INTRODUCTION TO STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL

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1 INTRODUCTION TO STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL

2 INTRODUCTION TO STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL Phillip I. Good A JOHN WILEY & SONS, INC., PUBLICATION

3 Copyright 2005 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, , fax , or on the web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) , fax (201) Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services please contact our Customer Care Department within the U.S. at , outside the U.S. at or fax Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Publication Data: Good, Phillip L Introduction to statistics through resampling methods and Microsoft Office Excel / Phillip I. Good. p. cm. Includes bibliographical references and index. ISBN-13: (acid-free paper) ISBN-10: (pbk : acid-free paper) 1. Resampling (Statistics) 2. Microsoft Excel (Computer file) I. Title. QA278.8.G dc Printed in the United States of America

4 Contents Preface xi 1. Variation (or What Statistics Is All About) Variation Collecting Data Summarizing Your Data Learning to Use Excel Reporting Your Results: the Classroom Data Picturing Data Displaying Multiple Variables Percentiles of the Distribution Types of Data Depicting Categorical Data From Observations to Questions Measures of Location Which Measure of Location? The Bootstrap Samples and Populations Drawing a Random Sample Ensuring the Sample is Representative Variation Within and Between Summary and Review Probability Probability Events and Outcomes Venn Diagrams Binomial Permutations and Rearrangements Back to the Binomial 47

5 vi CONTENTS The Problem Jury Properties of the Binomial Multinomial Conditional Probability Market Basket Analysis Negative Results Independence Applications to Genetics Summary and Review Distributions Distribution of Values Cumulative Distribution Function Empirical Distribution Function Discrete Distributions Poisson: Events Rare in Time and Space Applying the Poisson Comparing Empirical and Theoretical Poisson Distributions Continuous Distributions The Exponential Distribution The Normal Distribution Mixtures of Normal Distributions Properties of Independent Observations Testing a Hypothesis Analyzing the Experiment Two Types of Errors Estimating Effect Size Confidence Interval for Difference in Means Are Two Variables Correlated? Using Confidence Intervals to Test Hypotheses Summary and Review Testing Hypotheses One-Sample Problems Percentile Bootstrap Parametric Bootstrap Student s t Comparing Two Samples Comparing Two Poisson Distributions What Should We Measure? 94

6 CONTENTS vii Permutation Monte Carlo Two-Sample t-test Which Test Should We Use? p Values and Significance Levels Test Assumptions Robustness Power of a Test Procedure Testing for Correlation Summary and Review Designing an Experiment or Survey The Hawthorne Effect Crafting an Experiment Designing an Experiment or Survey Objectives Sample from the Right Population Coping with Variation Matched Pairs The Experimental Unit Formulate Your Hypotheses What Are You Going to Measure? Random Representative Samples Treatment Allocation Choosing a Random Sample Ensuring that Your Observations are Independent How Large a Sample? Samples of Fixed Size 121 Known Distribution 122 Almost Normal Data 125 Bootstrap Sequential Sampling 129 Stein s Two-Stage Sampling Procedure 129 Wald Sequential Sampling 129 Adaptive Sampling Meta-Analysis Summary and Review Analyzing Complex Experiments Changes Measured in Percentages Comparing More Than Two Samples 138

7 viii CONTENTS Programming the Multisample Comparison with Excel What Is the Alternative? Testing for a Dose Response or Other Ordered Alternative Equalizing Variances Stratified Samples Categorical Data One-Sided Fisher s Exact Test The Two-Sided Test Multinomial Tables Ordered Categories Summary and Review Developing Models Models Why Build Models? Caveats Regression Linear Regression Fitting a Regression Equation Ordinary Least Squares 162 Types of Data Least Absolute Deviation Regression Errors-in-Variables Regression Assumptions Problems with Regression Goodness of fit versus prediction Which Model? Measures of Predictive Success Multivariable Regression Quantile Regression Validation Independent Verification Splitting the Sample Cross-Validation with the Bootstrap Classification and Regression Trees Data Mining Summary and Review 193

8 CONTENTS ix 8. Reporting Your Findings What to Report Text, Table, or Graph? Summarizing Your Results Center of the Distribution Dispersion Reporting Analysis Results p Values? Or Confidence Intervals? Exceptions Are the Real Story Nonresponders The Missing Holes Missing Data Recognize and Report Biases Summary and Review Problem Solving The Problems Solving Practical Problems The Data s Provenance Inspect the Data Validate the Data Collection Methods Formulate Hypotheses Choosing a Statistical Methodology Be Aware of What You Don t Know Qualify Your Conclusions 218 Appendix: An Microsoft Office Excel Primer 221 Index to Excel and Excel Add-In Functions 227 Subject Index 229

9 Preface INTENDED FOR CLASS USE OR SELF-STUDY, this text aspires to introduce statistical methodology to a wide audience, simply and intuitively, through resampling from the data at hand. The resampling methods permutations and the bootstrap are easy to learn and easy to apply. They require no mathematics beyond introductory high-school algebra, yet are applicable in an exceptionally broad range of subject areas. Introduced in the 1930s, the numerous, albeit straightforward calculations resampling methods require were beyond the capabilities of the primitive calculators then in use. They were soon displaced by less powerful, less accurate approximations that made use of tables. Today, with a powerful computer on every desktop, resampling methods have resumed their dominant role and table lookup is an anachronism. Physicians and physicians in training, nurses and nursing students, business persons, business majors, research workers, and students in the biological and social sciences will find here a practical and easily grasped guide to descriptive statistics, estimation, testing hypotheses, and model building. For advanced students in biology, dentistry, medicine, psychology, sociology, and public health, this text can provide a first course in statistics and quantitative reasoning. For mathematics majors, this text will form the first course in statistics, to be followed by a second course devoted to distribution theory and asymptotic results. Hopefully, all readers will find my objectives are the same as theirs: To use quantitative methods to characterize, review, report on, test, estimate, and classify findings. Warning to the autodidact: You can master the material in this text without the aid of an instructor. But you may not be able to grasp even

10 xii PREFACE the more elementary concepts without completing the exercises. Whenever and wherever you encounter an exercise in the text, stop your reading and complete the exercise before going further. You ll need to download and install several add-ins for Excel to do the exercises, including BoxSampler, Ctree, DDXL, Resampling Statistics for Excel, and XLStat. All are available in no-charge trial versions. Complete instructions for doing the installations are provided in Chapter 1. For those brand new to Excel itself, a primer is included as an Appendix to the text. For a one-quarter short course, I d recommend taking students through Chapters 1 and 2 and part of Chapter 3. Chapters 3 and 4 would be completed in the winter quarter along with the start of chapter 5, finishing the year with Chapters 5, 6, and 7. Chapters 8 and 9 on Reporting Your Findings and Problem Solving convert the text into an invaluable professional resource. An Instructor s Manual is available to qualified instructors and may be obtained by contacting the Publisher. Please visit ftp://ftp.wiley.com/public/sci_tech_med/introduction_ statistics/ for instructions on how to request a copy of the manual. Twenty-eight or more exercises included in each chapter plus dozens of thought-provoking questions in Chapter 9 will serve the needs of both classroom and self-study. The discovery method is utilized as often as possible, and the student and conscientious reader are forced to think their way to a solution rather than being able to copy the answer or apply a formula straight out of the text. To reduce the scutwork to a minimum, the data sets for the exercises may be downloaded from ftp://ftp.wiley.com/public/sci_tech_med/statistics_ resampling. If you find this text an easy read, then your gratitude should go to Cliff Lunneborg for his many corrections and clarifications. I am deeply indebted to the students in the Introductory Statistics and Resampling Methods courses that I offer on-line each quarter through the auspices of statistics.com for their comments and corrections. Phillip I. Good Huntington Beach, CA frere_until@hotmail.com

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