CONTENTS
Figures, Tables, and Boxes xi
Preface xix
Introducing . . . Statistics in Context xx
Acknowledgments xxii
Contents Overview xxiii
CHAPTER 1 INTRODUCTION: STATISTICS—WHO NEEDS THEM? 2
Overview 3
Learning Objectives 3
Everyday Statistics 3
What Are Statistics? 4
Types of Statistics 4
THE HISTORICAL CONTEXT Roll Them Bones 4
Descriptive Statistics 5
Inferential Statistics 6
Variables 7
Independent and Dependent Variables 8
THINK ABOUT IT . . . How a Tan Affects Attractiveness 10
CHAPTER 2 TYPES OF DATA 32
Overview 33
Learning Objectives 33
Everyday Statistics 33
Data, Data Everywhere 34
Scales of Measurement 34
Qualitative Data 34
THE HISTORICAL CONTEXT S. S. Stevens and His Power Law 35
Quantitative Data 39
THINK ABOUT IT . . . Scales of Measurement 40
Organizing Data 42
Frequency Distributions 42
Ungrouped Frequency Distributions 45
THINK ABOUT IT . . . Frequency Distributions (Part 1) 50
Chance Error 11
Using Statistics 12
Some Cautionary Notes About Statistics 13
Statistics in Context 15
Summary 16
Terms You Should Know 17
Writing Assignment 17
Practice Problems 17
Think About It . . . 26
References 27
INTRODUCING SPSS: THE STATISTICAL PACKAGE FOR THE SOCIAL SCIENCES 28
Grouped Frequency Distributions 51
THINK ABOUT IT . . . Frequency Distributions (Part 2) 58
Scales of Measurement in Context 59 . . . And Frequency Distributions 62
Summary 62
Terms You Should Know 62
Glossary of Equations 63
Writing Assignment 63
Practice Problems 63
Think About It . . . 88
References 91
GETTING DATA INTO YOUR STATS PROGRAM 92
Reading in Data with SPSS 92
Reading in Data with R 97
CHAPTER 3 A PICTURE IS WORTH A THOUSAND WORDS: CREATING AND INTERPRETING GRAPHICS 100
Overview 101
Learning Objectives 101
Everyday Statistics 101
Visualizing Patterns in Data 102
THE HISTORICAL CONTEXT William Playfair and the Use of Graphics in Publishing 102
Bar Charts and Histograms 103
Discrete Data 104
Continuous Data 105
Stem-and-Leaf Graphs 106
Frequency Polygons 107
Pie Charts 108
THINK ABOUT IT . . . Interpreting Graphics 110
Other Graphics 111
Graphing Means 111
Graphing Relationships 112 Graphing Time 113
Graphics in Context: Rules for Creating Good Graphs 114
Rules for Creating a Good Graph 114
Summary 115
Terms You Should Know 115
Writing Assignment 115
A Note on Graphing with Statistical Software 116
Practice Problems 116
Think About It . . . 129
References 129
GRAPHING WITH SPSS AND R 130
Graphing with SPSS 130
Graphing with R 143
CHAPTER 4 MEASURES OF CENTRAL TENDENCY: WHAT’S SO AVERAGE ABOUT THE MEAN? 150
Overview 151
Learning Objectives 151
Everyday Statistics 151
Measures of Center 152
Measures of Center: What Is Typical? 152
THE HISTORICAL CONTEXT Adolphe Quetelet and the “Average Man” 153
The Mode and the Median 154
Finding the Position of the Mode 154
Finding the Position of the Median 155
The Mean 156
Mode, Median, and Mean: Which Is the “Best” Measure of Center? 158
THINK ABOUT IT . . . Estimating Measures of Center 160
Shapes of Distributions 161
Normal Distributions 162
Finding Center with Grouped Data 163
THINK ABOUT IT . . . Shapes of Distributions 165
Measures of Center in Context 166
Summary 168
Terms You Should Know 168
Glossary of Equations 168
Writing Assignment 168
Practice Problems 169
Think About It . . . 188
References 189
CHAPTER 5 VARIABILITY: THE “LAW OF LIFE” 190
Overview 191
Learning Objectives 191
Everyday Statistics 191
Measuring Variability 192
Consistency and Inconsistency in Data 192
THE HISTORICAL CONTEXT What Is the Shape of the Earth? 193
Measures of Variability 194
The Range 194
The Interquartile Range 195
Graphing the IQR 197
The Variance 198
Average Deviation from the Mean 198
The Standard Deviation 200
Finding the Variance in a Population 200
Finding the Standard Deviation in a Population 202
Finding Standard Deviation in a Population versus a Sample 204
Finding Variance and Standard Deviation: An Example 204
THINK ABOUT IT . . . The Range Rule 206
Standard Deviation in Context 207
Descriptive Statistics in Context 210
Summary 212
Terms You Should Know 212
Glossary of Equations 213
Writing Assignment 213
Practice Problems 215
Think About It . . . 231
References 231
DESCRIPTIVE STATISTICS WITH SPSS AND R 232
Descriptive Statistics with SPSS 232
Descriptive Statistics with R 243
CHAPTER 6 WHERE AM I? NORMAL DISTRIBUTIONS AND STANDARD SCORES
252
Overview 253
Learning Objectives 253
Everyday Statistics 253
Statistics So Far 254
Standard Scores 254
THE HISTORICAL CONTEXT Alfred Binet and Intelligence Testing 255
The z-Score 256
The “3-Sigma Rule” 259
Proportions in the Standard Normal Curve 262
The Benefits of Standard Scores 270
Comparing Scores from Different Distributions 270
Converting a z-Score into a Raw Score 272
Converting a Percentile Rank into a Raw Score 273
THINK ABOUT IT . . . The Range Rule Revisited 276
Standard Scores in Context 277
Summary 277
Terms You Should Know 278
Glossary of Equations 278
Writing Assignment 278
Practice Problems 279
Think About It . . . 292
References 293
CHAPTER 7 BASIC PROBABILITY THEORY 294
Overview 295
Learning Objectives 295
Everyday Statistics 295
Probability 296
Probability and Frequency 296
Basic Set Theory 296
THE HISTORICAL CONTEXT The Gambler’s Fallacy 297
Conditional Probability 300
Combining Probabilities 301
Using Probability 306
THINK ABOUT IT . . . Probability Theory and Card Games 309
Probability in Context 310
Summary 312
Terms You Should Know 313
Glossary of Equations 313
Practice Problems 313
Think About It . . . 321
References 321
CHAPTER 8 THE CENTRAL LIMIT THEOREM AND HYPOTHESIS TESTING
Overview 323
Learning Objectives 323
Everyday Statistics 323
Introduction: Error in Statistics 324
Inferential Statistics 324
The Scientific Method 324
THE HISTORICAL CONTEXT Kinnebrook’s Error and Statistics 325
The Central Limit Theorem 325
Measuring the Distribution of Large Sets of Events 325
The Law of Large Numbers and the Central Limit
Theorem 327
THINK ABOUT IT . . . The Law of Large Numbers and Dice Games 328
Drawing Samples from Populations 329
CHAPTER 9 THE z -TEST 354
Overview 355
Learning Objectives 355
Everyday Statistics 355
Error Revisited 356
THE HISTORICAL CONTEXT The Trial of the Pyx 358
How Different Is Different Enough? Critical
Values and p 359
Assumptions in Hypothesis Testing 359
The Outer 5%: The Rejection Region 360
THINK ABOUT IT . . . p-Values and Alpha Levels 362
Finding the z-Value in a Nondirectional Hypothesis 363
The z-Test 364
Another Example 369
CHAPTER 10 t-TESTS 388
Overview 389
Learning Objectives 389
Everyday Statistics 389
Inferential Testing So Far 390
William Gosset and the Development of the t-Test 390
“Student’s” Famous Test 392
The Sampling Distribution of the Means 329
The Three Statements That Make Up the Central Limit Theorem 330
Random Sampling 333
Using the Central Limit Theorem 337
Estimating Parameters and Hypothesis
Testing 338
The Null and Alternative Hypotheses 338
Directional Hypotheses 339
Hypothesis Testing in Context 342
Summary 344
Terms You Should Know 345
Glossary of Equations 345
Practice Problems 345
Think About It . . . 352
References 352
Statistics as Estimates 370
On Being Right: Type I and Type II Errors 371
An Example 371 p-Values 373
Inferential Statistics in Context: Galton and the Quincunx 373
Summary 375
Terms You Should Know 376
Glossary of Equations 376
Writing Assignment 376
Practice Problems 376
Think About It . . . 387
References 387
THE HISTORICAL CONTEXT Statistics and Beer 393
The Single-Sample t-Test 394
Degrees of Freedom 396
When Both σ and µ Are Unknown 400
Independent-Samples t-Test 402
The Standard Error of the Difference 403
Finding the Difference Between Two Means: An Example 404
Finding the Difference Between Means with Unequal Samples 406
Assumptions 411
THINK ABOUT IT . . . t-Tests and Sample Size 411
Dependent-Samples t-Tests 413
Introduction 413
Using a Dependent-Samples t-Test: An Example 413
Calculations and Results 414
THINK ABOUT IT . . . t-Tests and Variability 417
t-Tests in Context: “Garbage In, Garbage Out” 419
Summary 421
Terms You Should Know 422
Glossary of Equations 422
Writing Assignment 423
Practice Problems 423
Using the Formula for Unequal n’s with Equal n’s 433
Think About It . . . 435
References 436
CONDUCTING t-TESTS WITH SPSS AND R 437
t-Tests with SPSS 437
t-Tests with R 440
CHAPTER 11 ANALYSIS OF VARIANCE 442
Overview 443
Learning Objectives 443
Everyday Statistics 443
Comparing More Than Two Groups 444
Analysis of Variance: What Does It Mean? 444
THE HISTORICAL CONTEXT Fertilizer, Potatoes, and Fisher’s Analysis of Variance 445
A Hypothetical Study of Blood Doping 446
Assessing Between-Group and Within-Group Variability in Our Hypothetical Results 447
ANOVA Terminology 448
The One-Way ANOVA Procedure 449
Sums of Squares 449
THINK ABOUT IT . . . t for Two and F for Many 456
THINK ABOUT IT . . . The F-Statistic 460
Post-hoc Testing 460
The Tukey HSD Test with Equal n’s 462
The Tukey HSD Test with Unequal n’s 466 Models of F 470
One-Way ANOVA Assumptions 471
Factorial Designs or Two-Way ANOVAs 471
An Example: Albert Bandura’s Study of Imitating Violence 472
Graphing the Main Effects 474
The Logic of the Two-Way ANOVA 476
Using the Two-Way ANOVA Source Table 477
Interpreting the Results 479
ANOVA in Context: Interpretation and Misinterpretation 480
Summary 482
Terms You Should Know 482
Glossary of Equations 483
Writing Assignment 484
Practice Problems 485
Think About It . . . 495
References 496
USING SPSS AND R FOR ANOVA 496
One-Way ANOVA in SPSS 497
Two-Way ANOVA in SPSS 501
One-Way ANOVA in R 504
Two-Way ANOVA in R 508
CHAPTER 12 CONFIDENCE INTERVALS AND EFFECT
SIZE:
BUILDING A BETTER MOUSETRAP 512
Overview 513
Learning Objectives 513
Everyday Statistics 513
Using Estimations 514
Estimates and Confidence Intervals 515
THE HISTORICAL CONTEXT Jerzy Neyman: What’s a Lemma? 516
CONTENTS
CIs and the z-Test 518
THINK ABOUT IT . . . What Does a Confidence Interval Really Mean? (Part 1) 520
CIs and the Single-Sample t-Test 522
CIs and Independent- and Dependent-Samples t-Tests 524
THINK ABOUT IT . . . What Does a Confidence Interval Really Mean? (Part 2) 528
Effect Size: How Different Are These Means, Really? 529
Effect Size and ANOVA 533
Statistics in Context: The CI versus the Inferential Test 535
Summary 537
Terms You Should Know 537
Glossary of Equations 537
Writing Assignment 538
Practice Problems 538
Think About It . . . 547
References 548
CHAPTER 13 CORRELATION AND REGRESSION: ARE WE RELATED? 550
Overview 551
Learning Objectives 551
Everyday Statistics 551
The Correlation Coefficient 552
THE HISTORICAL CONTEXT Statistics and Sweet Peas 552
Positive and Negative Correlations 554
Weak and Strong Correlations 555
Calculating r 557
Testing Hypotheses About r 560
The Least Squares Regression Line, a.k.a. the Line of Best Fit 561
Connecting the Dots 561
Finding the Regression Line 562
THINK ABOUT IT . . . What Does Perfect Mean? 565
Some Cautionary Notes 566
Linear versus Curvilinear Relationships 566
Truncated Range 567
CHAPTER
14
Overview 599
THE CHI-SQUARE TEST
598
Coefficient of Determination 569
THINK ABOUT IT . . . Shared Variability and Restricted Range 570
Statistics in Context: Correlations and Causation 571
Summary 573
Terms You Should Know 573
Glossary of Equations 573
Writing Assignment 574
Practice Problems 575
Think About It . . . 587
References 588
USING SPSS AND R FOR CORRELATION AND REGRESSION 589
Pearson Correlation Coefficient in SPSS 589
Conducting a Regression in SPSS 591
Pearson Correlation Coefficient in R 595
Conducting a Regression in R 596
Learning Objectives 599
Everyday Statistics 599
The Chi-Square Test and Why We Need It 600
Parametric versus Nonparametric Testing 600
THE HISTORICAL CONTEXT The Questionnaire 601
Making Assumptions 602
The One-Way Chi-Square Test for Goodness of Fit 604
The Two-Way Chi-Square Test of Independence 609
An Example of the Two-Way Test: Americans’ Belief in Ghosts by Region 609
A Shortcut 611
A Special Case for Chi Square: The “2 by 2” Design 615
THINK ABOUT IT . . . The Risk Ratio 617
Nonparametric Tests in Context: Types of Data
Revisited 619
Summary 620
Terms You Should Know 621
Glossary of Equations 621
Practice Problems 621
Think About It . . . 629
References 629
CONDUCTING CHI-SQUARE TESTS WITH SPSS AND R 629
Chi-Square Test for Goodness-of-Fit in SPSS 629
Two-Way Chi-Square Test for Independence in SPSS 631
Chi-Square Test for Goodness-of-Fit in R 635
Two-Way Chi-Square Test for Independence in R 636
CHAPTER 15 NONPARAMETRIC TESTS 638
Overview 639
Learning Objectives 639
Everyday Statistics 639
Nonparametric Statistics 640
Review: How Parametric and Nonparametric Tests
Differ 640
THE HISTORICAL CONTEXT The Power of Statistics in Society 641
Performing Nonparametric Tests 642
Ranking the Data 643
The Spearman Correlation (rs) 644
The Spearman Correlation: An Example 644
The Results 647
The Mann–Whitney U-test 648
The Wilcoxon Signed-Rank, Matched-Pairs t-Test 652
The Wilcoxon Test: An Example 653
Our Results 655
Non-normal Distributions 656
THINK ABOUT IT . . . Thinking Ahead 659
Nonparametric Tests in Context 661
Summary 662
Terms You Should Know 663
Glossary of Equations 663
Writing Assignment 663
Practice Problems 664
Think About It . . . 675
References 676
CONDUCTING NONPARAMETRIC TESTS WITH SPSS AND R 677
Spearman’s Correlation in SPSS 677
Mann–Whitney U-Test in SPSS 679
Spearman’s Correlation in R 683
Mann–Whitney U-Test in R 684
CHAPTER 16 WHICH TEST SHOULD I USE, AND WHY? 686
Overview 687
Statistics in Context 687
Examples 690
One Last Word 696 References 696
APPENDIX A THE AREA UNDER THE NORMAL CURVE: CRITICAL z -VALUES 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: r-VALUES 712
APPENDIX G CRITICAL r s VALUES FOR THE SPEARMAN CORRELATION COEFFICIENT 713
APPENDIX H MANN–WHITNEY CRITICAL U -VALUES 716
APPENDIX I CRITICAL VALUES FOR THE WILCOXON SIGNED-RANK, MATCHED-PAIRS t-TEST 719
Answers to Odds End-of-Chapter Practice Problems 720
Credit 766
Index 770
x CONTENTS
FIGURES, TABLES, AND BOXES
FIGURES
Figure 1.1. An astragalus, or “knucklebone,” from the ankle of a hoofed animal.
Figure 1.2. The cover page from the Bills of Mortality for 1664.
Figure 1.3. Pierre Beauvallet’s portrait of Galileo Galilei (1564–1642). Galileo was found guilty of heresy for insisting that the earth revolved around the sun and spent the final 12 years of his life living under house arrest.
Figure 1.4. A model of the apparatus used by Galileo for his inclined plane experiment..
Figure 1.5. Magazine advertisement for Cavalier Cigarettes, dated 1943.
Figure 2.1. Qualitative and quantitative data viewed in terms of nominal, ordinal, interval, and ratio scales.
Figure 2.2. All intervals between adjacent categories are equal.
Figure 2.3. Options for presenting data in frequency distributions.
Figure 3.1. William Playfair’s first bar chart: Exports and imports of Scotland to and from different parts for 1 year, from Christmas 1780 to Christmas 1781.
Figure 3.2. Bar chart showing responses to the question “Do you smoke?”
Figure 3.3. Frequency histogram of sleep duration data (in minutes).
Figure 3.4. Stem-and-leaf graph showing walking times (in minutes) of 39 cardiac patients.
Figure 3.5. Stem-and-leaf graph shown as a frequency histogram.
Figure 3.6. Frequency polygon showing sleep duration data (in minutes).
Figure 3.7. Pie chart showing the relative frequency of answers to the question “Do you smoke?”
Figure 3.8. “Clock face” method for creating a pie chart.
Figure 3.9. How to show a missing block of data on the x-axis.
Figure 3.10. Exaggeration of a category.
Figure 3.11. Epidemiological curve showing the number of patients admitted to two referral hospitals with unexplained acute neurological illness, by date of admission, in Muzaffarpur, India, from May 26 to July 17, 2014.
Figure 3.12. Spot map of deaths from cholera in the Golden Square area of London, 1854. Redrawn from the original.
Figure 3.13. Deaths from cholera during 1854 outbreak in London.
Figure 4.1. Adolphe Quetelet.
Figure 4.2. The mode.
Figure 4.3. Negative skew caused by very low outliers.
Figure 4.4. Positive skew caused by very high outliers.
Figure 4.5. Normal distribution showing a balance of high and low outliers and all three measures of center holding the same value.
Figure 4.6. Shapes of distributions: positively skewed, normal, and negatively skewed.
Figure 4.7. Histograms to accompany question 4.
Figure 4.8. Stem-and-leaf plots of average driving distance on two professional golf tours.
Figure 4.9. Box-and-whisker plot of height (in inches) by sex of high school basketball players.
Figure 5.1. Two theories of the shape of the earth: (a) Newton’s theory that the earth is flattened at the poles; (b) the Cassinis’ theory that the earth is flattened at the equator.
Figure 5.2. Problem with the range as a measure of variability.
Figure 5.3. Box-and-whisker plot of the data in Box 5.3.
Figure 5.4. Deviations from the mean.
Figure 5.5. Box-and-whisker plot of IQ scores for five groups of adolescents.
Figure 6.1. Position of an observation within a normal distribution.
Figure 6.2. The 3-sigma rule (above the mean).
Figure 6.3. The 3-sigma rule (above and below the mean).
Figure 6.4. Calculation of proportion above a z-score.
Figure 6.5. Types of standard scores.
Figure 7.1. The French roulette wheel.
Figure 7.2. Probability distribution of Mah Jong cards.
Figure 7.3. Distributions of (a) PSQI scores and (b) sleep durations in the population.
Figure 8.1. Representation of the results of De Moivre’s experiment throwing sets of coins.
Figure 8.2. The average value of the roll of one die against the number of rolls made.
Figure 8.3. Comparison of the elements in a population and in a sampling distribution of the means.
Figure 8.4. The five steps involved in creating a sampling distribution of the means.
Figure 8.5. The central limit theorem (CLT) illustrated.
Figure 8.6. The logic of hypothesis testing.
Figure 8.7. Comparing null and alternative hypotheses.
Figure 9.1. Commemorative coins undergo conformity testing during the Trial of the Pyx at Goldsmith’s Hall in London, England, in January 2017.
Figure 9.2. Probability in a normal distribution (the SDM).
Figure 9.3. The outer 16% (on the left) and the outer 5% (on the right) of the sampling distribution of the means.
Figure 9.4. Relationship between null and alternative populations.
Figure 9.5. Results of z-test for effects of stress on sleep duration.
Figure 9.6. Examples of Galton’s Quincunx.
Figure 10.1. William Sealy Gosset (1908).
Figure 10.2. Relationship between sample size and shape of the t-distribution.
Figure 10.3. APA Style formatting for reporting statistical test results.
Figure 11.1. Ronald Aylmer Fisher.
Figure 11.2. The t-distribution and the F-distribution.
Figure 11.3. Bandura’s famous Bobo doll experiment. The female model is shown in the top row; children from the experimental group are shown in the middle and bottom rows.
Figure 11.4. Graphic representation of data from Bandura’s Bobo doll study.
Figure 11.5. Graphs for question 9.
Figure 12.1. Jerzy Neyman.
Figure 12.2. The null population.
xii FIGURES, TABLES, AND BOXES
Figure 12.3. Distributions for the null and alternative populations in our study of stressed-out sleeping students.
Figure 12.4. Confidence interval versus the z-test.
Figure 13.1. Sir Francis Galton.
Figure 13.2 Galton’s original scatterplot (to the nearest 0.01 inch)
Figure 13.3. Regression to the mean.
Figure 13.4. Two directions for correlations.
Figure 13.5. The strength of the correlation.
Figure 13.6. Scatterplot showing the relationship between height and cancer risk in women.
Figure 13.7. Possible “lines of best fit” for the data from Figure 13.6.
Figure 13.8. Residuals, or deviations, from the line of best fit.
Figure 13.9. Drawing the line of best fit on the graph.
Figure 13.10. Curvilinear relationship between anxiety and test performance.
Figure 13.11. Scatterplots for question 1.
Figure 14.1. Chi-square distributions.
Figure 14.2. Regions of the United States.
Figure 14.3. Typical Likert scales.
Figure 15.1. Charles Edward Spearman.
Figure 15.2. Held and Hein’s (1963) experimental setup: The “kitten carousel.”
Figure 15.3. Histograms of girls’ and boys’ height data.
Figure 15.4. Histograms of ranked height data for boys and girls
Figure 15.5. Cartoon pain rating scale for children.
Figure 16.1. Decision tree: Which test should I use?
TABLES
Table 1.1 Sleep duration and quality for 10 fictitious college undergraduates
Table 2.1 Smoking behavior of six students
Table 2.2 Ratings of female beauty by 10 participants
Table 2.3 Standard women’s clothing sizes (misses)
Table 2.4 Student sleep study: Night 1 sleep duration for 34 students (in minutes)
Table 2.5 Student sleep study: Night 1 sleep duration (in order)
Table 2.6 Student sleep study: Night 1 results, displayed as an ungrouped simple frequency distribution
Table 2.7 Student sleep study: Night 1 results, displayed as an ungrouped relative frequency distribution
Table 2.8 Student sleep study: Night 1 results, displayed as an ungrouped cumulative frequency distribution
Table 2.9 Student sleep study: Night 1 results, displayed as an ungrouped cumulative relative frequency distribution
Table 2.10 Sleep duration for 20 college undergraduates (in minutes)
Table 2.11 Student sleep study: Seven-night results, displayed as a simple ungrouped frequency distribution
Table 2.12 Student sleep study: Seven-night results, displayed as a grouped frequency distribution
Table 2.13 Student sleep study: Seven-night results, displayed as a grouped relative, cumulative, and cumulative relative frequency distribution
Table 2.14 Time-estimation errors (in milliseconds) by age
Table 2.15 Calorie count by type of food at popular fast-food restaurants
Table 2.16 Memory span (number of stimuli recalled) for control and experimental groups
Table 2.17 Cholesterol level (in mg/dl) in adolescents who attempted suicide (experimental group) and depressed adolescents who have not attempted suicide (control group)
Table 2.18 Survival time in motion sickness
Table 2.19 Scores of 14 participants on perceived change in creativity (PCC) scale
Table 2.20 Cigarette smoking in 20 schizophrenic and 20 nonschizophrenic men
Table 2.21 Impulsivity scores for 25 rats
Table 2.22 Grip strength (in pounds) in two different lighting conditions
Table 2.23 Selection ratios as a function of age of person portrayed
Table 2.24 Attractiveness ratings for line drawings of women with four WHRs
Table 2.25 Difference scores between personality ratings for self and ideal romantic partner
Table 2.26 Data sets A through D
Table 2.27 Deaths in London for the year 1662, from the Bills of Mortality by John Graunt
Table 2.28 Tracking the 2014 Ebola outbreak
Table 2.29 MARS scores for 30 students enrolled in statistics
Table 2.30 Number of “knocks” for each of 11 questions (“T” indicates target question)
Table 2.31 Need to knock on wood on a four-point scale
Table 3.1 Participant responses to the question “Do you smoke?”
Table 3.2 Simple frequency distribution of smoking data
Table 3.3 Grouped frequency distribution of sleep time data
Table 3.4 Number of minutes on treadmill for 39 cardiac patients
Table 3.5 Hair cortisol level (in ng/g) and sleep quality ratings (1–5)
Table 3.6 Sleep duration
Table 3.7 Heart rate (in beats per minute)
Table 3.8 Weight (in grams) for 20 mice
Table 3.9 Surface area of the corpus callosum (in cm2) in 10 twin pairs
Table 3.10 Time needed (in seconds) to complete visual search task while smelling unpleasant or pleasant odor
Table 3.11 Recidivism rates for 500 male convicts, by offense
Table 3.12 Total number of lugs per harvest, 1983–1991
Table 3.13 Average driving distance (in yards) of the top 25 drivers on the PGA tour
Table 3.14 Frequency distribution of responses to the question “Do you smoke?” for schizophrenic and nonschizophrenic men
Table 3.15 Response to the statement “I am a lucky person,” by birth month
Table 3.16 Superstitious beliefs reported by 100 individuals in Britain
Table 3.17 Perception of the “illusory dot” as a function of color
Table 3.18 Mean CU scores and mean time-estimation accuracy scores for 40 participants
Table 3.19 Age and time-estimation accuracy for 15 participants
Table 3.20 Number of male inmates with and without a history of alcohol abuse problems, by eye color
Table 3.21 Average alcohol consumption of light-eyed and dark-eyed females
Table 4.1 The mode in a frequency distribution
Table 4.2 Effect of changing a data point on measures of center
Table 4.3 Changing a data point to the data set
Table 4.4 Midpoints of intervals in a grouped frequency distribution
Table 4.5 Measures of center and scales of measurement
Table 4.6 Symbols for descriptive statistics in APA Style
Table 4.7 Sleep times
Table 4.8 Error (in milliseconds) on time estimation task
Table 4.9 Reaction time (in milliseconds) with and without TMS
Table 4.10 Weights (in grams) for 20 mice
Table 4.11
Table 4.12 Salary at “Chocolate Daydreams” Bakery for all 10 employees
Table 4.13 Grouped frequency distribution
Table 4.14 Hypothetical data set for calculating the 10% trimmed mean
Table 4.15 Number of faces recalled by depressed, manic, and healthy individuals
Table 4.16 Diurnal type score (DTS) and maternal response to depression question for 12 children
Table 4.17 Life expectancy (in years) by race, gender, and level of education
Table 4.18 Data from the fastest shot competition
Table 4.19 Data from the fastest shot competition: Data missing
Table 4.20 Ages (in years) of 30 fitness program participants
Table 4.21 Reaction time (RT; in seconds) of participants with and without caffeine
Table 4.22 Nutritional information from fast-food restaurants
Table 5.1 Sleep data
Table 5.2 APA Style symbols for descriptive statistics
Table 5.3 Time-estimation data
Table 5.4 Estimating variability in three data sets
Table 5.5 Body weight of the domestic cat (in pounds)
Table 5.6 Time needed (in seconds) to complete visual search task while smelling an unpleasant or a pleasant odor
Table 5.7 Scores on statistics final exam with and without a lucky charm
Table 5.8 Body weight of Sprague-Dawley rats (in grams)
Table 5.9 Volume of the amygdala and size of social network
Table 5.10 Attractiveness ratings
Table 5.10a A small data set
Table 5.10b Results
Table 5.11 Another small data set
Table 5.12 Error (in millimeters) during a motor-control test performed under unperturbed and perturbed conditions
Table 5.13 Earned run averages (ERAs) of three pitchers against 10 different opponents
Table 5.14 Weights of 30 cereal boxes (in kilograms)
Table 5.15 Starting reaction times (RT; in milliseconds) of finalists in the 100-meter sprint
Table 5.16 T-scores and education status of 30 patients at a fracture clinic
Table 6.1 Percentile rank
Table 6.2 Converting from percentile rank to raw score
xiv FIGURES, TABLES, AND BOXES
Table 6.3 APA Style symbols for descriptive statistics
Table 6.4 Data for question 1
Table 6.5 Scores on statistics final exam, 1992 and 2017
Table 6.6 Weights of 20 domestic cats (in pounds)
Table 6.7 Average BMD measures for women (in mg/cm2) by age and ethnic group
Table 6.8 National averages on the SAT in 2013 (with SD)
Table 6.9 Average levels of DBH in two groups of schizophrenic males
Table 6.10 Number of hours slept by infants in neonatal nursery
Table 6.11 Class grades for five students
Table 6.12 Mean spelling bee scores at three district elementary schools
Table 6.13 Normal distributions for question 25
Table 6.14 General science exam scores at three colleges
Table 6.15 Depression scores for five young adults
Table 6.16 Mean family incomes in five counties
Table 7.1 Distribution of cards in Mah Jong deck
Table 7.2 Results of 20,000 rolls of a die
Table 7.3 Snoring and heart disease in a sample of 2,484 adult males
Table 7.4 Age, smoking, and heart disease in a sample of male physicians
Table 7.5 PSQI scores and sleep durations for 20 medical students
Table 7.6 Emotional disturbance in the population of US adults, 18 years or older
Table 7.7 Favorite team sport named by 81 adult Americans
Table 8.1 Results of 20,000 rolls of a die
Table 8.2 Selection process for four samples
Table 8.3 Results of 25 rolls of a die
Table 9.1 Critical values for z-tests
Table 9.2 Type I and Type II errors
Table 9.3 Total cholesterol in 25 patients after taking new statin drug
Table 9.4 IQ score for 15 patients with hypocholesterolemia
Table 9.5 List of population parameters
Table 9.6 GPAs for RTC students
Table 9.7 Score on the Stanford–Binet IQ test for 10 students
Table 9.8 Body temperature for a sample of alcoholics during withdrawal
Table 9.9 Birth weight of babies born to mothers who smoked during pregnancy
Table 9.10 Tutees’ overall academic averages
Table 10.1 Abbreviated table of critical t-values
Table 10.2 Matched-pairs techniques
Table 10.3 Which test should I use? Four situations
Table 10.4 Number of words recalled from middle 20 words on the list
Table 10.5 Number of minutes of REM sleep during an 8-hour sleep period
Table 10.6 Number of minutes of REM sleep in patients matched for insomnia
Table 10.7 Scores on standardized test of anxiety
Table 10.8 Number of unfavorable traits attributed to minorities
Table 10.9 Amount of alcohol-spiked milk consumed (in milliliters)
Table 10.10 Compliance scores (0–25)
Table 10.11 Number of errors made on a driving simulator
Table 10.12 Number of minutes needed to solve a mechanical puzzle
Table 10.13 Supine diastolic pressure (in mm Hg)
Table 10.14 Perceived fairness scores
Table 10.15 Daily donation totals (in dollars)
Table 11.1 Table of significant F-values, α = .05
Table 11.2 Partial table of critical Tukey HSD values
Table 11.3 ANOVA terminology
Table 11.4 Number of aggressive acts toward Bobo as a function of AUDIT score
Table 11.5 Data for question 7
Table 11.6 Scores on manual dexterity test
Table 11.7 Number of colds experienced in four schools
Table 11.8 Time needed (in seconds) to learn the list of criteria for four levels of association
Table 11.9 Number of errors made on three different keyboards
Table 11.10 Depression scores for three trial groups
Table 11.11 Number of trials required to learn a maze for three groups of rats
Table 11.12 Memory scores for three groups
Table 11.13 Mean heart rates recorded during a stressful task for four groups
Table 11.14 Final grades of 30 students
Table 12.1 Interpretation of Cohen’s d
Table 12.2 Cortisol levels (in mg/dl) in children and adults after a traumatic event
Table 12.3 Levels of OPG (in ng/ml) in healthy controls and individuals with schizophrenia
Table 12.4 Cholesterol levels (in ng/ml) in suicide attempters and healthy controls
Table 12.5 Male versus female chimpanzee CPM scores
Table 12.6 PC scores for 12 students in academic difficulty
Table 12.7 Time (in seconds) needed to find food
Table 12.8 Walking times (in seconds) for primed and unprimed participants
Table 13.1 High school and college GPAs of four students
Table 13.2 Data for the Chapter 13 writing assignment
Table 13.3 Belief in luck and religiosity scores
Table 13.4 BMI measures and number of siblings for 12 kindergarten-age children
Table 13.5 Head circumference, Bayley Infant IQ Score, and duration of smoking during pregnancy
Table 13.6 Maternal age at birth and birth weight (in grams) of the newborn
Table 13.7 Hours spent studying and hours spent playing video games for five volunteers
Table 13.8 Exercise and milk consumption
Table 13.9 ACHA and mania scores for 20 individuals
Table 13.10 Overall quality score and price of nine cordless phones
Table 13.11 Height, weight, and head circumference for 20 female college students
Table 13.12 Hours worked per week and GPA for 15 college students
Table 13.13 Depression and rumination data
Table 14.1 Sample questions from Galton’s questionnaire
Table 14.2 Thirty consecutive roles of a single die
Table 14.3 Political party affiliation by region of the country
Table 14.4 Attitude toward abortion
Table 14.5 Attitude toward abortion: Revised questionnaire
Table 14.6 Worldwide distribution of blood type
Table 14.7 Student performance on the state achievement test using the new and the old textbook
Table 14.8 Distribution of flavors in a five-flavor roll of Life Savers
Table 14.9 Grade distribution for professor in his first year of teaching
Table 14.10 Student performance in statistics as a function of algebra prerequisite
Table 14.11 Methods of combating fatigue, by sex
Table 14.12 Number of years of college completed and residence
Table 14.13 Importance of statistics to chosen specialization in psychology
Table 14.14 Maternal encouragement and change in IQ scores
Table 14.15 Memory for father’s profanity as a function of censoring the father
Table 14.16 Lottery prize frequencies
Table 14.17 Average number of hours per week spent watching television, by season
Table 15.1 Parametric versus nonparametric tests
Table 15.2 Attitude toward online dating for men and women
Table 15.3 Proficiency of visually guided behavior of kittens
Table 15.4 Height (in inches) of 18 boys and 18 girls
Table 15.5 Data for the Chapter 15 writing assignment
Table 15.6 Estimated weekly TV viewing times
Table 15.7 Height (in inches) of 18 boys and 18 girls
Table 15.8 Teacher’s ranking of student intellectual ability and intelligence test scores
Table 15.9 Scores on the DPS before and after treatment for chronic pain
Table 15.10 Rating of pain by men and women
Table 15.11 Rating of pain by first-time and third-time patients of pediatrician
Table 15.12 Length of postoperative hospital stay (in days)
Table 15.13 Number of bar presses by eight rats
Table 15.14 Number of trials needed to learn criterion by two groups of rats
Table 15.15 Age and score on the HS for 10 individuals
Table 15.16 Weights (in pounds) of cats owned by families with children and by single people
Table 15.17 Average rank order for 10 events for novice and experienced observers
Table 15.18 Number of cigarettes smoked in a day by women and men
Table 15.19 IQ score and number of hours spent listening to Mozart
Table 15.20 Level of sexual arousal
Table 15.21 Movie enjoyment
Table 16.1 Sleep quality of 200 college students, by year in school
BOXES
Box 2.1
The mean and nominal data
Box 2.2 Calculating percentages
Box 2.3 Calculating percentages: Example
Box 2.4 Finding interval width
Box 2.5 Even multiples of the width
Box 2.6 Finding the upper limit
Box 2.7 Finding the midpoint
Box 2.8
Measuring beauty
xvi FIGURES, TABLES, AND BOXES
Box 3.1 Place values in Arabic numbers
Box 3.2 Converting to relative frequency
Box 3.3 Converting relative frequency to minutes
Box 3.4 Graphing the mean
Box 3.5 Scatterplots
Box 3.6 Time-series graphs
Box 4.1 Finding the median
Box 4.2 Calculating the mean
Box 4.3 Calculating the mean for the sleep data in Table 4.1
Box 4.4 Finding the midpoint of a 60-minute interval
Box 4.5 Calculating the mean from grouped data
Box 5.1 Calculating the range
Box 5.2 Finding the quartiles in a set of data
Box 5.3 Using quartiles to find the IQR
Box 5.4 Averaging deviation from the mean
Box 5.5 Calculating average deviation using a small data set
Box 5.6 Definition and calculation formulas for finding variance
Box 5.7 Written instructions for using the calculation formula to find variance
Box 5.8 Finding the variance of a small data set using definition and calculation formulas
Box 5.9 Definition and calculation formulas for finding standard deviation
Box 5.10 Finding the standard deviation of a small data set
Box 5.11 Finding the variance and standard deviation of sleeping college students
Box 5.12 Calculating standard deviation (SD) and mean deviation (MD)
Box 6.1 Calculating IQ
Box 6.2 Calculating the z-score
Box 6.3 Calculating the z-score: Example
Box 6.4 Calculating the z-score: Example using a different SD
Box 6.5 Calculating the z-scores of three different results
Box 6.6 Using the z-table: Example
Box 6.7 Sketch of the normal curve showing students who slept 480 minutes or longer
Box 6.8 Sketch of the normal curve showing students who slept between 240 and 480 minutes
Box. 6.9 Sketch of the normal curve showing students who slept 360 minutes or less
Box 6.10 Sketch of the normal curve showing students who slept between 120 and 180 minutes
Box 6.11 Calculating the percentage of students who slept between 120 and 180 minutes: First method
Box 6.12 Calculating the percentage of students who slept between 120 and 180 minutes: Second method
Box 6.13 Using z-scores to compare results from different distributions
Box 6.14 Solving for x
Box 6.15 Sketch of the normal curve showing a score in the 10th percentile
Box 6.16 Calculating a percentile rank into a raw score: Example
Box 7.1 The probability equation
Box 7.2 The probability equation: Example
Box 7.3 Finding the probability of two events separately
Box 7.4 Using the AND rule to find the probability of dependent events
Box 7.5 Using the OR rule to find the probability of independent events
Box 7.6 Combining the AND & OR rules
Box 7.7 Working out the solution to our AND & OR rule equation
Box 7.8 Calculating the probability of being dealt four aces
Box 7.9 The distribution of PSQI scores in the population
Box 8.1 A tiny population
Box 8.2 Calculating the mean and standard deviation of our tiny population
Box 8.3 10 samples of n = 4 each
Box 8.4 Calculating the mean and standard deviation of the sample means
Box 8.5 Samples and their means
Box 8.6 Null, directional alternative, and nondirectional alternative hypotheses
Box 9.1 The inferential z-formula
Box 9.2 The z-formula
Box 9.3 Research question: What is the effect of stress on sleep duration in college students?
Box 9.4 Calculation of z
Box 9.5 Research question: Does sleep deprivation affect digit span?
Box 9.6 Solving for z
Box 10.1 Calculating the sample standard deviation
Box 10.2 The z-test and t-test compared
Box 10.3 The z-score, z-test, and t-test compared
Box 10.4 Research question: Does regular daily exercise change sleep time?
Box 10.5 Does daily exercise improve sleep time? Calculating t
Box 10.6 Degrees of freedom: An example
Box 10.7 Checking our observed t-value against the critical t-value
Box 10.8 Formula for calculating t
Box 10.9 Error terms in single-sample and independent-samples t-tests
Box 10.10 Research question: Does warm milk decrease the time needed to fall asleep?
Box 10.11 Calculating t for our soporific milk study
Box 10.12 Comparing the observed and critical t-values for our sleep study
Box 10.13 Adjusting the t-formula for unequal n’s
Box 10.14 Our research question remains the same
Box 10.15 The test
Box 10.16 Formula for a dependent-samples t-test
Box 10.17 Are college students more distracted in the spring than in the fall?
Box 10.18 Calculating t
Box 10.19 Data when n1 = n2 = 20
Box 11.1 Hypothetical effect of different methods of blood doping
Box 11.2 Averaging out the effects of random chance between and within groups
Box 11.3 Definition formula for variance: The sum of squares
Box 11.4 General procedure for calculating F
Box 11.5 If the IV has no effect at all
Box 11.6 Finding the sum of squares between and within groups
Box 11.7 Finding the mean sum of squares between and within groups
Box 11.8 Calculating the total variability between groups (SSb) in our doping study
Box 11.9 Calculating the overall variability within groups (SSw) in our doping study
Box 11.10 Finding the total sum of squares
Box 11.11 Source table
Box 11.12 Calculating MS and F
Box 11.13 Completed source table
Box 11.14 Possible pairwise comparisons
Box 11.15 Calculating Tukey HSD when n’s are equal for each sample
Box 11.16 Possible pairwise comparisons
Box 11.17 Tukey HSD statistics
Box 11.18 Performing a Tukey HSD test when n’s are unequal
Box 11.19 Changes to the experiment when one subject drops out
Box 11.20 Tukey HSD comparison with unequal sample size
Box 11.21 Results of a Bobo doll experiment: Number of aggressive imitations
Box 11.22 Graphs showing (a) significant and (b) nonsignificant main effects of the IV
Box 11.23 Graphs showing (a) significant and (b) nonsignificant interactions of two IVs
Box 11.24 The logic of two-way ANOVA
Box 11.25 SPSS source table for a two-way ANOVA
Box 11.26 Questions to ask before selecting an inferential test
Box 12.1 Point versus interval estimates and confidence versus precision
Box 12.2 Results of our stressed-out students study
Box 12.3 Calculating the confidence interval around our sample mean
Box 12.4 Results of our exercise and sleep study
Box 12.5 Calculating a confidence interval around our sample mean
Box 12.6 Estimates of variability in an independent-samples t-test
Box 12.7 Calculating CIs for the z-test and single-sample t-test
Box 12.8 Calculating a CI for an independent-samples t-test
Box 12.9 Calculating a confidence interval for our sleepy milk study
Box 12.10 Results of our spring–fall distractedness study
Box 12.11 Calculating a confidence interval for a dependent-samples t-test
Box 12.12 Basic format of Cohen’s d
Box 12.13 Formulas for calculating effect size
Box 12.14 Calculating the size of the effect of stress on sleep time
Box 12.15 Eta squared: The effect size statistic
Box 12.16 Blood doping study: ANOVA and effect size source table
Box 12.17 Partial eta squared
xviii FIGURES, TABLES, AND BOXES
Box 12.18 Calculating the effect size for the two IVs in the Bobo doll study
Box 13.1 Two formulas for calculating r
Box 13.2 Height and risk of cancer in 15 women (hypothetical data)
Box 13.3 Null and alternative hypotheses concerning height and cancer risk
Box 13.4 Calculating r using the definition formula and the raw data formula
Box 13.5 The formula for a straight line (the regression line)
Box 13.6 Calculating the slope and y-intercept
Box 13.7 Calculating two Y-values
Box 13.8 Definition formula for finding r
Box 13.9 Calculating r2
Box 14.1 Research question: Are Americans sleep-deprived?
Box 14.2 Responses to Galton’s question, “What is your father’s occupation?”
Box 14.3 Expected versus observed frequency
Box 14.4 The formula for chi square (χ2)
Box 14.5 Calculating () χ= Σ 2 0 2 ff f e e
Box 14.6 Determining the significance of our observed chi square
Box 14.7 Survey responses: Do you believe in ghosts?
Box 14.8 Determining the expected frequencies for our regional belief in ghosts study
Box 14.9 A shortcut for finding expected frequencies in a two-way chi-square test
Box 14.10 Observed and expected frequencies
Box 14.11 Calculating the chi square
Box 14.12 Data and chi-square calculation for a 2 by 2 design
Box 15.1 Ranking three tennis players by age
Box 15.2 Ranking tennis players with tied scores
Box 15.3 Calculating the Spearman correlation coefficient
Box 15.4 Data for our age and competitiveness study
Box 15.5 Calculating the difference in rank between age and competitiveness scores
Box 15.6 Ranking the data in our survey on online dating
Box 15.7 Using the MWU formula to calculate U-values
Box 15.8 Steps in the Wilcoxon t-test
Box 15.9 Calculating the Wilcoxon t-value
