An Introduction to Statistics for Canadian Social Scientists

494 Pages·2016·18.755 MB·English

by  Michael Haan & Jenny Godley

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Published in Canada by
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Copyright © Oxford University Press Canada 2017
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Second Edition published in 2013
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Library and Archives Canada Cataloguing in Publication
Haan, Michael, 1974–, author
An introduction to statistics for Canadian social scientists / Michael
Haan and Jenny Godley. — Third edition.
Includes bibliographical references and index.
ISBN 978–0–19–902059–1 (paperback)
1. Social sciences—Statistical methods—Textbooks. I. Godley, Jenny,
author II. Title.
HA29.H22 2016 300.72’7 C2016-902883-6
Cover image: © iStock/sorbetto
Oxford University Press is committed to our environment.
Wherever possible, our books are printed on paper which comes from
responsible sources
Printed and bound in the United States of America
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Contents
Boxes xii
Preface xv
Highlights of the Third Edition xvi
About the Authors xvii
Acknowledgements xvii
Part I   |   Introduction and Univariate Statistics 1
1 Why Should I Want to Learn Statistics? 2
Learning Objectives 2
Introduction 2
Why Do So Many People Dislike Statistics? 3
When Did People Start to Think Statistically? 5
If I Don’t Plan to Use Statistics in My Career, Should I Still Learn about Them? 5
Organization of This Book 6
Conclusion 8
Glossary Terms 8
2 How Much Math Do I Need to Learn Statistics? 9
Learning Objectives 9
BEDMAS and the Order of Operations 9
Fractions and Decimals 11
Exponents 11
Logarithms 11
Data, Variables, and Observations 11
Levels of Measurement 12
When Four Levels of Measurement Become Three . . . or Even Two 15
Conclusion 15
Glossary Terms 15
Practice Questions 15
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vi Contents
3 Univariate Statistics 17
Learning Objectives 17
Frequencies 17
Translating Frequencies 19
Rules for Creating Bar Charts 19
Rates and Ratios 21
Percentages and Percentiles 22
Conclusion 24
Glossary Terms 24
Practice Questions 24
4 Introduction to Probability 26
Learning Objectives 26
Introduction 26
Some Necessary Terminology 27
Sample Space 27
Random Variables 28
Trials and Experiments 28
The Law of Large Numbers 28
Types of Probabilities 28
Empirical versus Theoretical Probabilities 29
Discrete Probabilities 29
The Probability of Unrelated Events 30
The Probability of Related Events 31
Mutually Exclusive Probabilities 32
Non–Mutually Exclusive Probabilities 33
Continuous Probabilities 34
Conclusion 34
Glossary Terms 34
Practice Questions 34
5 The Normal Curve 36
Learning Objectives 36
The History of the Normal (Gaussian) Distribution 36
Illustrating the Normal Curve 37
Some Useful Terms for Describing Distributions 40
Conclusion 42
Glossary Terms 42
Practice Questions 42
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Contents vii
6 Measures of Central Tendency and Dispersion 44
Learning Objectives 44
Introduction 44
Measures of Central Tendency 44
Mode 45
Median 45
Mean 45
Measures of Variability 48
Range 48
Mean Deviation 48
Variance and the Standard Deviation 49
Conclusion 51
Glossary Terms 52
Practice Questions 52
Note 53
7 Standard Deviations, Standard Scores, and the Normal Distribution 54
Learning Objectives 54
Introduction 54
How Does the Standard Deviation Relate to the Normal Curve? 54
More on the Normal Distribution 55
An Extension of the Standard Deviation: The Standard Score 59
One-Tailed Assessments 64
Probabilities and the Normal Distribution 68
Conclusion 70
Glossary Terms 70
Practice Questions 70
8 Sampling 72
Learning Objectives 72
Introduction 72
Probability Samples 73
Simple Random Sample 73
Systematic Random Sample 74
Stratified/Hierarchical Random Sample 75
Cluster Sample 76
Non-Probability/Non-Random Sampling Strategies 76
Convenience Sample 76
Snowball Sample 76
Quota Sample 77
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viii Contents
Sampling Error 77
Tips for Reducing Sampling Error 78
Conclusion 78
Glossary Terms 79
Practice Questions 79
9 Generalizing from Samples to Populations 81
Learning Objectives 81
Introduction 81
The Sample Distribution of Means and the Central Limit Theorem 81
Confidence Intervals 83
The t-Distribution 84
What Is a Degree of Freedom? 87
One-Tailed versus Two-Tailed Estimates 88
The Sample Distribution of Proportions 88
Using Degrees of Freedom and the t-Distribution to Estimate Population Proportions 89
The Binomial Distribution 90
Conclusion 91
Glossary Terms 91
Practice Questions 91
Part II   |   Bivariate Statistics 95
10 Testing Hypotheses: Comparing Large and Small Samples to
a Known Population 96
Learning Objectives 96
Introduction 96
What’s a Hypothesis? 97
One-Tailed and Two-Tailed Hypothesis Tests 99
The Return of Gosset: Student’s t-Distribution 102
Hypothesis Testing with One Small Sample and a Population 104
Calculating Confidence Intervals in the One-Sample Case 107
Single Sample Proportions 108
Measuring Association with the Same Group Measured Twice 109
Conclusion 111
Glossary Terms 112
Practice Questions 112
11 Testing Hypotheses: Comparing Two Samples 114
Learning Objectives 114
Introduction 114
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Contents ix
The Standard Error of the Difference between Means 115
Comparing Proportions with Two Samples 119
One- and Two-Tailed Tests, Again 121
Conclusion 122
Glossary Terms 123
Practice Questions 123
12 Bivariate Statistics for Nominal Data 124
Learning Objectives 124
Introduction 124
Analysis with Two Nominal Variables 125
The Chi-Square Test of Statistical Significance 127
Measures of Association for Nominal Data 131
Phi 131
Cramer’s V 134
The Proportional Reduction of Error: Lambda 134
Conclusion 138
Glossary Terms 138
Practice Questions 139
13 Bivariate Statistics for Ordinal Data 141
Learning Objectives 141
Introduction 141
Contingency Tables/Cross-Tabulations 142
Kruskal’s Gamma (γ) 144
Somers’ d 149
Kendall’s Tau-b 151
Spearman’s rho 152
What about Statistical Significance? 156
Conclusion: Which One to Use? 157
Glossary Terms 158
Practice Questions 158
14 Bivariate Statistics for Interval/Ratio Data 160
Learning Objectives 160
Introduction 160
Pearson’s r: The Correlation Coefficient 160
A Rough Interpretation of r 162
A Visual Representation of r 163
What r Tells Us about Explained Variance 165
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x Contents
A More Precise Interpretation of r 167
The Correlation Matrix 167
Using a t-Test to Assess the Significance of r 168
What to Do When Your Independent and Dependent Variables Are Measured at Different Levels of Measurement 169
Measuring Association between Interval/Ratio and Nominal or Ordinal Variables:
Using the Lowest Common Measure of Association 170
Conclusion 171
Glossary Terms 171
Practice Questions 171
15 One-Way Analysis of Variance 173
Learning Objectives 173
Introduction 173
What Is ANOVA? 173
The Sum of Squares: An Easier Way 176
The F-Distribution 178
Is This New? 183
Limitations of ANOVA 183
Conclusion 184
Glossary Terms 185
Practice Questions 185
Part III   |   Multivariate Techniques 187
16 Regression 1—Modelling Continuous Outcomes 188
Learning Objectives 188
Introduction 188
Ordinary Least-Squares Regression: The Idea 188
Onward from Bivariate Correlation: Multivariate Analysis 189
Regression: The Formula 191
Multiple Regression 198
Standardized Partial Slopes (Beta Weights) 201
The Multiple Correlation Coefficient 202
Requirements/Assumptions of Ordinary Least Squares Regression 203
Creating and Working with Dummy Variables 204
Interpreting Dummy Variable Coefficients 205
Inference and Regression 206
Conclusion: A Final Note on OLS Regression 210
Glossary Terms 210
Practice Questions 210
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