Statistics: A Tool for Social Research

548 Pages·2008·2.918 MB·English

by  Joseph F. Healey

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
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STATISTICS
A Tool for Social Research
Eighth Edition
Joseph F. Healey
Christopher Newport University
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Statistics: A Tool for Social Research, © 2009, 2005 Wadsworth Cengage Learning
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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