Introductory Statistics: A Conceptual Approach Using R

521 Pages·2013·4.525 MB·English

by  William B. Ware, John M. Ferron, Barbara M. Miller

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
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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