Endocrine Manifestations of Systemic Autoimmune Diseases

Cover

Table of contents

Preface

Chapter 1. Introduction

1.1 Statistics Defined

1.2 Types of Statistics

1.3 Levels of Discourse: Sample vs. Population

1.4 Levels of Discourse: Target vs. Sampled Population

1.5 Measurement Scales

1.6 Sampling and Sampling Errors

1.7 Exercises

Chapter 2. Elementary Descriptive Statistical Techniques

2.1 Summarizing Sets of Data Measured on a Ratio or Interval Scale

2.2 Tabular Methods

2.3 Quantitative Summary Characteristics

2.4 Correlation between Variables X and Y

2.5 Rank Correlation between Variables X and Y

2.6 Exercises

Chapter 3. Probability Theory

3.1 Mathematical Foundations: Sets, Set Relations, and Functions

3.2 The Random Experiment, Events, Sample Space, and the Random Variable

3.3 Axiomatic Development of Probability Theory

3.4 The Occurrence and Probability of an Event

3.5 General Addition Rule for Probabilities

3.6 Joint, Marginal, and Conditional Probability

3.7 Classification of Events

3.8 Sources of Probabilities

3.9 Bayes’ Rule

3.10 Exercises

Chapter 4. Random Variables and Probability Distributions

4.1 Random Variables

4.2 Discrete Probability Distributions

4.3 Continuous Probability Distributions

4.4 Mean and Variance of a Random Variable

4.5 Chebyshev’s Theorem for Random Variables

4.6 Moments of a Random Variable

4.7 Quantiles of a Probability Distribution

4.8 Moment-Generating Function

4.9 Probability-Generating Function

4.10 Exercises

Chapter 5. Bivariate Probability Distributions

5.1 Bivariate Random Variables

5.2 Discrete Bivariate Probability Distributions

5.3 Continuous Bivariate Probability Distributions

5.4 Expectations and Moments of Bivariate Probability Distributions

5.5 Chebyshev’s Theorem for Bivariate Probability Distributions

5.6 Joint Moment–Generating Function

5.7 Exercises

Chapter 6. Discrete Parametric Probability Distributions

6.1 Introduction

6.2 Counting Rules

6.3 Discrete Uniform Distribution

6.4 The Bernoulli Distribution

6.5 The Binomial Distribution

6.6 The Multinomial Distribution

6.7 The Geometric Distribution

6.8 The Negative Binomial Distribution

6.9 The Poisson Distribution

6.10 The Hypergeometric Distribution

6.11 The Generalized Hypergeometric Distribution

6.12 Exercises

Chapter 7. Continuous Parametric Probability Distributions

7.1 Introduction

7.2 The Uniform Distribution

7.3 The Normal Distribution

7.4 The Normal Approximation to Binomial Probabilities

7.5 The Normal Approximation to Poisson Probabilities

7.6 The Exponential Distribution

7.7 Gamma and Beta Functions

7.8 The Gamma Distribution

7.9 The Beta Distribution

7.10 Other Useful Continuous Distributions

7.11 Exercises

Chapter 8. Sampling and the Sampling Distribution of a Statistic

8.1 The Purpose of Random Sampling

8.2 Sampling Scenarios

8.3 The Arithmetic of Random Sampling

8.4 The Sampling Distribution of a Statistic

8.5 The Sampling Distribution of the Mean

8.6 A Weak Law of Large Numbers

8.7 Convergence Concepts

8.8 A Central Limit Theorem

8.9 The Sampling Distribution of a Proportion

8.10 The Sampling Distribution of the Variance

8.11 A Note on Sample Moments

8.12 Exercises

Chapter 9. The Chi-Square, Student’s t, and Snedecor’s F Distributions

9.1 Derived Continuous Parametric Distributions

9.2 The Chi-Square Distribution

9.3 The Sampling Distribution of the Variance When Sampling from a Normal Population

9.4 Student’s t Distribution

9.5 Snedecor’s F Distribution

9.6 Exercises

Chapter 10. Point Estimation and Properties of Point Estimators

10.1 Statistics as Point Estimators

10.2 Desirable Properties of Estimators as Statistical Properties

10.3 Small Sample Properties of Point Estimators

10.4 Large Sample Properties of Point Estimators

10.5 Techniques for Finding Good Point Estimators

10.6 Exercises

Chapter 11. Interval Estimation and Confidence Interval Estimates

11.1 Interval Estimators

11.2 Central Confidence Intervals

11.3 The Pivotal Quantity Method

11.4 A Confidence Interval for µ Under Random Sampling from a Normal Population with Known Variance

11.5 A Confidence Interval for µ Under Random Sampling from a Normal Population with Unknown Variance

11.6 A Confidence Interval for s2 Under Random Sampling from a Normal Population with Unknown Mean

11.7 A Confidence Interval for p Under Random Sampling from a Binomial Population

11.8 Joint Estimation of a Family of Population Parameters

11.9 Confidence Intervals for the Difference of Means When Sampling from Two Independent Normal Populations

11.10 Confidence Intervals for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons

11.11 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations

11.12 Confidence Interval for the Ratio of Two Variances When Sampling from Two Independent Normal Populations

11.13 Exercises

Chapter 12. Tests of Parametric Statistical Hypotheses

12.1 Statistical Inference Revisited

12.2 Fundamental Concepts for Testing Statistical Hypotheses

12.3 What Is the Research Question?

12.4 Decision Outcomes

12.5 Devising a Test for a Statistical Hypothesis

12.6 The Classical Approach to Statistical Hypothesis Testing

12.7 Types of Tests or Critical Regions

12.8 The Essentials of Conducting a Hypothesis Test

12.9 Hypothesis Test for µ Under Random Sampling from a Normal Population with Known Variance

12.10 Reporting Hypothesis Test Results

12.11 Determining the Probability of a Type II Error ß

12.12 Hypothesis Tests for µ Under Random Sampling from a Normal Population with Unknown Variance

12.13 Hypothesis Tests for p Under Random Sampling from a Binomial Population

12.14 Hypothesis Tests for s2 Under Random Sampling froma Normal Population

12.15 The Operating Characteristic and Power Functions of a Test

12.16 Determining the Best Test for a Statistical Hypothesis

12.17 Generalized Likelihood Ratio Tests

12.18 Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations

12.19 Hypothesis Tests for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons

12.20 Hypothesis Tests for the Difference of Proportions When Sampling from Two Independent Binomial Populations

12.21 Hypothesis Tests for the Difference of Variances When Sampling from Two Independent Normal Populations

12.22 Hypothesis Tests for Spearman’s Rank Correlation Coefficient .S

12.23 Exercises

Chapter 13. Nonparametric Statistical Techniques

13.1 Parametric vs. Nonparametric Methods

13.2 Tests for the Randomness of a Single Sample

13.3 Single-Sample Sign Test Under Random Sampling

13.4 Wilcoxon Signed Rank Test of a Median

13.5 Runs Test for Two Independent Samples

13.6 Mann-Whitney (Rank-Sum) Test for Two Independent Samples

13.7 The Sign Test When Sampling from Two Dependent Populations: Paired Comparisons

13.8 Wilcoxon Signed Rank Test When Sampling from Two Dependent Populations: Paired Comparisons

13.9 Exercises

Chapter 14. Testing Goodness of Fit

14.1 Distributional Hypotheses

14.2 The Multinomial Chi-Square Statistic: Complete Specification of H0

14.3 The Multinomial Chi-Square Statistic: Incomplete Specification of H0

14.4 The Kolmogorov-Smirnov Test for Goodness of Fit

14.5 The Lilliefors Goodness-of-Fit Test for Normality

14.6 The Shapiro-Wilk Goodness-of-Fit Test for Normality

14.7 The Kolmogorov-Smirnov Test for Goodness of Fit: Two Independent Samples

14.8 Assessing Normality via Sample Moments

14.9 Exercises

Chapter 15. Testing Goodness of Fit: Contingency Tables

15.1 An Extension of the Multinomial Chi-Square Statistic

15.2 Testing Independence

15.3 Testing k Proportions

15.4 Testing for Homogeneity

15.5 Measuring Strength of Association in Contingency Tables

15.6 Testing Goodness of Fit with Nominal-Scale Data: Paired Samples

15.7 Exercises

Chapter 16. Bivariate Linear Regression and Correlation

16.1 The Regression Model

16.2 The Strong Classical Linear Regression Model

16.3 Estimating the Slope and Intercept of the Population Regression Line

16.4 Mean, Variance, and Sampling Distribution of the LeastSquares Estimators . ß0 and . ß1

16.5 Precision of the Least Squares Estimators . ß0, . ß1:Confidence Intervals

16.6 Testing Hypotheses Concerning ß0, ß1

16.7 The Precision of the Entire Least Squares Regression Equation: A Confidence Band

16.8 The Prediction of a Particular Value of Y Given X

16.9 Decomposition of the Sample Variation of Y

16.10 The Correlation Model

16.11 Estimating the Population Correlation Coefficient .

16.12 Inferences about the Population Correlation Coefficient .

16.13 Exercises

Appendix A

Solutions to Selected Exercises

References and Suggested Reading

Index