Statistics

Robert Witte earned his Ph.D. at Stanford University. He is an Emeritus Professor of Psychology at San Jose State University, where he taught courses in statistics for more than three decades. He has had a number of publications in peer-reviewed journals, as well as a number of nationally-competitive research grants and a post-doctoral Research Fellowship at Indiana University.   John Witte is Professor of Epidemiology and Biostatistics at the University of California, San Francisco.  He received his PhD from the University of California, Los Angeles, and was previously on the faculty at the University of Southern California and Case Western Reserve University. He has published over 150 papers, and his research is primarily focused on statistical genetics and the genetic epidemiology of cancer. 

Preface iv

Acknowledgments vi

1 Introduction 3

1.1 Why Study Statistics? 4

1.2 What Is Statistics? 4

1.3 More about Inferential Statistics 6

1.4 Three Types of Data 9

1.5 Levels of Measurement 10

1.6 Types of Variables 14

1.7 How to Use This Book 19

Summary 20

Important Terms 21

Review Questions 21

PART 1 Descriptive Statistics: Organizing and Summarizing Data 25

2 Describing Data with Tables and Graphs 27

Tables (Frequency Distributions) 28

2.1 Frequency Distributions for Quantitative Data 28

2.2 Guidelines 29

2.3 Outliers 34

2.4 Relative Frequency Distributions 35

2.5 Cumulative Frequency Distributions 36

2.6 Frequency Distributions for Qualitative (Nominal) Data 38

2.7 Interpreting Distributions Constructed By Others 39

Graphs 40

2.8 Graphs for Quantitative Data 40

2.9 Typical Shapes 45

2.10 A Graph for Qualitative (Nominal) Data 47

2.11 Misleading Graphs 48

2.12 Doing It Yourself 50

Summary 50

Important Terms 52

Review Questions 53

3 Describing Data with Averages 59

3.1 Mode 60

3.2 Median 61

3.3 Mean 63

3.4 Which Average? 65

3.5 Averages for Qualitative and Ranked Data 68

Summary 70

Important Terms 70

Key Equation 71

Review Questions 71

4 Describing Variability 75

4.1 Intuitive Approach 76

4.2 Range 78

4.3 Variance 78

4.4 Standard Deviation 79

4.5 Details: Standard Deviation 84

4.6 Degrees Of Freedom (df ) 92

4.7 Interquartile Range (IQR) 94

4.8 Measures of Variability for Qualitative and Ranked Data 95

Summary 95

Important Terms 96

Key Equations 97

Review Questions 97

5 Normal Distributions and Standard (z) Scores 101

5.1 The Normal Curve 103

5.2 z Scores 105

5.3 Standard Normal Curve 106

5.4 Solving Normal Curve Problems 109

5.5 Finding Proportions 110

5.6 Finding Scores 116

5.7 More About z Scores 121

Summary 124

Important Terms 125

Key Equations 125

Review Questions 125

6 Describing Relationships: Correlation 131

6.1 An Intuitive Approach 132

6.2 Scatterplots 134

6.3 A Correlation Coefficient for Quantitative Data: R 137

6.4 Details: Computation Formula for r 142

6.5 Outliers Again 144

6.6 Other Types of Correlation Coefficients 145

6.7 Computer Output 146

Summary 149

Important Terms and Symbols 150

Key Equations 150

Review Questions 151

7 Regression 155

7.1 Two Rough Predictions 156

7.2 A Regression Line 157

7.3 Least Squares Regression Line 159

7.4 Standard Error of Estimate, sy|x 163

7.5 Assumptions 166

7.6 Interpretation of R2 167

7.7 Multiple Regression Equations 172

7.8 Regression Toward The Mean 172

Summary 175

Important Terms 175

Key Equations 175

Review Exercises 176

PART 2 Inferential Statistics: Generalizing Beyond Data 179

8 Populations, Samples, and Probability 181

Populations and Samples 182

8.1 Populations 182

8.2 Samples 183

8.3 Random Sampling 184

8.4 Tables of Random Numbers 185

8.5 Random Assignment of Subjects 186

8.6 Surveys or Experiments? 188

Probability 188

8.7 Definition 189

8.8 Addition Rule 189

8.9 Multiplication Rule 191

8.10 Probability and Statistics 195

Summary 197

Important Terms 197

Key Equations 198

Review Questions 198

9 Sampling Distribution of the Mean 205

9.1 What Is A Sampling Distribution? 206

9.2 Creating a Sampling Distribution from Scratch 207

9.3 Some Important Symbols 209

9.4 Mean of All Sample Means (uX ) 211

9.5 Standard Error of The Mean (σX ) 212

9.6 Shape of the Sampling Distribution 214

9.7 Other Sampling Distributions 216

Summary 217

Important Terms 217

Key Equations 217

Review Questions 218

10 Introduction to Hypothesis Testing: The z Test 221

10.1 Testing a Hypothesis about Sat Scores 222

10.2 z Test for a Population Mean 224

10.3 Step-By-Step Procedure 226

10.4 Statement of the Research Problem 226

10.5 Null Hypothesis H0 227

10.6 Alternative Hypothesis H1 228

10.7 Decision Rule 229

10.8 Calculations 230

10.9 Decision 230

10.10 Interpretation 231

Summary 232

Important Terms 233

Key Equations 233

Review Questions 234

11 MORE ABOUT HYPOTHESIS TESTING 237

11.1 Why Hypothesis Tests? 238

11.2 Strong or Weak Decisions 240

11.3 One-Tailed and Two-Tailed Tests 241

11.4 Choosing a Level of Significance α 245

11.5 Testing a Hypothesis about Vitamin C 247

11.6 Four Possible Outcomes 247

11.7 If H0 Really Is True 250

11.8 If H0 Really Is False Because of a Large Effect 251

11.9 If H0 Really Is False Because of a Small Effect 254

11.10 Influence of Sample Size 255

11.11 Power and Sample Size 258

Summary 261

Important Terms 263

Review Questions 263

12 Estimation (Confidence Intervals) 267

12.1 Point Estimate for μ 268

12.2 Confidence Interval (CI) FOR µ 268

12.3 Interpretation of a Confidence Interval 272

12.4 Level of Confidence 273

12.5 Effect of Sample Size 274

12.6 Hypothesis Tests or Confidence Intervals? 274

12.7 Confidence Interval for Population Percent 275

Summary 277

Important Terms 278

Key Equation 278

Review Questions 278

13 t Test for One Sample 281

13.1 Gas Mileage Investigation 282

13.2 Sampling Distribution of t 282

13.3 t Test 286

13.4 Common Theme of Hypothesis Tests 286

13.5 Reminder about Degrees of Freedom 287

13.6 Details: Estimating The Standard Error (sX–) 287

13.7 Details: Calculations for the t Test 288

13.8 Confidence Intervals for m Based on t 290

13.9 Assumptions 291

Summary 291

Important Terms 292

Key Equations 292

Review Questions 292

14 t Test for Two Independent Samples 295

14.1 EPO Experiment 296

14.2 Statistical Hypotheses 297

14.3 Sampling Distribution X-overbar1 – X-overbar2 299

14.4 t Test 301

14.5 Details: Calculations for the t Test 302

14.6 p-Values 306

14.7 Statistically Significant Results 309

14.8 Estimating Effect Size: Point Estimates and Confidence Intervals 311

14.9 Estimating Effect Size: Cohen’s d 314

14.10 Meta-Analysis 316

14.11 Reports in the Literature 317

14.12 Assumptions 319

14.13 Computer Output 319

Summary 320

Important Terms 321

Key Equations 321

Review Questions 322

15 t Test for Two Related Samples (Repeated Measures) 327

15.1 EPO Experiment with Repeated Measures 328

15.2 Statistical Hypotheses 331

15.3 Sampling Distribution of D-overbar 332

15.4 t Test 332

15.5 Details: Calculations for the t Test 333

15.6 Estimating Effect Size 336

15.7 Assumptions 338

15.8 Overview: Three t Tests for Population Means 338

15.9 t Test for The Population Correlation Coefficient, r 341

Summary 343

Important Terms 344

Key Equations 344

Review Questions 345

16 Analysis of Variance (One Factor) 349

16.1 Testing a Hypothesis about Sleep Deprivation and Aggression 350

16.2 Two Sources of Variability 352

16.3 F Test 354

16.4 Details: Variance Estimates 356

16.5 Details: Mean Squares (MS) and the F Ratio 362

16.6 Table for the F Distribution 364

16.7 ANOVA Summary Tables 365

16.8 F Test Is Nondirectional 367

16.9 Estimating Effect Size 367

16.10 Multiple Comparisons 370

16.11 Overview: Flow Chart for ANOVA 374

16.12 Reports in the Literature 374

16.13 Assumptions 376

16.14 Computer Output 376

Summary 376

Important Terms 378

Key Equations 378

Review Questions 378

17 Analysis of Variance (Repeated Measures) 383

17.1 Sleep Deprivation Experiment with Repeated Measures 384

17.2 F Test 385

17.3 Two Complications 387

17.4 Details: Variance Estimates 387

17.5 Details: Mean Square (MS) and the F Ratio 391

17.6 Table for F Distribution 393

17.7 ANOVA Summary Tables 393

17.8 Estimating Effect Size 395

17.9 Multiple Comparisons 396

17.10 Reports in the Literature 398

17.11 Assumptions 399

Summary 399

Important Terms 400

Key Equations 400

Review Questions 400

18 Analysis of Variance (Two Factors) 405

18.1 A Two-Factor Experiment: Responsibility in Crowds 406

18.2 Three F Tests 409

18.3 Interaction 410

18.4 Details: Variance Estimates 414

18.5 Details: Mean Squares (MS) and F Ratios 418

18.6 Table for the F Distribution 420

18.7 Estimating Effect Size 420

18.8 Multiple Comparisons 421

18.9 Simple Effects 422

18.10 Overview: Flow Chart for Two-Factor ANOVA 426

18.11 Reports in the Literature 427

18.12 Assumptions 428

18.13 Other Types of ANOVA 428

Summary 429

Important Terms 429

Key Equations 429

Review Questions 430

19 Chi-Square (X2) Test For Qualitative (Nominal) Data 435

One-Variable X2 Test 436

19.1 Survey of Blood Types 436

19.2 Statistical Hypotheses 436

19.3 Details: Calculating X2 437

19.4 Table for the X2 Distribution 440

19.5 X2 Test 440

Two-Variable X2 Test 443

19.6 Lost Letter Study 443

19.7 Statistical Hypotheses 444

19.8 Details: Calculating X2 445

19.9 Table for The X2 Distribution 446

19.10 X2 Test 448

19.11 Estimating Effect Size 449

19.12 Odds Ratios 450

19.13 Reports in the Literature 452

19.14 Some Precautions 453

19.15 Computer Output 454

Summary 455

Important Terms 455

Key Equations 455

Review Questions 456

20 Tests for Ranked (Ordinal) Data 461

20.1 Use Only When Appropriate 462

20.2 A Note on Terminology 462

20.3 Mann-Whitney U Test (Two Independent Samples) 463

20.4 Wilcoxon T Test (Two Related Samples) 468

20.5 Kruskal-Wallis H Test (Three or More Independent Samples) 472

20.6 General Comment: Ties 476

Summary 476

Important Terms 477

Review Questions 477

21 Postscript: Which Test? 481

21.1 Descriptive or Inferential Statistics? 482

21.2 Hypothesis Tests or Confidence Intervals? 482

21.3 Quantitative or Qualitative Data? 483

21.4 Distinguishing Between the Two Types of Data 484

21.5 One, Two, or More Groups? 485

21.6 Concluding Comments 486

Review Questions 486

Appendices 489

A Math Review 489

B Answers to Selected Questions 497

C Tables 535

D Glossary 549

Photo Credits 555

Index 556