Content: CATEGORICAL DATA ANALYSIS BY EXAMPLE
Contents
Preface
Acknowledgments
1 Introduction
1.1 What are Categorical Data?
1.2 A Typical Data Set
1.3 Visualization and Cross-Tabulation
1.4 Samples, Populations, and Random Variation
1.5 Proportion, Probability, and Conditional Probability
1.6 Probability Distributions
1.6.1 The Binomial Distribution
1.6.2 The Multinomial Distribution
1.6.3 The Poisson Distribution
1.6.4 The Normal Distribution
1.6.5 The Chi-Squared (2) Distribution
1.7 The Likelihood
2 Estimation and Inference for Categorical Data
2.1 Goodness of Fit. 2.1.1 Pearson's X2 Goodness-of-Fit Statistic2.1.2 The Link between X2 and the Poisson and 2-Distributions
2.1.3 The Likelihood-Ratio Goodness-of-Fit Statistic, G2
2.1.4 Why the G2 and X2 Statistics Usually have Similar Values
2.2 Hypothesis Tests for a Binomial Proportion (Large Sample)
2.2.1 The Normal Score Test
2.2.2 Link to Pearson's X2 Goodness-of-Fit Test
2.2.3 G2 for a Binomial Proportion
2.3 Hypothesis Tests for a Binomial Proportion (Small Sample)
2.3.1 One-Tailed Hypothesis Test
2.3.2 Two-Tailed Hypothesis Tests
2.4 Interval Estimates for a Binomial Proportion. 2.4.1 Laplace's Method2.4.2 Wilson's Method
2.4.3 The Agresti-Coull Method
2.4.4 Small Samples and Exact Calculations
References
3 The 2 x 2 Contingency Table
3.1 Introduction
3.2 Fisher's Exact Test (for Independence)
3.2.1 Derivation of the Exact Test Formula
3.3 Testing Independence with Large Cell Frequencies
3.3.1 Using Pearson's Goodness-of-Fit Test
3.3.2 The Yates Correction
3.4 The 2 x 2 Table in a Medical Context
3.5 Measuring Lack of Independence (Comparing Proportions)
3.5.1 Difference of Proportions
3.5.2 Relative Risk
3.5.3 Odds-Ratio
References. 4 The I x J Contingency Table4.1 Notation
4.2 Independence in the I x J Contingency Table
4.2.1 Estimation and Degrees of Freedom
4.2.2 Odds-Ratios and Independence
4.2.3 Goodness of Fit and Lack of Fit of the Independence Model
4.3 Partitioning
4.3.1 Additivity of G2
4.3.2 Rules for Partitioning
4.4 Graphical Displays
4.4.1 Mosaic Plots
4.4.2 Cobweb Diagrams
4.5 Testing Independence with Ordinal Variables
References
5 The Exponential Family
5.1 Introduction
5.2 The Exponential Family
5.2.1 The Exponential Dispersion Family
5.3 Components of a General Linear Model. 5.4 EstimationReferences
6 A Model Taxonomy
6.1 Underlying Questions
6.1.1 Which Variables are of Interest?
6.1.2 What Categories should be Used?
6.1.3 What is the Type of Each Variable?
6.1.4 What is the Nature of Each Variable?
6.2 Identifying the Type of Model
7 The 2 x J Contingency Table
7.1 A Problem with X2 (and G2)
7.2 Using the Logit
7.2.1 Estimation of the Logit
7.2.2 The Null Model
7.3 Individual Data and Grouped Data
7.4 Precision, Confidence Intervals, and Prediction Intervals
7.4.1 Prediction Intervals.