Drawing upon over 40 years of experience, the authors of Statistics, 11th Edition provide students with a clear and methodical approach to essential statistical procedures. The text clearly explains the basic concepts and procedures of descriptive and inferential statistical analysis. It features an emphasis on expressions involving sums of squares and degrees of freedom as well as a strong stress on the importance of variability. This accessible approach will help students tackle such perennially mystifying topics as the standard deviation, variance interpretation of the correlation coefficient, hypothesis tests, degrees of freedom, p-values, and estimates of effect size.
Table of Contents:
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
