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Statistics: A Tool for Social Research PDF

548 Pages·2008·2.918 MB·English
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FREQUENTLY USED FORMULAS CHAPTER 2 Proportions Proportion P (cid:2)P Z 1obtained2 (cid:1) s u f 1Pu11(cid:2)Pu2/N p(cid:1) N CHAPTER 9 Percentage Means % (cid:1) aNf b (cid:4)100 Z 1obtained2 (cid:1) 1X1s(cid:2)X22 x(cid:2)x CHAPTER 3 Standard deviation of the sampling distribution for sample means Mean X (cid:1) gN1Xi2 sx(cid:2)x (cid:1)BN1s(cid:2)21 1 (cid:5) N2s(cid:2)22 1 Pooled estimate of population proportion CHAPTER 4 N P (cid:5)N P Standard deviation P (cid:1) 1 s1 2 s2 u N (cid:5)N 1 2 g1X (cid:2)X22 s(cid:1) i Standard deviation of the sampling B N distribution for sample proportions CHAPTER 5 s (cid:1) 1P 11(cid:2)P 2 11N (cid:5)N 2/N N p(cid:2)p u u 1 2 1 2 Zscores Proportions X (cid:2)X 1P (cid:2)P 2 Z (cid:1) i Z 1obtained2 (cid:1) s1 s2 i s s p(cid:2)p CHAPTER 7 CHAPTER 10 Confidence interval for a sample mean Total sum of squares c.i.(cid:1)X (cid:3)Za s b SST(cid:1) aX2(cid:2)NX2 1N(cid:2)1 Sum of squares between Confidence interval for a sample proportion SSB (cid:1)aNk1Xk(cid:2)X22 P 11(cid:2)P 2 c.i.(cid:1)P (cid:3)Z u u Sum of squares within s B N SSW (cid:1) SST (cid:2) SSB CHAPTER 8 Degrees of freedom for SSW Means dfw(cid:1)N(cid:2)k X (cid:2)m Z 1obtained2 (cid:1) Degrees of freedom for SSB s/1N(cid:2)1 dfb(cid:1)k(cid:2)1 Mean square within Slope SSW (cid:1)1X(cid:2)X21Y(cid:2)Y 2 MSW(cid:1) b(cid:1) dfw (cid:1)1X(cid:2)X22 Mean square between Yintercept MSB(cid:1) SSB a(cid:1)Y (cid:2)bX dfb Pearson’s r Fratio (cid:1)1X(cid:2)X21Y(cid:2)Y 2 MSB r(cid:1) F(cid:1) 23(cid:1)1X(cid:2)X2243(cid:1)1Y(cid:2)Y 224 MSW CHAPTER 17 CHAPTER 11 Partial correlation coefficient Chi square r (cid:2) 1r 21r 2 1f (cid:2)f 22 r (cid:1) yx yz xz x2 1obtained2 (cid:1)a o e yx.z 21(cid:2)r2 21(cid:2)r2 f yz xz e Least-squares multiple regression line CHAPTER 13 Y(cid:1)a(cid:5)b X (cid:5)b X 1 1 2 2 Phi Partial slope for X 1 x2 f(cid:1) s r (cid:2)r r BN b (cid:1) a yba y1 y2 12b 1 s 1(cid:2)r2 1 12 Cramer’s V Partial slope for X 2 V(cid:1)B1N21Minimum xo2f r(cid:2)1, c(cid:2)12 b2(cid:1) assybary21(cid:2)(cid:2)rry12r12b 2 12 Lambda Yintercept E (cid:2)E l(cid:1) 1 2 a(cid:1)Y (cid:2)b X (cid:2)b X 1 1 2 2 E 1 Beta-weight for X 1 CHAPTER 14 s b*(cid:1)b a 1b Gamma 1 1 s y N (cid:2)N G(cid:1) s d Beta-weight for X2 N (cid:5)N s d s Spearman’s rho b*2 (cid:1)b2as2b y 6gD2 r (cid:1)1(cid:2) Standardized least-squares regression line s N1N2(cid:2)12 Z (cid:1)b*Z (cid:5)b*Z y 1 1 2 2 CHAPTER 15 Coefficient of multiple determination Least-squares regression line R2(cid:1)r2 (cid:5)r2 11(cid:2)r2 2 y1 y2.1 y1 Y(cid:1)a(cid:5)bX STATISTICS A Tool for Social Research This page intentionally left blank STATISTICS A Tool for Social Research Eighth Edition Joseph F. Healey Christopher Newport University Australia • Brazil • Japan • Korea • Mexico Singapore • Spain • United Kingdom United States Statistics: A Tool for Social Research, © 2009, 2005 Wadsworth Cengage Learning Eighth Edition ALL RIGHTS RESERVED. No part of this work covered Joseph F. Healey by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, Publisher: Michele Sordi electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Acquisitions Editor: Chris Caldeira Web distribution, information networks, or information Assistant Editor: Christina Beliso storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Editorial Assistant: Erin Parkins Copyright Act, without the prior written permission of the publisher. Marketing Manager: Michelle Williams Marketing Communications Manager: Linda Yip For product information and technology assistance, contact us at Project Manager, Editorial Production: Cengage Learning Academic Resource Center, Matt Ballantyne 1-800-423-0563 Creative Director: Rob Hugel For permission to use material from this text or product, submit all requests online at Art Director: Caryl Gorska www.cengage.com/permissions. Print Buyer: Karen Hunt Further permissions questions can be e-mailed to [email protected]. Permissions Editor: Tim Sisler Production Service: Newgen Library of Congress Control Number: 2007936259 Copy Editor: Elliot Simon ISBN-13: 978-0-495-09655-9 Cover Designer: Yvo ISBN-10: 0-495-09655-5 Cover Image: GettyImages/Photodisc/ Paul Burns; GettyImages/Photodisc/ Wadsworth Cengage Learning Paul Burns; GettyImages/Digital 10 Davis Drive Vision; GettyImages/Stockbyte; Belmont, CA 94002-3098 GettyImages/Westend61/i2 Stock; USA GettyImages/Photodisc; GettyImages/Digital Vision; Cengage Learning products are represented in Canada by Nelson Education, Ltd. GettyImages/Lauren Nicole; GettyImages/Digital Vision RF; For your course and learning solutions, visit GettyImages/Photodisc/Connie academic.cengage.com. Coleman; iStockPhoto/June and Aaron Photography Purchase any of our products at your local college store or at our preferred online store www.ichapters.com. Compositor: Newgen Printed in the United States of America 1 2 3 4 5 6 7 12 11 10 09 08 Brief Contents Preface xvii Prologue: Basic Mathematics Review xxiii Chapter 1 Introduction 1 Part I Descriptive Statistics 21 Chapter 2 Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts, and Graphs 22 Chapter 3 Measures of Central Tendency 63 Chapter 4 Measures of Dispersion 87 Chapter 5 The Normal Curve 115 Part II Inferential Statistics 139 Chapter 6 Introduction to Inferential Statistics: Sampling and the Sampling Distribution 140 Chapter 7 Estimation Procedures 155 Chapter 8 Hypothesis Testing I: The One-Sample Case 179 Chapter 9 Hypothesis Testing II: The Two-Sample Case 208 Chapter 10 Hypothesis Testing III: The Analysis of Variance 234 Chapter 11 Hypothesis Testing IV: Chi Square 260 Part III Bivariate Measures of Association 293 Chapter 12 Bivariate Association: Introduction and Basic Concepts 294 Chapter 13 Association Between Variables Measured at the Nominal Level 315 Chapter 14 Association Between Variables Measured at the Ordinal Level 333 Chapter 15 Association Between Variables Measured at the Interval-Ratio Level 361 Part IV Multivariate Techniques 395 Chapter 16 Elaborating Bivariate Tables 396 Chapter 17 Partial Correlation and Multiple Regression and Correlation 422 Appendix A Area Under the Normal Curve 453 Appendix B Distribution of t 457 Appendix C Distribution of Chi Square 459 Appendix D Distribution of F 461 vi BRIEF CONTENTS Appendix E Using Statistics: Ideas for Research Projects 463 Appendix F An Introduction to SPSS for Windows 469 Appendix G Code Book for the General Social Survey, 2006 477 Answers to Odd-Numbered End-of-Chapter Problems and Cumulative Exercises 485 Glossary 499 Credits 505 Index 507 Detailed Contents Preface xvii Prologue:Basic Mathematics Review xxiii Chapter 1 Introduction 1 1.1 Why Study Statistics? 1 1.2 The Role of Statistics in Scientific Inquiry 2 1.3 The Goals of This Text 6 1.4 Descriptive and Inferential Statistics 6 1.5 Discrete and Continuous Variables 9 1.6 Level of Measurement 9 Reading Statistics 1: Introduction 14 One Step at a Time: Determining the Level of Measurement of a Variable 15 SUMMARY / 16 • GLOSSARY / 16 • PROBLEMS 17 INTRODUCTION TO SPSS AND THE GENERAL SOCIAL SURVEY 19 Part I DESCRIPTIVE STATISTICS 21 Chapter 2 Basic Descriptive Statistics:Percentages, Ratios and Rates, Tables, Charts, and Graphs 22 2.1 Percentages and Proportions 22 Application 2.1 24 One Step at a Time: Finding Percentages and Proportions 25 2.2 Ratios, Rates, and Percentage Change 25 Application 2.2 26 Application 2.3 27 Application 2.4 28 One Step at a Time: Finding Ratios, Rates, and Percent Change 29 2.3 Frequency Distributions: Introduction 30 2.4 Frequency Distributions for Variables Measured at the Nominal and Ordinal Levels 31 2.5 Frequency Distributions for Variables Measured at the Interval-Ratio Level 32 Application 2.5 33 One Step at a Time: Finding Midpoints 35 One Step at a Time: Finding Real Limits 36 2.6 Constructing Frequency Distributions for Interval-Ratio-Level Variables: A Review 40

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