Statistics in context

801 Pages·2019·28.918 MB·English

by  Barbara Blatchley

STATISTICS
IN CONTEXT
BAR BAR A BLATCHLEY
Agnes Scott College
NEW YORK OXFORD
OXFORD UNIVERSITY PRESS
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Library of Congress Cataloging-in-Publication Data
Names: Blatchley, Barbara, author.
Title: Statistics in context / Barbara Blatchley.
Description: First Edition. | New York : Oxford University Press, 2018.
Identifiers: LCCN 2017036139 (print) | LCCN 2017052156 (ebook) | ISBN
9780190278991 (ebook) | ISBN 9780190278953 (hardback) | ISBN 9780190864682
(looseleaf)
Subjects: LCSH: Statistics—Textbooks. | BISAC: PSYCHOLOGY / Assessment,
Testing & Measurement. | PSYCHOLOGY / Statistics.
Classification: LCC QA276 (ebook) | LCC QA276 .B614 2018 (print) | DDC
519.5—dc23
LC record available at https://lccn.loc.gov/2017036139
9 8 7 6 5 4 3 2 1
Printed by Sheridan Books, Inc., United States of America
Printed in the United Stated of America
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CONTENTS IN BRIEF
CHAPTER 1 INTRODUCTION: STATISTICS—WHO NEEDS THEM? 2
CHAPTER 2 TYPES OF DATA 32
CHAPTER 3 A PICTURE IS WORTH A THOUSAND WORDS: CREATING AND
INTERPRETING GRAPHICS 100
CHAPTER 4 MEASURES OF CENTRAL TENDENCY: WHAT’S SO AVERAGE
ABOUT THE MEAN? 150
CHAPTER 5 VARIABILITY: THE “LAW OF LIFE” 190
CHAPTER 6 WHERE AM I? NORMAL DISTRIBUTIONS AND STANDARD
SCORES 252
CHAPTER 7 BASIC PROBABILITY THEORY 294
CHAPTER 8 THE CENTRAL LIMIT THEOREM AND HYPOTHESIS
TESTING 322
CHAPTER 9 THE z-TEST 354
CHAPTER 10 t-TESTS 388
CHAPTER 11 ANALYSIS OF VARIANCE 442
CHAPTER 12 CONFIDENCE INTERVALS AND EFFECT SIZE: BUILDING A
BETTER MOUSETRAP 512
CHAPTER 13 CORRELATION AND REGRESSION: ARE WE RELATED? 550
CHAPTER 14 THE CHI-SQUARE TEST 598
CHAPTER 15 NONPARAMETRIC TESTS 638
CHAPTER 16 WHICH TEST SHOULD I USE, AND WHY? 686
APPENDIX A THE PROPORTIONS UNDER THE STANDARD NORMAL CURVE 697
APPENDIX B THE STUDENT’S TABLE OF CRITICAL t-VALUES 702
APPENDIX C CRITICAL F-VALUES 705
APPENDIX D CRITICAL TUKEY HSD VALUES 707
APPENDIX E CRITICAL VALUES OF CHI SQUARE 709
APPENDIX F THE PEARSON CORRELATION COEFFICIENT:
CRITICAL r-VALUES 712
APPENDIX G CRITICAL r VALUES FOR THE SPEARMAN CORRELATION
S
COEFFICIENT 713
APPENDIX H MANN–WHITNEY CRITICAL U-VALUES 716
APPENDIX I CRITICAL VALUES FOR THE WILCOXON SIGNED-RANK,
MATCHED-PAIRS t-TEST 719
iii
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CONTENTS
Figures, Tables, and Boxes xi Acknowledgments xxii
Preface xix Contents Overview xxiii
Introducing . . . Statistics in Context xx
CHAPTER 1 INTRODUCTION: STATISTICS—WHO NEEDS THEM? 2
Overview 3 Chance Error 11
Learning Objectives 3 Using Statistics 12
Everyday Statistics 3 Some Cautionary Notes About Statistics 13
What Are Statistics? 4 Statistics in Context 15
Types of Statistics 4 Summary 16
Terms You Should Know 17
THE HISTORICAL CONTEXT Roll Them Bones 4
Writing Assignment 17
Descriptive Statistics 5
Practice Problems 17
Inferential Statistics 6
Think About It . . . 26
Variables 7
References 27
Independent and Dependent Variables 8
INTRODUCING SPSS: THE STATISTICAL PACKAGE
THINK ABOUT IT . . .  How a Tan Affects Attractiveness 10 FOR THE SOCIAL SCIENCES 28
CHAPTER 2 TYPES OF DATA 32
Overview 33 Grouped Frequency Distributions 51
Learning Objectives 33 THINK ABOUT IT . . . Frequency Distributions (Part 2) 58
Everyday Statistics 33
Scales of Measurement in Context 59
Data, Data Everywhere 34
. . . And Frequency Distributions 62
Scales of Measurement 34
Summary 62
Qualitative Data 34
Terms You Should Know 62
THE HISTORICAL CONTEXT S. S. Stevens and His Power
Glossary of Equations 63
Law 35
Writing Assignment 63
Quantitative Data 39
Practice Problems 63
THINK ABOUT IT . . . Scales of Measurement 40 Think About It . . .  88
Organizing Data 42 References 91
Frequency Distributions 42 GETTING DATA INTO YOUR STATS PROGRAM 92
Ungrouped Frequency Distributions 45
Reading in Data with SPSS 92
THINK ABOUT IT . . . Frequency Distributions (Part 1) 50
Reading in Data with R 97
iv
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CHAPTER 3 A PICTURE IS WORTH A THOUSAND WORDS: CREATING AND
INTERPRETING GRAPHICS 100
Overview 101 Graphing Relationships 112
Learning Objectives 101 Graphing Time 113
Everyday Statistics 101 Graphics in Context: Rules for Creating Good
Visualizing Patterns in Data 102 Graphs 114
THE HISTORICAL CONTEXT William Playfair and the Use Rules for Creating a Good Graph 114
of Graphics in Publishing 102 Summary 115
Terms You Should Know 115
Bar Charts and Histograms 103
Writing Assignment 115
Discrete Data 104
A Note on Graphing with Statistical Software 116
Continuous Data 105
Practice Problems 116
Stem-and-Leaf Graphs 106
Think About It . . .  129
Frequency Polygons 107
References 129
Pie Charts 108
THINK ABOUT IT . . . Interpreting Graphics 110 GRAPHING WITH SPSS AND R 130
Other Graphics 111 Graphing with SPSS 130
Graphing Means 111 Graphing with R 143
CHAPTER 4 MEASURES OF CENTRAL TENDENCY: WHAT’S SO AVERAGE
ABOUT THE MEAN? 150
Overview 151 THINK ABOUT IT . . . Estimating Measures of Center 160
Learning Objectives 151
Shapes of Distributions 161
Everyday Statistics 151
Normal Distributions 162
Measures of Center 152
Finding Center with Grouped Data 163
Measures of Center: What Is Typical? 152
THINK ABOUT IT . . . Shapes of Distributions 165
THE HISTORICAL CONTEXT Adolphe Quetelet and the Measures of Center in Context 166
“Average Man” 153
Summary 168
The Mode and the Median 154 Terms You Should Know 168
Finding the Position of the Mode 154 Glossary of Equations 168
Finding the Position of the Median 155 Writing Assignment 168
The Mean 156 Practice Problems 169
Mode, Median, and Mean: Which Is the “Best” Think About It . . .  188
Measure of Center? 158 References 189
CHAPTER 5 VARIABILITY: THE “LAW OF LIFE” 190
Overview 191 Consistency and Inconsistency in Data 192
Learning Objectives 191 THE HISTORICAL CONTEXT What Is the Shape of the
Everyday Statistics 191 Earth? 193
Measuring Variability 192
Measures of Variability 194
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The Range 194 Descriptive Statistics in Context 210
The Interquartile Range 195 Summary 212
Graphing the IQR 197 Terms You Should Know 212
The Variance 198
Glossary of Equations 213
Average Deviation from the Mean 198
Writing Assignment 213
The Standard Deviation 200
Practice Problems 215
Finding the Variance in a Population 200
Think About It . . .  231
Finding the Standard Deviation in a Population 202
References 231
Finding Standard Deviation in a Population versus a
Sample 204 DESCRIPTIVE STATISTICS WITH SPSS AND R 232
Finding Variance and Standard Deviation:
An Example 204 Descriptive Statistics with SPSS 232
Descriptive Statistics with R 243
THINK ABOUT IT . . . The Range Rule 206
Standard Deviation in Context 207
CHAPTER 6 W HERE AM I? NORMAL DISTRIBUTIONS AND STANDARD
SCORES 252
Overview 253 Converting a Percentile Rank
Learning Objectives 253 into a Raw Score 273
Everyday Statistics 253 THINK ABOUT IT . . . The Range Rule
Statistics So Far 254 Revisited 276
Standard Scores 254
Standard Scores in Context 277
THE HISTORICAL CONTEXT Alfred Binet and Intelligence Summary 277
Testing 255
Terms You Should Know 278
The z-Score 256 Glossary of Equations 278
The “3-Sigma Rule” 259 Writing Assignment 278
Proportions in the Standard Normal Curve 262 Practice Problems 279
The Benefits of Standard Scores 270 Think About It . . .  292
Comparing Scores from Different Distributions 270 References 293
Converting a z-Score into a Raw Score 272
CHAPTER 7 BASIC PROBABILITY THEORY 294
Overview 295 THINK ABOUT IT . . . Probability Theory and Card
Learning Objectives 295 Games 309
Everyday Statistics 295
Probability in Context 310
Probability 296
Summary 312
Probability and Frequency 296
Terms You Should Know 313
Basic Set Theory 296
Glossary of Equations 313
THE HISTORICAL CONTEXT The Gambler’s Fallacy 297
Practice Problems 313
Conditional Probability 300 Think About It . . .  321
Combining Probabilities 301 References 321
Using Probability 306
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CHAPTER 8 THE CENTRAL LIMIT THEOREM AND HYPOTHESIS TESTING 322
Overview 323 The Sampling Distribution of the Means 329
Learning Objectives 323 The Three Statements That Make Up the Central Limit
Everyday Statistics 323 Theorem 330
Introduction: Error in Statistics 324 Random Sampling 333
Inferential Statistics 324 Using the Central Limit Theorem 337
The Scientific Method 324 Estimating Parameters and Hypothesis
Testing 338
THE HISTORICAL CONTEXT Kinnebrook’s Error and
The Null and Alternative Hypotheses 338
Statistics 325
Directional Hypotheses 339
The Central Limit Theorem 325
Hypothesis Testing in Context 342
Measuring the Distribution of Large Sets of Events 325
Summary 344
The Law of Large Numbers and the Central Limit
Terms You Should Know 345
Theorem 327
Glossary of Equations 345
THINK ABOUT IT . . . The Law of Large Numbers and
Practice Problems 345
Dice Games 328
Think About It . . . 352
Drawing Samples from Populations 329 References 352
CHAPTER 9 THE z-TEST 354
Overview 355 Statistics as Estimates 370
Learning Objectives 355 On Being Right: Type I and Type II Errors 371
Everyday Statistics 355 An Example 371
Error Revisited 356 p-Values 373
THE HISTORICAL CONTEXT The Trial of the Pyx 358 Inferential Statistics in Context: Galton and the
Quincunx 373
How Different Is Different Enough? Critical
Summary 375
Values and p 359
Terms You Should Know 376
Assumptions in Hypothesis Testing 359
Glossary of Equations 376
The Outer 5%: The Rejection Region 360
Writing Assignment 376
THINK ABOUT IT . . . p-Values and Alpha Levels 362
Practice Problems 376
Finding the z-Value in a Nondirectional Hypothesis 363 Think About It . . .  387
The z-Test 364 References 387
Another Example 369
CHAPTER 10 t-TESTS 388
Overview 389 THE HISTORICAL CONTEXT Statistics and Beer 393
Learning Objectives 389
The Single-Sample t-Test 394
Everyday Statistics 389
Degrees of Freedom 396
Inferential Testing So Far 390
When Both σ and µ Are Unknown 400
William Gosset and the Development of the
Independent-Samples t-Test 402
t-Test 390
The Standard Error of the Difference 403
“Student’s” Famous Test 392
Finding the Difference Between Two Means: An
Example 404
CONTENTS vii
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Finding the Difference Between Means with Unequal Terms You Should Know 422
Samples 406 Glossary of Equations 422
Assumptions 411
Writing Assignment 423
THINK ABOUT IT . . . t-Tests and Sample Size 411 Practice Problems 423
Using the Formula for Unequal n’s with Equal n’s 433
Dependent-Samples t-Tests 413
Introduction 413 Think About It . . . 435
Using a Dependent-Samples t-Test: An Example 413 References 436
Calculations and Results 414 CONDUCTING t-TESTS WITH SPSS AND R 437
THINK ABOUT IT . . . t-Tests and Variability 417
t-Tests with SPSS 437
t-Tests in Context: “Garbage In, Garbage Out” 419 t-Tests with R 440
Summary 421
CHAPTER 11 ANALYSIS OF VARIANCE 442
Overview 443 Factorial Designs or Two-Way ANOVAs 471
Learning Objectives 443 An Example: Albert Bandura’s Study of Imitating Violence 472
Everyday Statistics 443 Graphing the Main Effects 474
Comparing More Than Two Groups 444 The Logic of the Two-Way ANOVA 476
Analysis of Variance: What Does It Mean? 444 Using the Two-Way ANOVA Source Table 477
Interpreting the Results 479
THE HISTORICAL CONTEXT Fertilizer, Potatoes, and
ANOVA in Context: Interpretation and
Fisher’s Analysis of Variance 445
Misinterpretation 480
A Hypothetical Study of Blood Doping 446
Summary 482
Assessing Between-Group and Within-Group Variability in
Terms You Should Know 482
Our Hypothetical Results 447
Glossary of Equations 483
ANOVA Terminology 448
Writing Assignment 484
The One-Way ANOVA Procedure 449
Sums of Squares 449 Practice Problems 485
Think About It . . . 495
THINK ABOUT IT . . . t for Two and F for Many 456
References 496
THINK ABOUT IT . . . The F-Statistic 460
USING SPSS AND R FOR ANOVA 496
Post-hoc Testing 460
One-Way ANOVA in SPSS 497
The Tukey HSD Test with Equal n’s 462
Two-Way ANOVA in SPSS 501
The Tukey HSD Test with Unequal n’s 466
One-Way ANOVA in R 504
Models of F 470
Two-Way ANOVA in R 508
One-Way ANOVA Assumptions 471
CHAPTER 12 CONFIDENCE INTERVALS AND EFFECT SIZE: BUILDING A
BETTER MOUSETRAP 512
Overview 513 CIs and the z-Test 518
Learning Objectives 513 THINK ABOUT IT . . . What Does a Confidence Interval
Everyday Statistics 513 Really Mean? (Part 1) 520
Using Estimations 514
CIs and the Single-Sample t-Test 522
Estimates and Confidence Intervals 515
CIs and Independent- and Dependent-Samples t-Tests 524
THE HISTORICAL CONTEXT Jerzy Neyman: What’s a
Lemma? 516
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THINK ABOUT IT . . . What Does a Confidence Interval Terms You Should Know 537
Really Mean? (Part 2) 528 Glossary of Equations 537
Writing Assignment 538
Effect Size: How Different Are These Means, Really? 529
Practice Problems 538
Effect Size and ANOVA 533
Think About It . . . 547
Statistics in Context: The CI versus the
Inferential Test 535 References 548
Summary 537
CHAPTER 13 CORRELATION AND REGRESSION: ARE WE RELATED? 550
Overview 551 Coefficient of Determination 569
Learning Objectives 551 THINK ABOUT IT . . . Shared Variability and
Everyday Statistics 551 Restricted Range 570
The Correlation Coefficient 552
Statistics in Context: Correlations and Causation 571
THE HISTORICAL CONTEXT Statistics and Sweet Peas 552
Summary 573
Positive and Negative Correlations 554 Terms You Should Know 573
Weak and Strong Correlations 555 Glossary of Equations 573
Calculating r 557
Writing Assignment 574
Testing Hypotheses About r 560
Practice Problems 575
The Least Squares Regression Line, a.k.a. the Line of
Think About It . . .  587
Best Fit 561
References 588
Connecting the Dots 561
USING SPSS AND R FOR CORRELATION AND
Finding the Regression Line 562
REGRESSION 589
THINK ABOUT IT . . . What Does Perfect Mean? 565
Pearson Correlation Coefficient in SPSS 589
Some Cautionary Notes 566
Conducting a Regression in SPSS 591
Linear versus Curvilinear Relationships 566
Pearson Correlation Coefficient in R 595
Truncated Range 567
Conducting a Regression in R 596
CHAPTER 14 THE CHI-SQUARE TEST 598
Overview 599 THINK ABOUT IT . . . The Risk Ratio 617
Learning Objectives 599
Nonparametric Tests in Context: Types of Data
Everyday Statistics 599
Revisited 619
The Chi-Square Test and Why We Need It 600
Summary 620
Parametric versus Nonparametric Testing 600
Terms You Should Know 621
THE HISTORICAL CONTEXT The Questionnaire 601
Glossary of Equations 621
Making Assumptions 602 Practice Problems 621
The One-Way Chi-Square Test for Goodness Think About It . . .  629
of Fit 604 References 629
The Two-Way Chi-Square Test of Independence 609
CONDUCTING CHI-SQUARE TESTS WITH
An Example of the Two-Way Test: Americans’ Belief in
SPSS AND R 629
Ghosts by Region 609
A Shortcut 611 Chi-Square Test for Goodness-of-Fit in SPSS 629
A Special Case for Chi Square: The “2 by 2” Design 615
CONTENTS ix
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