Statistical Concepts : A Second Course for title: Education and the Behavioral Sciences author: Lomax, Richard G. publisher: Lawrence Erlbaum Associates, Inc. isbn10 | asin: 0805830510 print isbn13: 9780805830514 ebook isbn13: 9780585278537 language: English Statistics--Study and teaching (Higher) , subject Mathematical statistics--Study and teaching (Higher) publication date: 1998 lcc: QA276.12.L66 1998eb ddc: 519.5 Statistics--Study and teaching (Higher) , Mathematical statistics--Study and teaching subject: (Higher) Page iii Statistical Concepts A Second Course for Education and the Behavioral Sciences Richard G. Lomax Boston College Originally published 1992. Copyright © 1998 by Lawrence Erlbaum Associates, Inc. All rights reserved. No part of this book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without the prior written permission of the publisher. Lawrence Erlbaum Associates, Inc., Publishers 10 Industrial Avenue Mahwah, New Jersey 07430 Library of Congress Cataloging-in-Publication Data Lomax, Richard G. Statistical concepts: a second course for education and the behavioral sciences / by Richard G. Lomax. p. cm. Originally published: New York: Longman, c1992. Includes bibliographical references (p. - ) and index. ISBN 0-8058-3051-0 (paperback: alk. paper) 1. Statistics. I. Title. QA276.12.L66 1998 519.5dc21 97-46865 CIP Books published by Lawrence Erlbaum Associates are printed on acid-free paper, and their bindings are chosen for strength and durability. Printed in the United States of America 10 9 8 7 6 5 4 3 2 Page v Credits Tables found in the Appendix have been reprinted from the following sources: Tables 1, 2, 3, 4, 5, from Pearson, E.S., & Hartley, H.O. (1970), Biometrika tables for statisticians, respectively Tables 18, 12, 14, 1, 47, by permission of the Biometrika Trustees; Table 6 from Dunnett, C.W. (1955), A multiple comparison procedure for comparing several treatments with a control, Journal of the American Statistical Association, 50, 1096-1121, by permission of the American Statistical Association, and from Dunnett, C.W. (1964), New tables for multiple comparisons with a control, Biometrics, 20, 482-491, by permission of the Biometric Society; Table 7 from Games, P. A. (1977), An improved t table for simultaneous control of g contrasts, Journal of the American Statistical Association, 72, 531-534, by permission of the American Statistical Association, Table 8 from Harter, H.L. (1960), Tables of range and studentized range, Annals of Mathematical Statistics, 31, 1122-1147, by permission of the Institute of Mathematical Statistics; Table 9 from Duncan, D.B. (1955), Multiple range and multiple F tests, Biometrics, 11, 1-42, by permission of the Biometric Society; Table 10 from Pearson, E.S., & Hartley, H.O. (1970), Biometrika tables for statisticians, Table 8, by permission of the Biometrika Trustees; and Table 11 from Bryant, J.L., & Paulson, A.S. (1976), An extension of Tukey's method of multiple comparisons to experimental designs with random concomitant variables, Biometrika, 63, 631-638, by permission of the Biometrika Trustees. Page vii This book is dedicated to Lea and Kristen and to students who have seen the light Page ix Contents List of Figures xiii List of Tables xv Preface xix Chapter 1 1 A Review of Simple Linear Regression Introduction to the Concepts of Simple Linear 2 Regression The Population Simple Linear Regression Equation 5 The Sample Simple Linear Regression Equation 6 Summary 38 References 39 Optional Section 1.1Proof that and 40 Optional Section 1.2Partitioning the Variance of Y 41 Chapter Problems 43 Chapter 2 48 Multiple Regression Partial and Semipartial Correlations 49 Multiple Linear Regression 53 Variable Selection Procedures 74 Page x Nonlinear Regression 79 Summary 82 References 82 Chapter Problems 83 Chapter 3 87 One-Factor Analysis of VarianceFixed-Effects Model Characteristics of the One-Factor ANOVA Model 89 The Layout of the Data 92 ANOVA Theory 93 The ANOVA Model 99 Expected Mean Squares 105 Assumptions and Violation of Assumptions 107 The Unequal n's Procedure 111 The Kruskal-Wallis One-Factor Analysis of Variance 112 The Relationship of ANOVA to Regression Analysis 115 Summary 118 References 118 Optional Section 3.1Proof of the Sums of Squares 119 Partitioning Chapter Problems 120 Chapter 4 125 Multiple Comparison Procedures