Research design and statistical analysis

877 Pages·2003·16.437 MB·English

by  Jerome L Myers, A Well

Research Design and Statistical Analysis
Second Edition

Research Design and
Statistical Analysis
Second Edition
Jerome L.Myers
Arnold D.Well
University of Massachusetts

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Copyright © 2003 by Lawrence Erlbaum Associates, Inc.
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Library of Congress Cataloging-in-Publication Data
Myers, Jerome L.
Research design and statistical analysis/Jerome L.Myers, Arnold D.Well.—2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN 0-8058-4037-0 (case only: alk. paper)
1. Experimental design. 2. Mathematical statistics. I. Well, A. (Arnold) II. Title.
QA279.M933 2002
519.5(cid:237)dc21
2002015266
ISBN 1-4106-0703-8 Master e-book ISBN
To Nancy and Susan

Contents

Preface xv

CHAPTER 1 INTRODUCTION 1

1.1 Variability and the Need for Statistics 1
1.2 Systematic Versus Random Variability 3
1.3 Error Variance Again 5
1.4 Reducing Error Variance 5
1.5 Overview of the Book 6
1.6 Concluding Remarks 7

CHAPTER 2 LOOKING AT DATA: UNIVARIATE DISTRIBUTIONS 10

2.1 Introduction 10
2.2 Exploring a Single Sample 10
2.3 Comparing Two Data Sets 18
2.4 Other Measures of Location and Spread: The Mean and
20
Standard Deviation
2.5 Standardized (z) Scores 28
2.6 Measures of the Shape of a Distribution 30
2.7 Concluding Remarks 34

CHAPTER 3LOOKING AT DATA: RELATIONS BETWEEN
QUANTITATIVE VARIABLES 39
3.1 Introduction 39

3.2 Some Examples 39
3.3 Linear Relations 45
3.4 The Pearson Product-Moment Correlation Coefficient 47
3.5 Linear Regression 54
2 59
3.6 The Coefficient of Determination, r
3.7 Influential Data Points and Resistant Measures of Regression 60
3.8 Describing Nonlinear Relations 60
3.9 Concluding Remarks 60
viii Contents

CHAPTER 4 PROBABILITY AND THE BINOMIAL DISTRIBUTION 66

4.1 Introduction 66
4.2 Discrete Random Variables 67
4.3 Probability Distributions 68
4.4 Some Elementary Probability 72
4.5 The Binomial Distribution 81
4.6 Means and Variances of Discrete Distributions 86
4.7 Hypothesis Testing 87
4.8 Independence and the Sign Test 94
4.9 More About Assumptions and Statistical Tests 97
4.10 Concluding Remarks 97

CHAPTER 5 ESTIMATION AND HYPOTHESIS TESTS: THE NORMAL
10 8
DISTRIBUTION
5.1 Introduction 108
5.2 Continuous Random Variables 108
5.3 The Normal Distribution 110
5.4 Point Estimates of Population Parameters 112
5.5 Inferences About Population Means: The One-Sample Case 121
5.6 Inferences About Population Means:
127
T he Correlated-SamplesCase
5.7 The Power of the z Test 129
5.8 Hypothesis Tests and CIs 132
5.9 Validity of Assumptions 133
5.10 Comparing Means of Two Independent Populations 135
5.11 The Normal Approximation to the Binomial Distribution 139
5.12 Concluding Remarks 141

CHAPTER 6 ESTIMATION, HYPOTHESIS TESTS, AND EFFECT SIZE:
THE t DISTRIBUTION 153
6.1 Introduction 153
6.2 Inferences About a Population Mean 154
6.3 The Standardized Effect Size 158
6.4 Power of the One-Sample t Test 160
6.5 The t Distribution: Two Independent Groups 166
Contents ix
6.6 Standardized Effect Size for Two Independent Means 171
6.7 Power of the Test of Two Independent Means 172
6.8 Assumptions Underlying the Two-Group t Test 173
6.9 Contrasts Involving More than Two Means 176
6.10 Correlated Scores or Independent Groups? 181
6.11 Concluding Remarks 183

CHAPTER 7 THE CHI-SQUARE AND F DISTRIBUTIONS 190

7.1 Introduction 190
2 191
7.2 The (cid:548) Distribution
7.3 Inferences About the Population Variance 193
7.4 The F Distribution 196
7.5 Inferences About Population Variance Ratios 200
7.6 Relations Among Distributions 204
7.7 Concluding Remarks 205

CHAPTER 8 BETWEEN-SUBJECTS DESIGNS: ONE FACTOR 210

8.1 Introduction 210
8.2 Exploring the Data 211
8.3 The Analysis of Variance 214
8.4 The Model for the One-Factor Design 221
8.5 Assessing the Importance of the Independent Variable 228
8.6 Power of the F Test 235
8.7 Assumptions Underlying the F Test 238
8.8 Concluding Remarks 250

CHAPTER 9 CON TRASTS AMONG MEANS 257

9.1 Introduction 257
9.2 Definitions and Examples of Contrasts 258
9.3 Calculations of the t Statistic for Testing Hypotheses 259

About Contrasts
9.4 The Proper Unit for the Control of Type 1 Error 266
9.5 Planned Versus Post Hoc Contrasts 268
9.6 Controlling the FWE for Families of K Planned Contrasts 269