Statistics : a new approach

목차 (Table of Contents)

• CONTENTS
• Part Ⅰ. The Nature of Statistics
• 1 THE FIELD Of STATISTICS = 3
• 1.1 What Is Statistics? = 3
• 1.2 Statistics and Scientific Method = 5
• 1.2.1 Four Stages in Scientific Inquiry = 5
• 1.2.2 Concrete Examples of the Four Stages = 8
• 1.3 Applications of Statistics = 10
• 1.4 Factors Related to the Growth of Statistics = 13
• 1.4.1 Increased Demand for Statistics = 13
• 1.4.2 Decreasing Costs of Statistics = 15
• 1.5 Conclusion = 16
• 2 EFFECTIVE USES OF STATISTICS = 17
• 2.1 Common Sense and Statistics = 17
• 2.2 Some Uses of Statistics in World War Ⅱ = 19
• 2.3 Some Uses of Statistics in Business = 20
• 2.4 Some Uses of Statistics in the Social Sciences = 23
• 2.5 Some Uses of Statistics in the Biological Sciences = 25
• 2.6 Some Uses of Statistics in the Physical Sciences = 26
• 2.7 Some Uses of Statistics in the Humanities = 27
• 2.8 Three Detailed Examples = 28
• 2.8.1 Nature and Purpose of the Examples = 28
• 2.8.2 Long-Term Trends in the Frequency of Mental Disease = 29
• 2.8.2.1 PURPOSE OF STUDY = 29
• 2.8.2.2 WHAT WAS KNOWN ALREADY? = 32
• 2.8.2.3 HOW THE DATA WERE OBTAINED = 33
• 2.8.2.4 ANALYSIS = 37
• 2.8.2.5 CONCLUSIONS = 44
• 2.8.3 Vitamins and Endurance = 46
• 2.8.3.1 THE PROBLEM = 46
• 2.8.3.2 STATISTICAL PLANNING = 47
• 2.8.3.3 EXECUTION OF THE EXPERIMENT = 51
• 2.8.3.4 ANALYSIS OF THE FINDINGS = 52
• 2.8.4 Artificial Rain-Making = 56
• 2.9 Conclusion = 62
• 3 MISUSES OF STATISTICS = 64
• 3.1 The Interpretation of Statistics = 64
• 3.2 Misuses Due to Shifting Definitions = 65
• 3.3 Misuses Due to Inaccurate Measurement or Classification of Cases = 68
• 3.4 Misuses Due to Methods of Selecting Cases = 70
• 3.5 Misuses Due to Inappropriate Comparisons = 74
• 3.6 Misuses Due to Shifting Composition of Groups = 77
• 3.7 Misuses Due to Misinterpretation of Association or Correlation = 78
• 3.8 Misuses Due to Disregard of Dispersion = 80
• 3.9 Misuses Due to Technical Errors = 81
• 3.10 Misuses Due to Misleading Statements = 82
• 3.11 Misuses Due to Misleading Charts = 85
• 3.12 Conclusion = 88
• DO IT YOURSELF = 89
• 4 BASIC IDEAS = 100
• 4.1 Introduction = 100
• 4.2 Samples and Populations = 101
• 4.3 Sampling Demonstration = 102
• 4.3.1 Apparatus and Method = 102
• 4.3.2 Preliminary Sample = 104
• 4.3.3 Fifty Samples from Population Ⅰ = 105
• 4.3.4 Fifty SamPles from Population Ⅱ = 106
• 4.3.5 Conclusions from the Demonstrations = 108
• 4.4 Variability of Samples = 110
• 4.5 Reasons for Using Samples = 112
• 4.6 Randomness in Sampling = 115
• 4.6.1 Meaning of Randomness = 115
• 4.6.2 Reasons for Randomness = 116
• 4.6.3 Randomness vs. Expert Selection = 117
• 4.6.4 Probability Samples = 120
• 4.7 Law of Large Numbers = 121
• 4.8 Statistical Control = 123
• 4.9 Statistical Description = 124
• 4.10 Conclusion = 126
• DO IT YOURSELF = 127
• 5 OBSERVATION AND MEASUREMENT = 130
• 5.1 Introduction = 130
• 5.2 The Relationship between a Number and the Real World = 132
• 5.3 Internal Evidence = 136
• 5.3.1 Inconsistencies = 136
• 5.3.2 Irregularities = 137
• 5.3.3 Extreme Values = 139
• 5.3.4 Spurious Regularity = 141
• 5.4 Recording Data = 142
• 5.5 Kinds of Observations = 144
• 5.5.1 Univariate and Bivariate Observations = 144
• 5.5.2 Quantitative Variables = 145
• 5.5.2.1 CONTINUOUS AND DISCRETE QUANTITATIVE VARIABLES = 145
• 5.5.2.2 QUANTITATIVE COMPARISONS = 146
• 5.5.3 Qualities or Attributes = 149
• 5.6 Obtaining Information by Communication = 150
• 5.6.1 Interviewing = 151
• 5.6.2 Questionnaires = 152
• 5.6.3 Coding = 157
• 5.7 Conclusion = 159
• DO IT YOURSELF = 161
• Part Ⅱ. Statistical Description
• 6 THE ART OF ORGANIZING DATA = 167
• 6.1 Introduction = 167
• 6.2 Univariate Frequency Distributions: Quantitative Observations = 171
• 6.2.1 Organizing Data = 171
• 6.2.2 Graphs = 177
• 6.2.3 Tables = 182
• 6.2.4 Relative or Percentage Distributions = 184
• 6.2.5 An Example of Interpretation = 189
• 6.3 Univariate Frequency Distributions: Qualitative Observations = 191
• 6.3.1 Tables = 191
• 6.3.2 Graphs = 191
• 6.4 Bivariate Frequency Distributions = 194
• 6.4.1 Bivariate vs. Two Univariate Distributions = 194
• 6.4.2 Absolute and Relative Joint Frequency Distributions = 196
• 6.4.3 Extension to Multivariate Frequency Distributions = 199
• 6.4.4 Graphical Representation of the Bivariate Frequency Distribution = 199
• 6.5 The Use of Frequency Distributions in the Summarization of Investigations = 203
• 6.6 Conclusion = 205
• DO IT YOURSELF = 206
• 7 AVERAGES = 211
• 7.1 Descriptive Statistics = 211
• 7.2 The Mode = 213
• 7.3 The Median = 215
• 7.4 The Mean = 219
• 7.4.1 The Arithmetic Mean = 219
• 7.4.2 Weighted Means = 223
• 7.4.3 Proportions as Means = 226
• 7.4.4 Other Means = 226
• 7.4.4.1 ROOT MEAN SQUARE = 226
• 7.4.4.2 GEOMETRIC MEAN = 226
• 7.4.4.3 HARMONIC MEAN = 227
• 7.4.5 Computing Arithmetic Means = 230
• 7.4.5.1 A DIGRESSION ON COMPUTATIONS = 234
• 7.5 Which Average? = 236
• 7.6 Interpretation of Averages = 237
• 7.6.1 Allowance for Dispersion = 237
• 7.6.2 A Mean Has Both a Numerator and a Denominator = 238
• 7.6.3 Distinction between "Change of the Average" and " Average of the Changes" = 239
• 7.7 Conclusion = 240
• DO IT YOURSELF = 241
• 8 VARIABILITY = 244
• 8.1 Variability and Its Importance = 244
• 8.2 The Range = 245
• 8.3 The Mean (or Average) Deviation = 247
• 8.3.1 Calculation of the Mean Deviation = 248
• 8.4 Positional Measures of Dispersion = 249
• 8.5 The Standard Deviation = 251
• 8.5.1 Nature and Interpretation of the Standard Deviation = 251
• 8.5.2 Computation of the Standard Deviation = 253
• 8.5.3 The Relative Standard Deviation = 256
• 8.6 The Lorenz Curve = 257
• 8.7 "Regression" Fallacy in the Comparison of Variabilities = 258
• 8.7.1 Nature and Explanation of the Fallacy = 258
• 8.8 Conclusion = 263
• DO IT YOURSELF = 265
• 9 ASSOCIATION = 268
• 9.1 Association and Cause and Effect = 268
• 9.2 How to Read a Table = 270
• 9.3 Association in Frequency Data = 279
• 9.3.1 One Variable Prior = 280
• 9.3.2 Neither Variable Prior = 282
• 9.3.3 Measures Based on Predictability of Order = 282
• 9.3.4 Which Measure to Use? = 284
• 9.4 Interpreting Association = 284
• 9.5 Standardized Averages = 290
• 9.6 An Extended Example = 292
• 9.6.1 Lawyers' Income and Military Service = 293
• 9.6.2 Lawyers' Income and Education = 298
• 9.6.3 Lawyers' Income and Law School = 299
• 9.6.4 The Achilles' Heel of This and Similar Studies = 300
• 9.7 Conclusion = 300
• DO IT YOURSELF = 303
• Part Ⅲ. Statistical Inference
• 10. RANDOMNESS AND PROBABILITY = 309
• 10.1 Statistical Inference = 309
• 10.1.1 Uncertainty = 310
• 10.1.2 Populations = 311
• 10.1.3 Samples = 314
• 10.1.4 Parameters and Statistics = 315
• 10.2 Probability = 315
• 10.3 Randomness = 317
• 10.4 Independence = 319
• 10.5 Probability and Predictability = 320
• 10.6 Probability Calculations = 323
• 10.6.1 The Addition Rule for Mutually Exclusive Occurrences = 324
• 10.6.2 The Multiplication Rule for Independent Occurrences = 324
• 10.6.3 Illustrative Computations and Generalization of the Rules = 325
• 10.7 Conditional Probability = 327
• 10.8 Pitfalls in Calculating Probabilities = 330
• 10.9 Simple Random Sampling = 334
• 10.9.1 General Method = 334
• 10.9.2 A Detailed Example = 334
• 10.10 Misconceptions about Randomness = 337
• 10.11 Other Probability Sampling Methods = 339
• 10.12 Conclusion = 340
• DO IT YOURSELF = 341
• 11 SAMPLING DISTRIBUTIONS AND THE NORMAL DISTRIBUTION = 345
• 11.1 The Nature of a Sampling Distribution = 345
• 11.2 How Sampling Distributions Are Deduced = 348
• 11.2.1 An Illustrative Calculation for a Binomial Population = 348
• 11.2.1.1 EFFECT OF VARYING THE PARAMETER = 352
• 11.2.1.2 EFFECT OF INCREASING THE SAMPLE SIZE = 354
• 11.2.2 An Illustrative Calculation for a Uniform Population = 354
• 11.2.2.1 EFFECT OF INCREASING SAMPLE SIZE = 357
• 11.3 The Normal Distribution = 357
• 11.3.1 The Central Limit Theorem = 357
• 11.3.2 Characteristics of the Normal Distribution = 360
• 11.3.3 The Standard Normal Distribution = 362
• 11.3.4 Tables of the Standard Normal Distribution = 363
• 11.4 The Sampling Distribution of the Mean = 366
• 11.4.1 The Mean of the Sample Means = 366
• 11.4.2 The Standard Error of a Mean = 367
• 11.4.3 The Effect of Population Size on the Standard Error of a Mean = 368
• 11.4.4 An Example = 372
• 11.4.4.1 CONTINUITY ADJUSTMENT = 372
• 11.5 The Sampling Distribution of a Proportion = 375
• 11.5.1 The Mean of the Sample Proportions = 376
• 11.5.2 The Standard Error of a Proportion = 376
• 11.5.3 An Example = 377
• 11.6 Conclusion = 379
• DO IT YOURSELF = 381
• 12 STATISTICAL TESTS AND DECISION PROCEDURES = 384
• 12.1 Introduction = 384
• 12.2 A Decision Problem = 386
• 12.3 A Decision Procedure = 387
• 12.4 Risks of a Wrong Decision = 387
• 12.5 Operating-characteristic Curve = 388
• 12.6 Adjusting the Decision Criterion = 388
• 12.7 Null and Alternative Hypotheses = 392
• 12.8 Balancing the Risks of Error = 393
• 12.9 Adjusting the Sample Size = 396
• 12.10 Types of Alternative Hypotheses = 399
• 12.10.1 One-Sided and Two-Sided Alternatives = 399
• 12.10.2 Choice between One-Sided and Two-Sided Alternatives = 402
• 12.11 Formulating Hypotheses = 404
• 12.12 Conclusion = 408
• DO IT YOURSELF = 409
• 13 FURTHER TEST PROCEDURES = 412
• 13.1 Introduction = 412
• 13.2 Tests of Means = 413
• 13.2.1 Testing an Assumption about a Population Mean = 413
• 13.2.1.1 A TECHNICAL REFINEMENT: STUDENT'S DISTRIBUTION = 417
• 13.2.2 Comparing Two Population Means = 418
• 13.2.2.1 INDEPENDENT SAMPLES = 418
• 13.2.2.2 MATCHED SAMPLES = 420
• 13.2.3 Comparing Several Populations Means: Analysis of Variance = 422
• 13.2.3.1 THE F DISTRIBUTION = 426
• 13.2.3.2 SELECTED COMPARISONS = 426
• 13.3. Tests of Proportions = 427
• 13.3.1 Testing an Assumption about a Population Proportion = 427
• 13.3.2 Comparing Two Sample Proportions = 429
• 13.3.2.1 INDEPENDENT SAMPLES = 429
• 13.3.2.2 MATCHED SAMPLES = 431
• 13.3.3 Comparing Several Population Proportions = 433
• 13.3.3.1 THE CHI-SQUARE (χ²) DISTRIBUTION = 435
• 13.4 Technical Notes = 436
• 13.4.1 Technical Note 1: Student's t Distribution (Secs. 13.2.1 and 13.2.2.2) = 436
• 13.4.2 Technical Note 2: Student's t for Two Independent Samples (Sec. 13.2.2.1) = 437
• 13.4.3 Technical Note 3: The F Distribution (Sec. 13.2.3) = 438
• 13.4.4 Technical Note 4: The χ²Distribution (Sec. 13.3.3) = 438
• 13.5 Conclusion = 439
• DO IT YOURSELF = 441
• 14 ESTIMATION = 443
• 14.1 Introduction = 443
• 14.2 Principles of Estimation = 444
• 14.2.1 Point Estimation = 444
• 14.2.1.1 THE PROBLEM = 444
• 14.2.1.2 MAXIMUM LIKELIHOOD = 445
• 14.2.1.3 UNBIASEDNESS AND EFFICIENCY = 447
• 14.2.1.4 MINIMAX ESTIMATION = 448
• 14.2.2 Interval Estimates: Confidence Intervals = 449
• 14.3 Estimation of Means = 453
• 14.3.1 Review of Sampling Distribution of Means = 453
• 14.3.2 Point Estimates of Means = 454
• 14.3.3 Confidence Intervals for the Mean = 454
• 14.4 Estimation of Proportions = 457
• 14.4.1 Review of Sampling Distribution of Proportions = 457
• 14.4.2 Point Estimates of Proportions = 458
• 14.4.3 Confidence Intervals for Proportions = 458
• 14.5 Confidence Intervals and Decision Procedures = 461
• 14.5.1 Relation of Estimates to Tests = 461
• 14.5.2 Sample Size = 463
• 14.5.3 Asymmetrical Confidence Intervals = 464
• 14.6 Other Problems of Estimation = 465
• 14.7 Technical Notes = 466
• 14.7.1 Technical Note 1: Use of Student's t in Confidence Limits for Means (Sec. 14.3.3) = 466
• 14.7.2 Technical Note 2: Quadratic Confidence Limits for Proportions (Sec. 14.4.3) = 467
• 14.8 Conclusion = 468
• DO IT YOURSELF = 470
• Part Ⅳ. Special Topics
• 15 DESIGN OF INVESTIGATIONS = 475
• 15.1 The Problem of Design = 475
• 15.2 Simple Illustrations of Good Design = 477
• 15.3 Design of Experiments = 479
• 15.3.1 Randomized Groups = 479
• 15.3.2 Randomized Blocks = 480
• 15.3.3 Factorial Designs = 481
• 15.3.4 Latin Squares = 482
• 15.4 Surveys = 483
• 15.4.1 Simple Random Sampling = 483
• 15.4.2 Proportional Stratified Sampling = 484
• 15.4.3 Nonproportional Stratified Sampling = 485
• 15.4.4 Cluster Sampling = 487
• 15.4.5 Systematic Sampling = 488
• 15.4.6 Area Sampling = 489
• 15.5 Conclusion = 490
• DO IT YOURSELF = 492
• 16 STATISTICAL QUALITY CONTROL = 494
• 16.1 Nature and Purposes of Statistical Quality Control = 494
• 16.1.1 Process Control = 495
• 16.1.2 Acceptance Inspection = 496
• 16.1.3 Producer's or Seller's Risk vs. Consumer's or Buyer's Risk = 496
• 16.1.4 Operating Characteristics in Quality Control = 497
• 16.2 Process Control = 498
• 16.2.1 Basic Principles of Process Control = 498
• 16.2.2 Illustrative Control Charts = 501
• 16.2.3 Selection of Control Limits = 508
• 16.3 Acceptance Inspection = 509
• 16.3.1 Principles of Acceptance Inspection = 509
• 16.3.2 Importance of the Operating-characteristic Curve = 511
• 16.3.3 Illustrative Sampling Inspection Plans = 513
• 16.3.4 Average Amount of Sampling = 516
• 16.3.5 Effect of Lot Size = 518
• 16.4 Conclusion = 520
• DO IT YOURSELF = 521
• 17 RELATIONSHIPS BETWEEN VARIABLES = 524
• 17.1 Introductory Survey = 524
• 17.1.1 Introduction = 524
• 17.1.2 A Homely Example = 524
• 17.1.3 Least Squares = 526
• 17.1.4 Pitfalls = 526
• 17.1.5 Multiple Correlation = 527
• 17.1.6 Pitfalls in Multiple Correlation = 528
• 17.1.7 Curvilinear Correlation = 528
• 17.1.8 Correlation and Causation = 529
• 17.2 Fitting a Regression Line = 530
• 17.2.1 Regression as a Problem of Estimation = 530
• 17.2.2 Six Primary Computations from the Data = 533
• 17.2.3 The Slope = 534
• 17.2.4 The Intercept = 535
• 17.2.5 Equation of the Line = 535
• 17.2.6 Check on Accuracy = 535
• 17.3 Sampling Variability = 536
• 17.3.1 Standard Error of Estimate = 536
• 17.3.2 Confidence Interval for the Slope = 538
• 17.3.3 Confidence Band for the Line = 539
• 17.3.4 Confidence Interval for a New Observation = 541
• 17.4 Some Special Topics = 542
• 17.4.1 Interchanging the Dependent and Independent Variables = 542
• 17.4.2 Several Independent Variables = 542
• 17.4.3 Curvilinear Regression = 543
• 17.4.4 Correlation Coefficients = 544
• 17.4.5 Hazards of Ratios = 546
• 17.5 An Illustration = 549
• 17.6 Conclusion = 555
• DO IT YOURSELF = 556
• 18 TIME SERIES = 559
• 18.1 Time Series Problems = 559
• 18.2 Serial Correlation = 560
• 18.3 An Illustrative Time Series = 565
• 18.4 Runs = 569
• 18.4.1 Runs of Several Kinds of Observations = 569
• 18.4.1.1 TWO KINDS OF OBSERVATION = 569
• 18.4.1.2 MORE THAN TWO KINDS OF OBSERVATION = 571
• 18.4.2 Movements Up and Down = 572
• 18.4.2.1 RUNS UP AND DOWN = 572
• 18.4.2.2 PREDOMINANCE OF UPWARD OR DOWNWARD CHANGES = 573
• 18.5 Moving Averages = 575
• 18.6 Seasonal Variation = 580
• 18.6.1 Purpose of Seasonal Adjustment = 580
• 18.6.2 Ratio to Moving Average Method = 581
• 18.6.3 Difference from Moving Average Method = 584
• 18.6.4 The Choice of Methods of Seasonal Adjustment = 586
• 18.7 Conclusion = 587
• DO IT YOURSELF = 588
• 19 SHORTCUTS = 591
• 19.1 The Place of Shortcuts = 591
• 19.2 Confidence Intervals and Significance Tests for an Average = 593
• 19.3 Comparing Two Averages = 594
• 19.3.1 Independent Samples = 594
• 19.3.2 Matched Samples = 596
• 19.4 Comparing Several Averages = 599
• 19.4.1 Independent Samples = 599
• 19.4.2 Matched Samples = 601
• 19.5 Relation between Two Variables = 603
• 19.6 Binomial Probability Paper = 604
• 19.6.1 The Nature of the Graph Paper = 604
• 19.6.2 Chi-square Probabilities = 606
• 19.6.3 Variance Ratio (F) Probabilities = 608
• 19.6.4 Binomial Probabilities = 610
• 19.6.4.1 INTRODUCTION = 610
• 19.6.4.2 TESTING A HYPOTHESIS ABOUT P = 612
• 19.6.4.3 CONFIDENCE INTERVAL ESTIMATE FOR P = 613
• 19.6.4.4 COMPARING TWO PROPORTIONS = 615
• 19.7 Conclusion = 616
• DO IT YOURSELF = 618
• Appendix
• SQUARES AND SQUARE ROOTS = 623
• RANDOM NUMBERS = 631
• INDEX = 637