Endocrine Manifestations of Systemic Autoimmune Diseases (eBook)

Cover 1
Table of contents 8
Preface 16
Chapter 1. Introduction 20
1.1 Statistics Defined 20
1.2 Types of Statistics 20
1.3 Levels of Discourse: Sample vs. Population 21
1.4 Levels of Discourse: Target vs. Sampled Population 23
1.5 Measurement Scales 24
1.6 Sampling and Sampling Errors 26
1.7 Exercises 26
Chapter 2. Elementary Descriptive Statistical Techniques 28
2.1 Summarizing Sets of Data Measured on a Ratio or Interval Scale 28
2.2 Tabular Methods 30
2.3 Quantitative Summary Characteristics 35
2.4 Correlation between Variables X and Y 57
2.5 Rank Correlation between Variables X and Y 61
2.6 Exercises 65
Chapter 3. Probability Theory 72
3.1 Mathematical Foundations: Sets, Set Relations, and Functions 72
3.2 The Random Experiment, Events, Sample Space, and the Random Variable 78
3.3 Axiomatic Development of Probability Theory 81
3.4 The Occurrence and Probability of an Event 83
3.5 General Addition Rule for Probabilities 84
3.6 Joint, Marginal, and Conditional Probability 85
3.7 Classification of Events 91
3.8 Sources of Probabilities 96
3.9 Bayes’ Rule 98
3.10 Exercises 101
Chapter 4. Random Variables and Probability Distributions 112
4.1 Random Variables 112
4.2 Discrete Probability Distributions 113
4.3 Continuous Probability Distributions 120
4.4 Mean and Variance of a Random Variable 125
4.5 Chebyshev’s Theorem for Random Variables 130
4.6 Moments of a Random Variable 132
4.7 Quantiles of a Probability Distribution 136
4.8 Moment-Generating Function 138
4.9 Probability-Generating Function 146
4.10 Exercises 151
Chapter 5. Bivariate Probability Distributions 166
5.1 Bivariate Random Variables 166
5.2 Discrete Bivariate Probability Distributions 166
5.3 Continuous Bivariate Probability Distributions 173
5.4 Expectations and Moments of Bivariate Probability Distributions 181
5.5 Chebyshev’s Theorem for Bivariate Probability Distributions 188
5.6 Joint Moment–Generating Function 188
5.7 Exercises 193
Chapter 6. Discrete Parametric Probability Distributions 206
6.1 Introduction 206
6.2 Counting Rules 207
6.3 Discrete Uniform Distribution 213
6.4 The Bernoulli Distribution 214
6.5 The Binomial Distribution 216
6.6 The Multinomial Distribution 222
6.7 The Geometric Distribution 225
6.8 The Negative Binomial Distribution 227
6.9 The Poisson Distribution 231
6.10 The Hypergeometric Distribution 237
6.11 The Generalized Hypergeometric Distribution 244
6.12 Exercises 245
Chapter 7. Continuous Parametric Probability Distributions 254
7.1 Introduction 254
7.2 The Uniform Distribution 255
7.3 The Normal Distribution 257
7.4 The Normal Approximation to Binomial Probabilities 272
7.5 The Normal Approximation to Poisson Probabilities 276
7.6 The Exponential Distribution 277
7.7 Gamma and Beta Functions 283
7.8 The Gamma Distribution 285
7.9 The Beta Distribution 289
7.10 Other Useful Continuous Distributions 295
7.11 Exercises 304
Chapter 8. Sampling and the Sampling Distribution of a Statistic 312
8.1 The Purpose of Random Sampling 312
8.2 Sampling Scenarios 313
8.3 The Arithmetic of Random Sampling 320
8.4 The Sampling Distribution of a Statistic 325
8.5 The Sampling Distribution of the Mean 327
8.6 A Weak Law of Large Numbers 335
8.7 Convergence Concepts 338
8.8 A Central Limit Theorem 341
8.9 The Sampling Distribution of a Proportion 345
8.10 The Sampling Distribution of the Variance 352
8.11 A Note on Sample Moments 357
8.12 Exercises 361
Chapter 9. The Chi-Square, Student’s t, and Snedecor’s F Distributions 368
9.1 Derived Continuous Parametric Distributions 368
9.2 The Chi-Square Distribution 369
9.3 The Sampling Distribution of the Variance When Sampling from a Normal Population 373
9.4 Student’s t Distribution 376
9.5 Snedecor’s F Distribution 381
9.6 Exercises 387
Chapter 10. Point Estimation and Properties of Point Estimators 392
10.1 Statistics as Point Estimators 392
10.2 Desirable Properties of Estimators as Statistical Properties 394
10.3 Small Sample Properties of Point Estimators 395
10.4 Large Sample Properties of Point Estimators 427
10.5 Techniques for Finding Good Point Estimators 438
10.6 Exercises 450
Chapter 11. Interval Estimation and Confidence Interval Estimates 458
11.1 Interval Estimators 458
11.2 Central Confidence Intervals 460
11.3 The Pivotal Quantity Method 461
11.4 A Confidence Interval for µ Under Random Sampling from a Normal Population with Known Variance 462
11.5 A Confidence Interval for µ Under Random Sampling from a Normal Population with Unknown Variance 465
11.6 A Confidence Interval for s2 Under Random Sampling from a Normal Population with Unknown Mean 466
11.7 A Confidence Interval for p Under Random Sampling from a Binomial Population 470
11.8 Joint Estimation of a Family of Population Parameters 474
11.9 Confidence Intervals for the Difference of Means When Sampling from Two Independent Normal Populations 477
11.10 Confidence Intervals for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons 483
11.11 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations 489
11.12 Confidence Interval for the Ratio of Two Variances When Sampling from Two Independent Normal Populations 490
11.13 Exercises 492
Chapter 12. Tests of Parametric Statistical Hypotheses 502
12.1 Statistical Inference Revisited 502
12.2 Fundamental Concepts for Testing Statistical Hypotheses 503
12.3 What Is the Research Question? 505
12.4 Decision Outcomes 506
12.5 Devising a Test for a Statistical Hypothesis 507
12.6 The Classical Approach to Statistical Hypothesis Testing 510
12.7 Types of Tests or Critical Regions 512
12.8 The Essentials of Conducting a Hypothesis Test 514
12.9 Hypothesis Test for µ Under Random Sampling from a Normal Population with Known Variance 515
12.10 Reporting Hypothesis Test Results 520
12.11 Determining the Probability of a Type II Error ß 523
12.12 Hypothesis Tests for µ Under Random Sampling from a Normal Population with Unknown Variance 529
12.13 Hypothesis Tests for p Under Random Sampling from a Binomial Population 531
12.14 Hypothesis Tests for s2 Under Random Sampling froma Normal Population 535
12.15 The Operating Characteristic and Power Functions of a Test 538
12.16 Determining the Best Test for a Statistical Hypothesis 547
12.17 Generalized Likelihood Ratio Tests 556
12.18 Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations 565
12.19 Hypothesis Tests for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons 572
12.20 Hypothesis Tests for the Difference of Proportions When Sampling from Two Independent Binomial Populations 574
12.21 Hypothesis Tests for the Difference of Variances When Sampling from Two Independent Normal Populations 576
12.22 Hypothesis Tests for Spearman’s Rank Correlation Coefficient .S 578
12.23 Exercises 580
Chapter 13. Nonparametric Statistical Techniques 588
13.1 Parametric vs. Nonparametric Methods 588
13.2 Tests for the Randomness of a Single Sample 591
13.3 Single-Sample Sign Test Under Random Sampling 599
13.4 Wilcoxon Signed Rank Test of a Median 602
13.5 Runs Test for Two Independent Samples 606
13.6 Mann-Whitney (Rank-Sum) Test for Two Independent Samples 609
13.7 The Sign Test When Sampling from Two Dependent Populations: Paired Comparisons 616
13.8 Wilcoxon Signed Rank Test When Sampling from Two Dependent Populations: Paired Comparisons 618
13.9 Exercises 622
Chapter 14. Testing Goodness of Fit 628
14.1 Distributional Hypotheses 628
14.2 The Multinomial Chi-Square Statistic: Complete Specification of H0 628
14.3 The Multinomial Chi-Square Statistic: Incomplete Specification of H0 635
14.4 The Kolmogorov-Smirnov Test for Goodness of Fit 640
14.5 The Lilliefors Goodness-of-Fit Test for Normality 649
14.6 The Shapiro-Wilk Goodness-of-Fit Test for Normality 650
14.7 The Kolmogorov-Smirnov Test for Goodness of Fit: Two Independent Samples 651
14.8 Assessing Normality via Sample Moments 653
14.9 Exercises 657
Chapter 15. Testing Goodness of Fit: Contingency Tables 662
15.1 An Extension of the Multinomial Chi-Square Statistic 662
15.2 Testing Independence 662
15.3 Testing k Proportions 668
15.4 Testing for Homogeneity 670
15.5 Measuring Strength of Association in Contingency Tables 674
15.6 Testing Goodness of Fit with Nominal-Scale Data: Paired Samples 680
15.7 Exercises 683
Chapter 16. Bivariate Linear Regression and Correlation 688
16.1 The Regression Model 688
16.2 The Strong Classical Linear Regression Model 689
16.3 Estimating the Slope and Intercept of the Population Regression Line 692
16.4 Mean, Variance, and Sampling Distribution of the LeastSquares Estimators . ß0 and . ß1 695
16.5 Precision of the Least Squares Estimators . ß0, . ß1:Confidence Intervals 698
16.6 Testing Hypotheses Concerning ß0, ß1 699
16.7 The Precision of the Entire Least Squares Regression Equation: A Confidence Band 703
16.8 The Prediction of a Particular Value of Y Given X 706
16.9 Decomposition of the Sample Variation of Y 710
16.10 The Correlation Model 714
16.11 Estimating the Population Correlation Coefficient . 716
16.12 Inferences about the Population Correlation Coefficient . 717
16.13 Exercises 724
Appendix A 736
Solutions to Selected Exercises 786
References and Suggested Reading 804
Index 808