Statistics in a Nutshell : [a desktop quick reference]

594 Pages·2013·6.73 MB·English

by  Sarah Boslaugh

STATISTICS
IN A NUTSHELL
Second Edition
Sarah Boslaugh
Beijing • Cambridge • Farnham • Köln • Sebastopol • Tokyo
Statistics in a Nutshell, Second Edition
by Sarah Boslaugh
Copyright © 2013 Sarah Boslaugh. All rights reserved.
Printed in the United States of America.
Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472.
O’Reilly books may be purchased for educational, business, or sales promotional use. Online
editions are also available for most titles (http://my.safaribooksonline.com). For more infor-
mation, contact our corporate/institutional sales department: 800-998-9938 or
[email protected].
Editor: Mary Treseler Indexer: Potomac Indexing, LLC
Production Editor: Kristen Borg Cover Designer: Randy Comer
Copyeditor: nSight, Inc. Interior Designer: David Futato
Proofreader: Katie DePasquale Illustrator: Rebecca Demarest
July 2008: First Edition.
November 2012: Second Edition.
Revision History for the Second Edition:
2012-10-31 First release
See http://oreilly.com/catalog/errata.csp?isbn=9781449316822 for release details.
Nutshell Handbook, the Nutshell Handbook logo, and the O’Reilly logo are registered trade-
marks of O’Reilly Media, Inc. Statistics in a Nutshell, the image of a thornback crab, and related
trade dress are trademarks of O’Reilly Media, Inc.
Many of the designations used by manufacturers and sellers to distinguish their products are
claimed as trademarks. Where those designations appear in this book, and O’Reilly Media,
Inc., was aware of a trademark claim, the designations have been printed in caps or initial caps.
While every precaution has been taken in the preparation of this book, the publisher and
author assume no responsibility for errors or omissions, or for damages resulting from the use
of the information contained herein.
ISBN: 978-1-449-31682-2
[LSI]
1351705222
Table of Contents
Preface ............................................................. ix
1. Basic Concepts of Measurement ................................... 1
Measurement 2
Levels of Measurement 2
True and Error Scores 8
Reliability and Validity 10
Measurement Bias 14
Exercises 17
2. Probability .................................................... 21
About Formulas 22
Basic Definitions 23
Defining Probability 30
Bayes’ Theorem 34
Enough Exposition, Let’s Do Some Statistics! 36
Exercises 38
3. Inferential Statistics ............................................ 45
Probability Distributions 46
Independent and Dependent Variables 53
Populations and Samples 54
The Central Limit Theorem 59
Hypothesis Testing 64
Confidence Intervals 67
p-values 68
The Z-Statistic 70
Data Transformations 72
iii
Exercises 75
4. Descriptive Statistics and Graphic Displays ......................... 83
Populations and Samples 83
Measures of Central Tendency 84
Measures of Dispersion 90
Outliers 96
Graphic Methods 97
Bar Charts 100
Bivariate Charts 111
Exercises 117
5. Categorical Data .............................................. 121
The R×C Table 122
The Chi-Square Distribution 125
The Chi-Square Test 127
Fisher’s Exact Test 132
McNemar’s Test for Matched Pairs 134
Proportions: The Large Sample Case 136
Correlation Statistics for Categorical Data 138
The Likert and Semantic Differential Scales 145
Exercises 147
6. The t-Test .................................................... 155
The t Distribution 155
The One-Sample t-Test 157
The Independent Samples t-Test 160
Repeated Measures t-Test 164
Unequal Variance t-Test 167
Exercises 168
7. The Pearson Correlation Coefficient .............................. 173
Association 174
Scatterplots 175
The Pearson Correlation Coefficient 182
The Coefficient of Determination 187
Exercises 188
8. Introduction to Regression and ANOVA ........................... 193
The General Linear Model 193
Linear Regression 195
Analysis of Variance (ANOVA) 206
Calculating Simple Regression by Hand 212
Exercises 214
iv | Table of Contents
9. Factorial ANOVA and ANCOVA ................................... 223
Factorial ANOVA 223
ANCOVA 233
Exercises 238
10. Multiple Linear Regression ..................................... 243
Multiple Regression Models 243
Exercises 267
11. Logistic, Multinomial, and Polynomial Regression .................. 273
Logistic Regression 273
Multinomial Logistic Regression 279
Polynomial Regression 282
Overfitting 285
Exercises 287
12. Factor Analysis, Cluster Analysis, and Discriminant Function Analysis .. 291
Factor Analysis 291
Cluster Analysis 299
Discriminant Function Analysis 302
Exercises 305
13. Nonparametric Statistics ....................................... 307
Between-Subjects Designs 308
Within-Subjects Designs 317
Exercises 321
14. Business and Quality Improvement Statistics ...................... 325
Index Numbers 325
Time Series 331
Decision Analysis 334
Quality Improvement 339
Exercises 347
15. Medical and Epidemiological Statistics ........................... 351
Measures of Disease Frequency 351
Ratio, Proportion, and Rate 352
Prevalence and Incidence 354
Crude, Category-Specific, and Standardized Rates 357
The Risk Ratio 362
The Odds Ratio 367
Confounding, Stratified Analysis, and the Mantel-Haenszel Common
Odds Ratio 370
Power Analysis 375
Table of Contents | v
Sample Size Calculations 377
Exercises 380
16. Educational and Psychological Statistics .......................... 385
Percentiles 386
Standardized Scores 388
Test Construction 390
Classical Test Theory: The True Score Model 393
Reliability of a Composite Test 394
Measures of Internal Consistency 395
Item Analysis 400
Item Response Theory 403
Exercises 408
17. Data Management ............................................ 411
An Approach, Not a Set of Recipes 412
The Chain of Command 413
Codebooks 413
The Rectangular Data File 415
Spreadsheets and Relational Databases 418
Inspecting a New Data File 418
String and Numeric Data 422
Missing Data 423
18. Research Design .............................................. 425
Basic Vocabulary 426
Observational Studies 428
Quasi-Experimental Studies 431
Experimental Studies 436
Gathering Experimental Data 437
Example Experimental Design 447
19. Communicating with Statistics .................................. 449
General Notes 449
20. Critiquing Statistics Presented by Others .......................... 457
Evaluating the Whole Article 457
The Misuse of Statistics 458
Common Problems 459
Quick Checklist 461
Issues in Research Design 463
Descriptive Statistics 466
Inferential Statistics 470
A. Review of Basic Mathematics ................................... 473
vi | Table of Contents
B. Introduction to Statistical Packages .............................. 499
C. References ................................................... 513
D. Probability Tables for Common Distributions ...................... 527
E. Online Resources .............................................. 539
F. Glossary of Statistical Terms .................................... 543
Index ............................................................. 553
Table of Contents | vii