A Course in Categorical Data Analysis

by Leonard; Thomas

• ISBN13: 9781584881803
• ISBN10: 1584881801
• eBook ISBN(s): 9781000154658
• Format: Nonspecific Binding
• Copyright: 1999-11-22
• Publisher: Chapman & Hall/
• More Book Details

Summary

Categorical data-comprising counts of individuals, objects, or entities in different categories-emerge frequently from many areas of study, including medicine, sociology, geology, and education. They provide important statistical information that can lead to real-life conclusions and the discovery of fresh knowledge. Therefore, the ability to manipulate, understand, and interpret categorical data becomes of interest-if not essential-to professionals and students in a broad range of disciplines.Although t-tests, linear regression, and analysis of variance are useful, valid methods for analysis of measurement data, categorical data requires a different methodology and techniques typically not encountered in introductory statistics courses. Developed from long experience in teaching categorical analysis to a multidisciplinary mix of undergraduate and graduate students, A Course in Categorical Data Analysis presents the easiest, most straightforward ways of extracting real-life conclusions from contingency tables. The author uses a Fisherian approach to categorical data analysis and incorporates numerous examples and real data sets. Although he offers S-PLUS routines through the Internet, readers do not need full knowledge of a statistical software package.In this unique text, the author chooses methods and an approach that nurtures intuitive thinking. He trains his readers to focus not on finding a model that fits the data, but on using different models that may lead to meaningful conclusions. The book offers some simple, innovative techniques not highighted in other texts that help make the book accessible to a broad, interdisciplinary audience. A Course in Categorical Data Analysis enables readers to quickly use its offering of tools for drawing scientific, medical, or real-life conclusions from categorical data sets.

Table of Contents

Preface
Special Software
Sampling Distributions	1	(34)
Experimental design for a population proportion	1	(5)
Further properties of the binomial distribution	6	(2)
Statistical procedures for the binomial distribution	8	(4)
The Poisson distribution	12	(3)
Statistical procedures for the Possion distribution	15	(2)
The multinomial distribution	17	(2)
Sir Ronald Fisher's conditioning result	19	(1)
More general sampling models	20	(2)
Generalising the binomial distribution	22	(3)
The discrete exponential family of distributions	25	(4)
Generalising the multinomial distribution	29	(6)
Exercises	30	(5)
Two-by-Two Contingency Tables	35	(30)
Conditional probability and independence	35	(1)
Independence of rows and columns	36	(1)
Investigating independence, given observational data	37	(4)
Edwards' theorem	41	(3)
Log-contrasts and the multinomial distribution	44	(1)
The log-measure-of-association test	45	(3)
The product binomial model	48	(3)
The independent Poisson model	51	(5)
Fisher's exact test	56	(2)
Power properties of our test procedures	58	(7)
Exercises	59	(6)
Simpson's Paradox and 23 Tables	65	(20)
Probability theory	65	(2)
The Cornish pixie/Irish leprechaun example	67	(2)
Interpretation of Simpson's paradox	69	(2)
The three-directional approach	71	(4)
Measure of association analysis for 23 tables	75	(3)
Medical example	78	(2)
Testing equality for two 2 x 2 tables	80	(2)
The three-directional approach to the analysis of 23 tables (summary)	82	(3)
Exercises	82	(3)
The Madison Drug and Alcohol Abuse Study	85	(10)
Experimental design	85	(3)
Statistical results (phase 3) of study	88	(3)
Further validation of results	91	(4)
Exercises	93	(2)
Goodman's Full-Rank Interaction Analysis	95	(24)
Introductory example (no totals fixed)	95	(3)
Methodological developments (no totals fixed)	98	(4)
Numerical example (a four-corners model)	102	(1)
Methodological developments (overall total fixed)	103	(2)
Business school example (overall total fixed)	105	(1)
Methodological developments (row totals fixed)	106	(2)
Advertising example (row totals fixed)	108	(2)
Testing for equality of unconditional cell probabilities	110	(1)
Analysis of Berkeley admissions data	111	(3)
Further data sets	114	(5)
Exercises	114	(5)
Further Examples and Extensions	119	(12)
Hypertension, obesity, and alcohol consumption	119	(6)
The Bristol cervical screening data	125	(3)
The multiple sclerosis data	128	(1)
The Dundee dental health data	129	(2)
Exercises	130	(1)
Conditional Independence Models for Two-Way Tables	131	(8)
Fixed zeroes and missing observations	131	(2)
Incomplete tables	133	(1)
Perfectly fitting further cells	134	(1)
Complete tables	135	(1)
Further data sets	136	(3)
Exercises	137	(2)
Logistic Regression	139	(14)
Review of general methodology	139	(6)
Analysing your data using Splus	145	(2)
Analysis of the mice exposure data	147	(1)
Analysis of space shuttle failure data	148	(1)
Further data sets	149	(4)
Exercises	150	(3)
Further Regression Models	153	(12)
Regression models for Poisson data	153	(2)
The California earthquake data	155	(1)
A generalisation of logistic regression	156	(4)
Logistic regression for matched case-control studies	160	(2)
Further data	162	(3)
Exercises	162	(3)
Final Topics	165	(10)
Continuous random variables	165	(1)
Logistic discrimination analysis	166	(3)
Testing the slope and quadratic term	169	(1)
Extensions	170	(2)
Three-way contingency tables	172	(3)
Exercises	173	(2)
References	175	(6)
Index	181