Fundamental Statistics for the Social and Behavioral Sciences 2 To my kids, Meagan and Will, and my parents, Katsumi and Grayce Tokunaga. 3 Fundamental Statistics for the Social and Behavioral Sciences Howard T. Tokunaga San Jose State University 4 FOR INFORMATION: SAGE Publications, inc. 2455 Teller Road Thousand Oaks, California 91320 E-mail: [email protected] SAGE Publications Ltd. 1 Oliver's Yard 55 City Road London EC1Y 1SP United Kingdom SAGE Publications India Pvt. Ltd. B 1/I 1 Mohan Cooperative Industrial Area Mathura Road, New Delhi 110 044 India SAGE Publications Asia-Pacific Pte. Ltd. 3 Church Street #10-04 Samsung Hub Singapore 049483 Copyright © 2016 by SAGE Publications, Inc. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All trademarks depicted within this book, including trademarks appearing as part of a screenshot, figure, or other image are included solely for the purpose of illustration and are the property of their respective holders. The use of the trademarks in no way indicates any relationship with, or endorsement by, the holders of said trademarks. SPSS is a registered trademark of International Business Machines Incorporated. Printed in the United States of America Cataloging-in-Publication Data is available for this title from the Library of Congress. ISBN 978-1-4833-1879-0 5 This book is printed on acid-free paper. 15 16 17 18 19 10 9 8 7 6 5 4 3 2 1 Acquisitions Editor: Vicki Knight Editorial Assistant: Yvonne McDuffee Associate Editor: Katie Bierach Production Editor: Kelly DeRosa Copy Editor: Gillian Dickens Typesetter: C&M Digitals (P) Ltd. Proofreader: Jennifer Grubba Indexer: Marilyn Augst Cover Designer: Candice Harman Marketing Manager: Nicole Elliott 6 Detailed Contents Preface Acknowledgments About the Author Chapter 1. Introduction to Statistics Chapter 2. Examining Data: Tables and Figures Chapter 3. Measures of Central Tendency Chapter 4. Measures of Variability Chapter 5. Normal Distributions Chapter 6. Probability and Introduction to Hypothesis Testing Chapter 7. Testing One Sample Mean Chapter 8. Estimating the Mean of a Population Chapter 9. Testing the Difference between Two Means Chapter 10. Errors in Hypothesis Testing, Statistical Power, and Effect Size Chapter 11. One-Way Analysis of Variance (ANOVA) Chapter 12. Two-Way Analysis of Variance (ANOVA) Chapter 13. Correlation and Linear Regression Chapter 14. Chi-Square Tables Appendix: Review of Basic Mathematics Glossary References Index 7 Preface It may surprise students to learn they have something in common with writers of books such as this one: When you get close to finishing a writing assignment, you get a bit tired and a bit lazy. The first attempt at this preface was written shortly after final drafts of chapters were sent to my editor at SAGE, Vicki Knight. After reading it, she said, “It's not bad, but it reads like the ‘typical’ Preface. I think it would be useful for the reader to have a sense of why you wrote this book and why you wrote it the way you did.” In responding to my editor's plea for self-analysis, I found that this book's journey began in college. When I entered college, I thought my path would take me to law school; however, taking an Intro to Psych class my freshman year made me realize I enjoy the challenge of trying to understand the human mind. The school I attended, UC Santa Cruz, was a fairly unconventional university, but somehow in the midst of a sea of humanistic psychologists, I became attracted to the empirical and methodological aspects of psychology. This was a result of taking classes with instructors such as David Harrington and Dane Archer, who showed me that statistics could appeal to students if taught using a gentle, guiding approach that addresses questions relevant to students' lives. After graduating from college, I was able to get a job as a research assistant for a human resource consulting firm. Despite my lack of work experience, I was hired primarily as a result of having taken statistics and research methods courses, which taught me that learning statistics has benefits both inside and outside of the classroom. Several years later, I started grad school at UC Berkeley, where two events critical to this book took place. First, serving as a teaching assistant, I found I really enjoyed helping students, particularly in statistics and research methods classes that were often viewed with fear and suspicion. Second, I took graduate classes from Geoff Keppel, who had developed his own unique method and system for analyzing experimental research designs. His lectures and books were instrumental in showing me that statistics can be taught in a systematic way that highlights similarities rather than differences between different research situations. Geoff managed to transform something as daunting sounding as a “3 × 2 × 4 research design” into the mathematical equivalent of playing with wooden toy alphabet blocks labeled “A,” “B,” and “C.” For a long time, I thought my gratitude to Geoff was an isolated occurrence. However, the appreciation others have for his approach to teaching statistics was made apparent to me several years later when I watched him receive an American Psychological Association (APA) Lifetime Achievement award. After leaving Cal, I took on a teaching position at San Jose State, where my teaching responsibilities included an introductory statistics course aimed at students with a wide range of background, ability, and motivation. As I needed to select a textbook to use in this course, for the first time I looked carefully at the wide range of offerings. What I found 8 striking (and still find striking) was that the majority of books focused on providing formulas and very small sets of data designed to demonstrate how to correctly calculate the correct numbers from these formulas. Little emphasis, however, was given to what these numbers meant or implied. Given my own experiences learning statistics, I thought a book was needed that discusses statistics in a thematic manner, focusing on how they are used to answer questions and test ideas within the larger research process. The primary purpose of this book is to not just teach students how to calculate statistics but how to interpret the results of statistical analyses in light of a study's research hypothesis and to communicate one's results and interpretations to a broader audience. Hopefully, this book will not only help students understand the purpose and use of statistics but also give them a greater understanding of how research studies are conceived, conducted, and communicated. The 14 chapters of this book may be placed into three general categories. The first four chapters are designed to introduce students to the research process and how data that have been collected may be organized, presented, and summarized. Chapters 5 through 10 discuss the process of conducting statistical analyses to test research questions and hypotheses, as well as issues and controversies regarding this process. The final four chapters of this book, Chapters 11 to 14, discuss different statistical procedures used in research situations that vary in the number of independent variables in the study as well as how the independent and dependent variables have been measured. 9 A Few Tips for Students To you, the college student about to read this book as part of taking a statistics course: “Welcome!” and “Great job!” I welcome you because you're about to embark on a semester-long journey that I hope will enhance your skills and widen your perspective; I congratulate you because it's a journey not everyone is willing to take. At the present moment, I know my encouragement and appreciation may be of little comfort to you as you might be somewhat anxious about having to learn statistics. Some of you might be anxious about having to learn statistical concepts and formulas; some of you might be anxious because the research process seems pretty complicated. Talking with students who have taken my courses over the years has helped me assemble the following advice: 10