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Introductory Statistics: A Conceptual Approach Using R PDF

521 Pages·2013·4.525 MB·English
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INTRODUCTORY STATISTICS A CONCEPTUAL APPROACH USING R WILLIAM B. WARE, JOHN M. FERRON AND BARBARA M. MILLER Introductory Statistics Introductory Statistics: A Conceptual Approach Using R William B. Ware University of North Carolina at Chapel Hill John M. Ferron University of South Florida Barbara M. Miller Elon University First published 2013 by Routledge 711 Third Avenue, New York, NY 10017 Simultaneously published in the UK by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2013 Taylor & Francis The right of William B. Ware, John M. Ferron, and Barbara M. Miller to be identified as the authors of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data Ware, William B., author. Introductory statistics : a conceptual approach using R / William B. Ware, University of North Carolina at Chapel Hill, John M. Ferron, University of South Florida, Barbara M. Miller, Elon University.–1 [edition]. pages cm Includes bibliographical references and index. 1. Mathematical statistics–Textbooks. 2. R (Computer program language) I. Ferron, John M., author. II. Miller, Barbara Manning, author. III. Title. QA276.W365 2013 519.5–dc23 2012024922 ISBN: 978–0–8058–3651–6 (hbk) ISBN: 978–0–415–99600–6 (pbk) ISBN: 978–0–203–83737–5 (ebk) Typeset in Times New Roman and Helvetica Neue by Swales and Willis Ltd, Exeter, Devon Dedications To all the people from whom I’ve learned. In particular, I would point to my parents, Helen and Howard; my teachers in the Verona (NJ) public schools; my high school principal who encour- aged me to teach, Edwin A. Willard; my professors at Dartmouth College and Northwestern Uni- versity; my children, and especially my wife, Barbara. But most of all, I dedicate this book to the memory of my doctoral chair, Norman Dale Bowers; he was my teacher, my mentor, and my friend. After my final defense, he suggested that we write a book. Norman, now we have and, in this work, your spirit lives on. WBW I am very grateful to my major professor and mentor Dr William Ware. Over the years he has taught me a great deal about statistics and a great deal about teaching. I would also like to thank my colleagues, both faculty and students, in the Department of Educational Measurement and Research at USF. They have created a very supportive environment that has helped me continue to learn statistics and to further develop as a teacher. Finally, I would like to thank my wife, Pam, who has been so supportive over the years, my children, Emily and Anne Marie, and my parents and siblings. JMF I am particularly indebted to the first author of this text, Dr William Ware, who encouraged my interest and exploration of statistics. He embodies the highest ideals of teaching and is an inspira- tion for the professor I hope to become. To all of my teachers in the Bluefield, WV, public school system, and professors at West Virginia University and UNC-CH, thank you. Lastly, I would also like to thank my husband, Kenn Gaither, and my parents, Frazier and Phyllis Miller, from whom I learn every day. BMM Contents List of Illustrations ix Preface xvii PART I 1 Introduction and Background 3 PART II DESCRIPTIVE STATISTICS 2 Describing Quantitative Data with Frequency Distributions 29 3 Describing Quantitative Data: Summary Statistics 56 4 Describing Categorical Data: Frequency Distributions, Graphics, and Summary Statistics 96 5 Describing the Position of a Case within a Set of Scores 108 6 Describing the Relationship between Two Quantitative Variables: Correlation 123 7 Describing the Relationship between Two Quantitative Variables: Regression 155 PART III THE FUNDAMENTALS OF STATISTICAL INFERENCE 8 The Essentials of Probability 193 9 Probability and Sampling Distributions 210 viii CONTENTS 10 The Normal Distribution 228 PART IV STATISTICAL INFERENCE 11 The Basics of Statistical Inference: Tests of Location 257 12 Other One-Sample Tests for Location 276 13 More One-Sample Tests 301 14 Two-Sample Tests of Location 331 15 Other Two-Sample Tests: Variability and Relationships 357 PART V k-SAMPLE TESTS 16 Tests on Location: Analysis of Variance and Other Selected Procedures 385 17 Multiple Comparison Procedures 420 18 Looking Back … and Beyond 439 Appendix A—Statistical Tables 447 Appendix B—An Introduction to R 478 Subject Index 488 Author Index 496 BOOK WEBSITE (AS APPROPRIATE FOR EACH CHAPTER) Answers to Practice Questions Answers to Exercises Large Data Set from the ECLS Study Codebook for the ECLS Data Set Other Computer Solutions: SPSS and SAS (see book website) R Scripts Data Files in Text Format Illustrations FIGURES Figure 1.1 A conceptual diagram of the population–sample distinction, with notation. 10 Figure 2.1 Histogram of the Fall Reading Scores for the White kindergarteners. 36 Figure 2.2 Histogram of the Fall Reading Scores for the African American kindergarteners. 37 Figure 2.3 Two different histograms depicting the same data. 37 Figure 2.4 Histogram of the data depicted in Figure 2.3, showing the break in the vertical axis. 38 Figure 2.5 Two ways to present unemployment data over a 4-year period. 39 Figure 2.6 The histogram and frequency polygon of the Fall Reading Scores for White kindergarteners, superimposed on the same graph. 39 Figure 2.7 A frequency polygon depicting the Fall Reading Scores of African American kindergarteners. 40 Figure 2.8 Ogives plotted for the White and African American students. 41 Figure 2.9 Stem-and-leaf displays for the Fall Reading Scores for both the White and African American students. 42 Figure 2.10 Several different frequency distributions. 43 Figure 2.11 Histogram of the Fall Reading Scores for White students entering kindergarten. 47 Figure 2.12 Histogram of the Fall Reading Scores for White students entering kindergarten, with jittering. 48 Figure 2.13 Histogram of the Fall Reading Scores for White students entering kindergarten, with jittering and the density distribution. 48 Figure 2.14 Histogram of the Fall Reading Scores for African American students entering kindergarten, with jittering. 50 Figure 2.15 Histogram of the Fall Reading Scores for African American students entering kindergarten, with jittering and the density distribution. 51 Figure 3.1 Separating the scores within an interval to find the median. 59 Figure 3.2 The mean as a product-moment statistic. 62 Figure 3.3 Comparing the density distributions for the mean, median, and mode. 65 Figure 3.4 Two distributions having the same center, but different variability. 65 Figure 3.5 Depicting the interquartile range. 66 Figure 3.6 Several distributions for discussing the shape of a distribution. 75 Figure 3.7 A generic box-and-whisker plot. 76 Figure 3.8 Several distributions differing in shape, with their skewness and kurtosis values. 78 Figure 3.9 Histogram of IRT math scores for White students entering kindergarten. 80 ix

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