7 11/19/09 4:50:14 PM © 2010 by Taylor & Francis Group, LLC
- 13. C6583_C000e.indd 8 11/19/09 4:50:14 PM © 2010 by Taylor & Francis Group, LLC
- 14. ix Contents Preface. ................................................................................................................... xiii Acknowledgments..............................................................................................xvii 1 Introduction......................................................................................................1 1.1 What This Book Is About. ..............................................................................1 1.1.1 Graphical Displays of Data................................................................2 1.1.2 Descriptive Representations of Data................................................2 1.1.3 Basic Statistical Inference. ..................................................................3 1.1.4 Regression Analysis...........................................................................3 1.1.5 Analysis of Variance...........................................................................3 1.2 Types of Studies..............................................................................................4 1.3 What Is Statistics?...........................................................................................5 1.4 Types of Variables...........................................................................................6 1.5 Classification of Variables..............................................................................7 1.6 Entering Data into MINITAB®......................................................................9 Exercises..................................................................................................................12 2 Graphing Variables.......................................................................................15 2.1 Introduction...................................................................................................15 2.2 Histograms....................................................................................................15 2.3 Using MINITAB to Create Histograms.....................................................17 2.4 Stem-and-Leaf Plots. .....................................................................................18 2.5 Using MINITAB to Create a Stem-and-Leaf Plot.....................................23 2.6 Bar Charts......................................................................................................24 2.7 Using MINITAB to Create a Bar Chart......................................................24 2.8 Box Plots.........................................................................................................25 2.9 Using MINITAB to Create Box Plots..........................................................30 2.10 Scatter Plots. ...................................................................................................31 2.11 Using MINITAB to Create Scatter Plots. ....................................................35 2.12 Marginal Plots...............................................................................................39 2.13 Using MINITAB to Create Marginal Plots................................................39 Exercises..................................................................................................................39 3 Descriptive Representations of Data and Random Variables..............49 3.1 Introduction...................................................................................................49 3.2 Descriptive Statistics ...................................................................................49 3.3 Measures of Center.......................................................................................50 3.4 Measures of Spread......................................................................................54 3.5 Using MINITAB to Calculate Descriptive Statistics................................58 C6583_C000toc.indd 9 11/19/09 4:51:15 PM © 2010 by Taylor & Francis Group, LLC
- 15. x Contents 3.6 Random Variables and Their Distributions.............................................. 61 3.7 Sampling Distributions................................................................................63 Exercises.................................................................................................................. 74 4 Basic Statistical Inference............................................................................83 4.1 Introduction...................................................................................................83 4.2 Confidence Intervals. ....................................................................................83 4.3 Using MINITAB to Calculate Confidence Intervals for a Population Mean...........................................................................................89 4.4 Hypothesis Testing: A One-Sample t-Test for a Population Mean........91 4.5 Using MINITAB for a One-Sample t-Test..................................................97 4.6 Power Analysis for a One-Sample t-Test................................................. 103 4.7 Using MINITAB for a Power Analysis for a One-Sample t-Test.......... 104 4.8 Confidence Interval for the Difference between Two Means............... 110 4.9 Using MINITAB to Calculate a Confidence Interval for the Difference between Two Means............................................................... 112 4.10 Testing the Difference between Two Means........................................... 115 4.11 Using MINITAB to Test the Difference between Two Means.............. 118 4.12 Using MINITAB to Create an Interval Plot............................................. 119 4.13 Using MINITAB for a Power Analysis for a Two-Sample t-Test.......... 121 4.14 Confidence Intervals and Hypothesis Tests for Proportions...............127 4.15 Using MINITAB for a One-Sample Proportion...................................... 131 4.16 Power Analysis for a One-Sample Proportion.......................................133 4.17 Differences between Two Proportions....................................................135 4.18 Using MINITAB for Two-Sample Proportion Confidence Intervals and Hypothesis Tests. ................................................................ 139 4.19 Power Analysis for a Two-Sample Proportion....................................... 141 Exercises................................................................................................................ 144 Reference ..............................................................................................................154 5 Simple Linear Regression..........................................................................155 5.1 Introduction.................................................................................................155 5.2 Simple Linear Regression Model..............................................................156 5.3 Model Assumptions................................................................................... 163 5.4 Finding the Equation of the Line of Best Fit...........................................164 5.5 Using MINITAB for Simple Linear Regression...................................... 167 5.6 Regression Inference.................................................................................. 171 5.7 Inferences about the Population Regression Parameters......................172 5.8 Using MINITAB to Test the Population Slope Parameter..................... 175 5.9 Confidence Intervals for the Mean Response for a Specific Value of the Predictor Variable............................................................................177 5.10 Prediction Intervals for a Response for a Specific Value of the Predictor Variable....................................................................................... 178 5.11 Using MINITAB to Find Confidence and Prediction Intervals. ...........180 Exercises................................................................................................................190 C6583_C000toc.indd 10 11/19/09 4:51:15 PM © 2010 by Taylor Francis Group, LLC
- 16. Contents xi 6 More on Simple Linear Regression. .........................................................193 6.1 Introduction................................................................................................. 193 6.2 Coefficient of Determination. .................................................................... 193 6.3 Using MINITAB to Find the Coefficient of Determination.................. 195 6.4 Sample Coefficient of Correlation. ............................................................ 196 6.5 Correlation Inference. .................................................................................200 6.6 Using MINITAB for Correlation Analysis..............................................204 6.7 Assessing Linear Regression Model Assumptions...............................204 6.8 Using MINITAB to Create Exploratory Plots of Residuals...................206 6.9 Formal Test of the Normality Assumption............................................. 217 6.10 Using MINITAB for the Ryan–Joiner Test............................................... 219 6.11 Assessing Outliers...................................................................................... 219 6.12 Assessing Outliers: Leverage Values.......................................................221 6.13 Using MINITAB to Calculate Leverage Values......................................222 6.14 Assessing Outliers: Internally Studentized Residuals..........................225 6.15 Using MINITAB to Calculate Internally Studentized Residuals.........226 6.16 Assessing Outliers: Cook’s Distances......................................................228 6.17 Using MINITAB to Find Cook’s Distances.............................................228 6.18 How to Deal with Outliers........................................................................229 Exercises................................................................................................................231 References. .............................................................................................................238 7 Multiple Regression Analysis. ..................................................................239 7.1 Introduction.................................................................................................239 7.2 Basics of Multiple Regression Analysis...................................................239 7.3 Using MINITAB to Create a Matrix Plot.................................................242 7.4 Using MINITAB for Multiple Regression. ...............................................245 7.5 Coefficient of Determination for Multiple Regression..........................248 7.6 Analysis of Variance Table........................................................................248 7.7 Testing Individual Population Regression Parameters.........................253 7.8 Using MINITAB to Test Individual Regression Parameters. ................256 7.9 Multicollinearity.........................................................................................257 7.10 Variance Inflation Factors..........................................................................258 7.11 Using MINITAB to Calculate Variance Inflation Factors...................... 261 7.12 Multiple Regression Model Assumptions...............................................264 7.13 Using MINITAB to Check Multiple Regression Model Assumptions...............................................................264 7.14 Quadratic and Higher-Order Predictor Variables.................................268 7.15 Using MINITAB to Create a Quadratic Variable....................................268 Exercises................................................................................................................273 8 More on Multiple Regression...................................................................277 8.1 Introduction.................................................................................................277 8.2 Using Categorical Predictor Variables.....................................................277 8.3 Using MINITAB for Categorical Predictor Variables............................279 C6583_C000toc.indd 11 11/19/09 4:51:16 PM © 2010 by Taylor Francis Group, LLC
- 17. xii Contents 8.4 Adjusted R2..................................................................................................284 8.5 Best Subsets Regression.............................................................................289 8.6 Using MINITAB for Best Subsets Regression.........................................296 8.7 Confidence and Prediction Intervals for Multiple Regression.............298 8.8 Using MINITAB to Calculate Confidence and Prediction Intervals for a Multiple Regression Analysis. .........................................299 8.9 Assessing Outliers......................................................................................302 Exercises................................................................................................................303 9 Analysis of Variance (ANOVA)................................................................307 9.1 Introduction.................................................................................................307 9.2 Basic Experimental Design. .......................................................................307 9.3 One-Way ANOVA.......................................................................................309 9.4 Model Assumptions................................................................................... 316 9.5 Assumption of Constant Variance........................................................... 317 9.6 Normality Assumption..............................................................................322 9.7 Using MINITAB for One-Way ANOVAs.................................................323 9.8 Multiple Comparison Techniques............................................................338 9.9 Using MINITAB for Multiple Comparisons...........................................343 9.10 Power Analysis and One-Way ANOVA. ..................................................344 Exercises................................................................................................................348 References. .............................................................................................................351 10 Other Topics. .................................................................................................353 10.1 Introduction.................................................................................................353 10.2 Two-Way Analysis of Variance.................................................................353 10.3 Using MINITAB for a Two-Way ANOVA. ...............................................360 10.4 Nonparametric Statistics. ...........................................................................377 10.5 Wilcoxon Signed-Rank Test.......................................................................378 10.6 Using MINITAB for the Wilcoxon Signed-Rank Test............................382 10.7 Kruskal–Wallis Test....................................................................................388 10.8 Using MINITAB for the Kruskal–Wallis Test......................................... 391 10.8 Basic Time Series Analysis........................................................................398 Exercises................................................................................................................ 411 Appendix A.......................................................................................................... 415 Index......................................................................................................................427 C6583_C000toc.indd 12 11/19/09 4:51:16 PM © 2010 by Taylor Francis Group, LLC
- 18. xiii xiii Preface There are numerous statistics books that are available for readers who are learning statistics for the first time. What distinguishes this book from many is that it presents statistics with an emphasis toward applications for readers who are not experts in statistics, but who want to learn about basic inferen- tial techniques and be able to implement such techniques in practice using a statistical software package. One characteristic of this text is that it is written in such a way that the material is presented in a seamless manner, thus mak- ing it easier to read and follow. By using a seamless step-by-step approach, readers are introduced to a topic, presented with the calculations in detail, provided with how to interpret the findings, and given an illustration of how to perform the same analysis with a statistical software program. Although this approach may be somewhat different than is presented in other texts, readers may find it easier to learn statistics by being exposed to all the calcu- lations and software details. This text is written to be beginner-friendly and is oriented toward the prac- tical use of statistics. The presentation leans less toward the theoretical side of statistics and is focused more on addressing the expectations of students and practitioners who are not experts in statistics but who are interested in getting an appreciation for applying statistical techniques using a statistical software program. One of the key features of this text is that the mathematical calcula- tions are presented in step-by-step detail. Presenting such detail on how the calculations are actually done by hand and the kinds of inferences that can be made comes from teaching a course on applied inference to undergradu- ate and graduate students who understood only the most basic statistical con- cepts, but who plan to use statistics in their senior or master’s theses. Many beginning readers of statistics tend to struggle when they are not presented with step-by-step details and are left to fill in the gaps of how a particular statistic is calculated. Although the prerequisite level of mathematics for this text is intermediate algebra, many novices still like to see the nuts-and-bolts of the calculations so they can get a better understanding of the concepts and to connect with what the software program is actually doing. Another key feature of this text is that instructions on how to use the statistical software package MINITAB® are incorporated in detail immediately following a topic. By presenting the software explanations immediately following a given topic, this allows the reader to learn about the topic and then see how to use a statistical package to arrive at the same conclusions as found when doing the calculations by hand. This style of presentation comes from watching many beginners become increasingly frustrated when trying to read through statistics text books where it was necessary to flip through the pages to try to relate the presentation of the C6583_C000g.indd 13 11/19/09 4:50:35 PM © 2010 by Taylor Francis Group, LLC
- 19. xiv Preface topic with the appropriate software package and commands. A part of creating a seamless presentation required using only a single statistical software package, specifically MINITAB. Using only a single software package provides the reader with the opportunity to focus on the details of a specific package without having to filter through the commands or output from other programs. The audience for this text can come from diverse disciplines. I chose to write this text to be useful for just about any field of study and especially for those students who attend colleges and universities that may not offer discipline-specific statistics courses. By not targeting any specific discipline, this allowed me to present examples and discussions based on data and sce- narios that are common to many students in their everyday lives. Perhaps the biggest challenge in writing this text is that many disciplines have their own spin on what topics should be presented as well as how they should be presented. Though such differences in emphasis and presentation across the various fields can often be seen as a source of tension, it pushed me to think more deeply about the subject and how to best express the concepts of applied statistical inference in a general and understandable way. In this text I tried to present the material as simply as possible without sacrificing the necessary technical details. Also, given differences in notation and ter- minology across fields, on many occasions I incorporated the notation and terminology that is used by MINITAB. The choice to use MINITAB as the single statistical software program for this text was an easy one. MINITAB is a very simple and easy to use statisti- cal package. But yet, MINITAB is also very sophisticated and many fields such as business and engineering actively use it. The clear menus and infor- mative dialog boxes make it a natural choice for a text such as this which is written for a novice with little or no experience using a statistical software package. The printouts are clear and easy to follow, while still presenting enough relevant information, and the graphics are excellent. Like many things in life, good data is hard to find. For the data sets used in this text, some were intentionally contrived and modified in order to be manageable enough to illustrate the step-by-step calculations and the infer- ences that can be made. By using smaller data sets, this allowed for the mathematical calculations to be done out in their entirety so that readers can follow through the step-by-step calculations if they wish. Other sets of data presented are either entire sets of actual data that are available from the public domain or subsets of data available from the public domain. Each chapter has a set of homework problems that were created to give the reader some practice in using the techniques and methods described in the text with real data. This text was written to establish the foundation for students to build on should they decide to study more advanced inferential statistics. Virtually every type of statistical inference in practice, from beginning to advanced, relies on confidence intervals, hypothesis testing, validating model C6583_C000g.indd 14 11/19/09 4:50:35 PM © 2010 by Taylor Francis Group, LLC
- 20. Preface xv assumptions, and power analysis. Since this book was written with these considerations emphasized throughout, it is my hope that readers will be able to generalize the basic framework of applied inference at just about any level. The topics covered and the order with which the topics are presented in this text may not follow most traditional texts. However, I decided to write a text that was oriented toward the practical use of statistics for those who may be contemplating using statistics in their own work. Chapter 1 presents a basic introduction to some common terminology that one is likely to encounter when learning statistics. Although conventions and definitions may differ across disciplines, I tried to use more common definitions and terminology throughout the text while also trying to stay consistent with notation and terminology that is used in MINITAB. Chapter 2 presents some basic graphs as well as how to create such graphs using MINITAB. The presentation of graphs such as the stem-and-leaf plot and the box plot are aligned with the conventions used in MINITAB. For instance, the stem-and-leaf plot generated in MINITAB will have an extra col- umn that includes the cumulative frequencies below and above the median, and the quartiles for the box plot are calculated by using interpolation. Chapter 3 presents basic descriptive statistics using both traditional hand- calculations along with MINITAB. The calculations are done out in detail to give students the chance to feel more comfortable with the notation and symbols that are introduced. Although somewhat untraditional, I also intro- duce random variables and sampling distributions in this chapter as I saw it as a natural extension of a way to describe variables. Chapter 4 presents basic statistical inference. I begin by deriving confi- dence intervals using the t-distribution, and I also emphasize the interpreta- tion of confidence intervals as students seem to get confused with what a confidence interval is really estimating. I also begin the discussion about hypothesis tests by testing a single population mean. I repeatedly elaborate on how inferences are made with confidence intervals and hypothesis test- ing by referring back to the sampling distribution of the sample mean. This chapter also covers basic inferences for proportions. Chapter 4 also provides a conceptual introduction to power analysis as well as how to use MINITAB to conduct a power analysis. Chapter 5 describes simple linear regression. To understand simple linear regression, one must have a good intuitive feel for what the line of best fit is. I elaborate on this topic by first presenting how a line for two random points can be used to express the relationship between two variables. I then show how the line of best fit is “better” in the sense that it is the single line that best fits the data. This chapter also provides an introduction to the model assumptions for simple linear regression and how to make inferences with the line of best fit. Chapter 6 provides more detail for simple linear regression by describ- ing the coefficient of determination, the sample correlation coefficient, and how to assess model assumptions. One key feature of this chapter is that it C6583_C000g.indd 15 11/19/09 4:50:35 PM © 2010 by Taylor Francis Group, LLC
- 21. xvi Preface introduces the Ryan–Joiner test as a formal test of the normality assumption. There is also a discussion on how to assess outliers by using leverage values, studentized residuals, and Cook’s distances. Chapter 7 provides an introduction to multiple regression analysis. The ANOVA table and the issue of multicollinearity are introduced. Chapter 8 provides more detail for multiple regression by introducing how to include categorical predictor variables, how to pick the best model, and how to assess outliers. Chapter 9 provides a conceptual introduction to basic experimental design and the basics of a one-way ANOVA. This chapter introduces Bartlett’s and Levene’s tests as a formal way to establish the assumption of constant vari- ance. Multiple comparison techniques are also introduced as well as power analysis for a one-way ANOVA. Chapter 10 provides a discussion of a two-way ANOVA in addition to some basic non-parametric analyses and basic time series analysis. The calculations for the test statistics for the Wilcoxon signed-rank test and the Kruskall–Wallis test are worked out in great detail to help the reader gain a greater understanding of the complexities of these tests. C6583_C000g.indd 16 11/19/09 4:50:36 PM © 2010 by Taylor Francis Group, LLC
- 22. xvii Acknowledgments There are so many people who contributed to this project over the past few years. I am particularly grateful to my friend and colleague Frank Bensics, who graciously agreed to edit many versions of this manuscript. His many suggestions, comments, and corrections brought a new perspective to the work. I am also grateful to my friend and colleague Zbigniew Prusak, who not only provided valuable comments about the content and presentation of the text, but who also sat in on my class on numerous occasions and provided valuable feedback about how students struggle when learning statistics. David Grubbs, Susan Horwitz, and the staff at Taylor Francis were most helpful. Not only was I encouraged to write the text as I saw fit, I also received continuous support, patience, and guidance along the way. I would also like to thank the reviewers for the numerous comments and corrections that help guide my writing. Finally, I would like to extend my gratitude and appreciation to my fiends, family, and colleagues who directly and indirectly contributed to this project. Correspondence Although a great amount of effort has gone into making this text clear and accurate, if you have any suggestions or comments regarding errors, content, or feel that some clarification is needed, please contact me at lesiks@ccsu.edu. I am interested in hearing your feedback and comments. Portions of the input and output contained in this publication/book are printed with permission of Minitab Inc. All material remains the exclusive property and copyright of Minitab Inc. All rights reserved. MINITAB® and all other trademarks and logos for the Company’s products and services are the exclusive property of Minitab Inc. All other marks referenced remain the property of their respective owners. See minitab.com for more information. C6583_C000h.indd 17 11/20/09 5:29:10 PM © 2010 by Taylor Francis Group, LLC
- 23. 1 1 Introduction 1.1 What This Book Is About Statistical inference involves collecting and analyzing data in order to answer a meaningful question of interest. For instance, a researcher in education may want to know if using computers in an algebra classroom is effective in helping students build their mathematical skills. A researcher in psychology may want to know whether children who play violent video games tend to have more disturbing thoughts than children who do not play violent video games. In other fields, such as environmental science, researchers may want to know what factors contribute to global warming by asking questions such as which makes and models of automobiles emit larger amounts of green- house gas. Once a researcher has described a problem he or she wishes to investigate, he or she will set out to collect or identify a set of data that consists of infor- mation about a variable or variables of interest. There are two basic types of data that can be collected, quantitative data and qualitative data. Quantitative data is numeric in form. The main purpose of collecting quan- titative data is to describe some phenomenon using numbers. For example, quantitative data could be collected to assess the effect of advertising on gross product sales. On the other hand, qualitative data is categorical in nature and describes some phenomenon using words. For instance, qualitative data can be used to describe what the learning environment is like in a given mathematics classroom by using words to describe the types of interactions between the students and the teacher and how students appear to be engaged in learning. Determining whether to collect quantitative or qualitative data is typi- cally driven by the characteristic or relationship that is being assessed and the type of data that is available. The purpose of this book is to introduce some of the different statistical methods and techniques that can be used to analyze data in a meaningful way. The methods and techniques that we will be considering in this book are broadly categorized as follows: Graphical displays of data Descriptive representations of data C6583_C001.indd 1 11/19/09 4:51:39 PM © 2010 by Taylor Francis Group, LLC
- 24. 2 Applied Statistical Inference with MINITAB Basic statistical inference Regression analysis Analysis of variance 1.1.1 Graphical Displays of Data Graphical displays of data visually describe some of the characteristics of a set of data by using different types of charts and graphs. The advantage to using charts and graphs to display data is that a large amount of informa- tion can be displayed in a concise manner. For example, suppose you are interested in comparing the fuel efficiency for the following four different makes and models of vehicles: the Toyota Corolla®, the Honda Civic®, the Ford Focus®, and the Chevrolet Aveo®. You could obtain the average miles per gallon for both city and highway driving for each of the models you are interested in and then graph the comparison between the different brands of cars by using a bar chart, as illustrated in Figure 1.1. Notice that Figure 1.1 graphically displays the city and highway miles per gallon for each of the different makes and models of cars, and thus allows you to make comparisons between the different cars. 1.1.2 Descriptive Representations of Data Descriptive representations of data consist of methods and techniques that can be used to describe and summarize data. For instance, if you have ever shopped for a new car you may have noticed that the sticker on the window Car City/Highway 40 30 20 10 0 MPG Chart of MPG City Highway City Highway Toyota Corolla Honda Civic Ford Focus Chevrolet Aveo City Highway City Highway Figure 1.1 Bar chart comparing city and highway mileage per gallon based on the different brands of cars. C6583_C001.indd 2 11/19/09 4:51:40 PM © 2010 by Taylor Francis Group, LLC
- 25. Introduction 3 of the car provides the average miles per gallon of gasoline for both city and highway driving. This value describes, on average, the gas mileage that you can expect from the vehicle. For example, the sticker on the window of the 2007 Ford Focus® suggests that, on average, the vehicle will get 27 miles per gallon of gasoline driving in the city and 37 miles per gallon driving on the highway (http:/ /www.fueleconomy.gov/feg/byclass.htm). 1.1.3 Basic Statistical Inference Basic statistical inference relies on estimating or predicting an unknown char- acteristic of interest by using available data. For example, suppose that a crimi- nologist wants to know whether the average yearly crime rate in the United States has increased over the last year. Because it can be very difficult and time- consuming to obtain the yearly crime rate for every single community in the United States, the criminologist may decide to collect a representative sample of the communities in the United States along with their respective crime rates for the past 2 years. Then by using the available information obtained from this representative sample of communities, the criminologist could then try to make an inference or prediction about whether the crime rate has increased over the past year for the entire United States. 1.1.4 Regression Analysis Regression analysis is a statistical technique that consists of developing and validating models that can be used to describe how one variable is related to another variable or collection of different variables. For instance, the price of a house is determined by many factors, such as square footage, lot size, number of bedrooms, number of bathrooms, and age. Regression analysis would allow you to develop a model that describes how the price of a house is related to these factors. 1.1.5 Analysis of Variance Analysis of variance is a statistical technique that can be used to estimate whether there are differences in averages between more than two groups based on some characteristic. For example, suppose you are interested in determining whether there is a difference in the number of pages you can print with four different brands of printer toner. One way to assess this could be to set up an experiment where you have four identical brands of print- ers and a total of sixteen printer cartridges (four printer cartridges of each brand). Then you could put the printer cartridges in each of the printers and count up the total number of pages that each printer printed with the given cartridge. An analysis of variance could then be used to see if there is a dif- ference in the average (or mean) number of pages printed across the different brands of printer cartridges. C6583_C001.indd 3 11/19/09 4:51:40 PM © 2010 by Taylor Francis Group, LLC
- 26. Discovering Diverse Content Through Random Scribd Documents
- 27. THE TEMPLE GARDEN, SEIGWANJI streets, and were being cleaned up in preparation for the day’s performances. The town is studded with tall fire-proof go-downs, in which the precious vehicles are safely stored during the rest of the year. Near Maibara there were large orchards of persimmons with brilliant- colored fruit, which, as Andrew Marvel says of the oranges, “hang like gold lamps in a green night.” They were particularly beautiful in the well- designed garden of Seigwanji, where I made some sketches. It is a fine example of a temple garden, and some massive evergreen oaks form an impressive background to the gray stones, the carefully trained pines, and the trimly clipped shrubs; but except for the persimmons, a few reddening maple leaves, some late blooms of platycodon, and the scarlet berries of a little ardisia, it was all green and gray. In the cottage gardens near Suzukawa, a little station on the Tokaido to the south of Fuji where I made a short halt late in October, I began to see some chrysanthemum flowers; they were not particularly fine or effective, but I found plenty to paint there, and wished very much that the days and my remaining weeks in Japan were not getting so short. The village lies behind a range of sand dunes, which are overgrown with
- 28. MINIATURE PAGODA IN THE TEMPLE GARDEN, SEIGWANJI ancient pines, and beyond them is the shore of Suruga Bay, a grand expanse of gray volcanic sand, called by the Japanese Tago- no-ura, where fishermen are always hauling at nets in lines of naked brown figures against the blue sea, or wandering back in groups across the sands in long dark- blue coats, with pale- blue and white handkerchiefs tied over their heads, carrying their nets and parcels of fish wrapped in straw. At my tea-house, the Koshuya, I reaped the result of their labors, and got excellent dinners of red or gray tai, lobsters, and huge prawns, cooked by a man who was a real artist and took a pride in his profession. The first really fine chrysanthemums I saw were in Yokohama, when I got back there early in November; I was disappointed to find that they were in temporary sheds put up to protect them from rain and sun, and not in masses out-of-
- 29. doors, as I expected to see them; but they were excellently grown, and in the softened light of the oil-paper shades their colors showed to great advantage. The plants are treated much as they are with us, raised in pots from cuttings taken in the spring, and encouraged with plenty of manure until the buds are formed; before flowering they are removed from their pots and planted out in bold groups of color in the beds which have been prepared for them. Some plants are reduced to a single stem, on which only one enormous blossom is allowed to develop; these are generally arranged in a line, with each flower stiffly tied to a horizontal bamboo support, and the effect is very sad; but the excellence of the gardeners is best shown in growing large bushes, which have been known to carry as many as four hundred flowers of medium size, all in perfect condition, on the same day. An English gardener who had visited every show within reach of Tōkyō, including the Emperor’s celebrated collection in the palace grounds, told me that he had seen no individual blossoms equal to the best dozen or so at a first-rate London exhibition, but that these great plants with their hundreds of flowers were A CHRYSANTHEMUM SHOW AT YOKOHAMA
- 30. triumphs of horticulture. The most curious examples of chrysanthemum- growing were to be seen in the Dangozaka quarter of Tōkyō. The long hilly street is bordered on each side with gardens enclosed with high bamboo fences, and in every one, by paying three rin, you could see groups of life- size figures mainly covered with chrysanthemum leaves and flowers. They represented scenes from history, the drama, or Buddhist mythology, and were constructed with frame-works of bamboo, inside which the flower-pots were concealed, the shoots being brought through the openings and trained over the outer surface. The heads and hands were made of painted wood, and swords and other accessories were added to make them more life-like; the draperies of living leaves and flowers were skilfully arranged in large folds, and, as in most of the popular shows, they depicted the costumes of Daimio and Samurai of the past. At each entrance I was given a sort of play-bill, a roughly printed broad-sheet with a wood-cut and a description of the different groups, serving as an advertisement of the gardener’s establishment. One of the finest places for autumn colors is the large garden behind the arsenal in the Koishikawa quarter, laid out by a former Prince of Mito as a quiet retreat for his old age. It covers several acres, and is certainly very beautiful, with its lakes and islands, solemn groves and shrines; but it is silent and deserted; the people are only admitted by a special permission; and I liked better the maples which line the banks of the Taki-no-gawa near Oji, where crowds were quietly enjoying themselves, sipping tea and saké as they sat in front of the tea-houses and gazed down on the trees, or strolling along in picturesque groups under the crimson canopy of foliage. The little river glides along with barely a ripple, and it reflected all the glory of the leaves which stretched over it in sprays of scarlet and gold, reminding me of a Japanese poem, “I wish to cross the river, but fear to cut the brocade on its surface.” Another poem, dating from the time when it was customary to present silk or cloth to the Shinto gods instead of the “gohei,” which now serve as a symbol, shows the national admiration of the autumn leaves: “This time I bring no offering; the gods can take the damask of the maple- trees on Tamukeyama.” There are many other trees in the rich flora of Japan which are as gay as the maples, though no others which show as great a variety of color; the dark leaves of the tulip-tree turn to a rich cadmium yellow, and the icho
- 31. (Salisburia) is covered with pale gold, while many of the shrubs, grasses, and herbaceous plants with bright and varied tints help to relieve the solemn everlasting green of the pines and cryptomerias which clothe the eternal hills. And so in a blaze of glory the Japanese year ends; but long before these last leaves have fallen the camellias are once more in flower, and continue until the plum blossom comes in February, a connecting link in the chain of beauty and flowers which encircles this happy land. One of my last days in Tōkyō was spent in showing my drawings to the students of the Uyeno School of Art, where Professor Okakura, the president, who combines with a good knowledge of Western art a great reverence for that of his own country, is attempting with no small success to keep up the artistic tradition, and to revive those artistic industries which were falling into decay. He had invited artists of other schools, some of whom had studied in Paris and Rome, but I was most interested in the remarks and questions of the purely Japanese students, and in their eagerness to discover any motive, besides the reproduction of nature, in work so different from their own. At the Asakusa matsuri they were already selling emblems suited for the new year—the rice-rake to scrape
- 32. THE ARSENAL GARDEN, KOISHIKAWA, TŌKYŌ together dollars; the rice-bag, daikon, and red tai, suggestive of good fare; and the target with an arrow in the bull’s-eye, meaning, “May you hit the mark!” arranged round a mask of the goddess of fortune; and with a stock of these to bring me good-luck, I sailed away on the 10th of December across the dreary and flowerless Pacific.
- 35. LYCHNIS GRANDIFLORA, MISAKA-TOGE BOOKS WITH ILLUSTRATIONS BY ALFRED PARSONS ——— A SELECTION FROM THE SONNETS OF WILLIAM WORDSWORTH. Illustrated by Alfred Parsons. 4to, Full Leather, Gilt Edges, $5 00. (In a Box.) THE WARWICKSHIRE AVON. Notes by A. T. Quiller-Couch. Illustrations by Alfred Parsons. 8vo, Ornamental Half Leather, $2 00. THE QUIET LIFE. Certain Verses by Various Hands: the Motive set forth in a Prologue and Epilogue by Austin Dobson; the whole Adorned with Numerous Drawings by Edwin A. Abbey and Alfred Parsons. 4to, Ornamental Leather, Gilt Edges, $7 50. (In a Box.) OLD SONGS. With Drawings by Edwin A. Abbey and Alfred Parsons. With Mounted India Proof Frontispiece, left loose for framing. 4to, Ornamental Leather Cover, Gilt Edges, $7 50. (In a Box.) ——— Published by HARPER BROTHERS, New York. FOOTNOTES: [A] Before I left Tennenji he wrote in one of my sketch-books the poem inscribed above in Japanese characters. The reading is, “Yukuri no Omi no midzu-umi no fukaki kokoro wa chiyomo chigiran,” and it may be roughly translated thus: Deep as the
- 36. water of Lake Biwa, my heart has been ever true and changeless since chance brought us together. [B] “Daikon” is a large kind of white radish, which is boiled and cut in strips and served as a savor with every meal; it is very tough, and both the smell and the flavor are repulsive. A well-known Yokohama poet has written some verses on the subject, which show a great knowledge of culinary French, and a rooted dislike to the vegetable which is shared by most foreigners. It commences in this way: Cook loquitur (gently). Won’t daikon do To stew With carrots and a bean or two? Methinks ’twould give a savor rare To cutlets à la Financière. Won’t daikon do? Master (decisively). No—daikon will not do!
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