Statistics in a Nutshell: A Desktop Quick Reference

478 Pages·2008·2.45 MB·English

by  Sarah Boslaugh

STATISTICS
IN A NUTSHELL
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STATISTICS
IN A NUTSHELL
Sarah Boslaugh and Paul Andrew Watters
Beijing • Cambridge • Farnham • Köln • Sebastopol • Taipei • Tokyo
Statistics in a Nutshell
by Sarah Boslaugh and Paul Andrew Watters
Copyright © 2008 Sarah Boslaugh. All rights reserved.
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July 2008: First Edition.
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ISBN: 978-0-596-51049-7
[M]
Chapter1
Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi
1. Basic Concepts of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Measurement 2
Levels of Measurement 2
True and Error Scores 7
Reliability and Validity 8
Measurement Bias 15
Exercises 18
2. Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
About Formulas 22
Basic Definitions 23
Defining Probability 29
Bayes’s Theorem 32
Enough Exposition, Let’s Do Some Statistics! 34
Exercises 36
3. Data Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
An Approach, Not a Set of Recipes 42
The Chain of Command 43
Codebooks 43
The Rectangular Data File 45
Spreadsheets and Relational Databases 47
Inspecting a New Data File 48
v
String and Numeric Data 51
Missing Data 51
4. Descriptive Statistics and Graphics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Populations and Samples 54
Measures of Central Tendency 55
Measures of Dispersion 58
Outliers 62
Graphic Methods 63
Bar Charts 65
Bivariate Charts 75
Exercises 81
5. Research Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Observational Studies 86
Experimental Studies 88
Gathering Experimental Data 90
Inference and Threats to Validity 96
Eliminating Bias 101
Example Experimental Design 105
6. Critiquing Statistics Presented by Others . . . . . . . . . . . . . . . . . . . . . 107
The Misuse of Statistics 107
Common Problems 108
Quick Checklist 110
Research Design 111
Descriptive Statistics 113
Inferential Statistics 118
7. Inferential Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Probability Distributions 126
Independent and Dependent Variables 132
Populations and Samples 133
The Central Limit Theorem 137
Hypothesis Testing 140
Confidence Intervals 144
p-values 145
Data Transformations 146
Exercises 149
8. The t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
The t Distribution 151
vi | Table of Contents
t-Tests 152
One-Sample t-Test 155
Two-Sample t-Test 157
Repeated Measures t-Test 160
Unequal Variance t-Test 162
Effect Size and Power 164
Exercises 165
9. The Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Measuring Association 169
Graphing Associations Through Scatterplots 170
Pearson’s Product-Moment Correlation Coefficient 176
Coefficient of Determination 180
Spearman Rank-Order Coefficient 183
Advanced Techniques 185
10. Categorical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
The R×C Table 189
The Chi-Square Distribution 190
The Chi-Square Test 191
Fisher’s Exact Test 196
McNemar’s Test for Matched Pairs 197
Correlation Statistics for Categorical Data 199
The Likert and Semantic Differential Scales 202
Exercises 203
11. Nonparametric Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Nonnormal Data 208
Between Subjects Designs 209
Within-Subjects Designs 217
Exercises 221
12. Introduction to the General Linear Model . . . . . . . . . . . . . . . . . . . . 224
The General Linear Model 225
Linear Regression 226
Analysis of Variance (ANOVA) 232
Exercises 239
13. Extensions of Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Factorial ANOVA 244
MANOVA 250
Table of Contents | vii
ANCOVA 253
Repeated Measures ANOVA 255
Mixed Designs 257
14. Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Multiple Regression Models 264
Common Problems with Multiple Regression 277
Exercises 279
15. Other Types of Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Logistic Regression 284
Logarithmic Transformations 287
Polynomial Regression 288
Overfitting 292
16. Other Statistical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
Factor Analysis 298
Cluster Analysis 305
Discriminant Function Analysis 309
Multidimensional Scaling 312
17. Business and Quality Improvement Statistics . . . . . . . . . . . . . . . . . 315
Index Numbers 315
Time Series 319
Decision Analysis 323
Quality Improvement 328
Exercises 335
18. Medical and Epidemiological Statistics . . . . . . . . . . . . . . . . . . . . . . . 339
Measures of Disease Frequency 339
Ratio, Proportion, and Rate 340
Prevalence and Incidence 342
Crude, Category-Specific, and Standardized Rates 345
The Risk Ratio 348
The Odds Ratio 352
Confounding, Stratified Analysis, and the
Mantel-Haenszel Common Odds Ratio 354
Power Analysis 358
Sample Size Calculations 361
Exercises 362
viii | Table of Contents