A course in categorical data analysis

✍ Scribed by Leonard, Thomas; Papasouliotis, Orestis

• Publisher: Chapman & Hall/CRC Press
• Year: 2020;2018
• Tongue: English
• Leaves: 204
• Series: Texts in statistical science
• Edition: First edition
• Category: Library

✦ Synopsis

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

Cover......Page 1
Half Title......Page 2
Title Page......Page 6
Copyright Page......Page 7
Dedication......Page 8
Table of Contents......Page 10
Preface......Page 14
Special Software......Page 20
1.1 Experimental design for a population proportion......Page 22
1.2 Further properties of the binomial distribution......Page 27
1.3 Statistical procedures for the binomial distribution......Page 29
1.4 The Poisson distribution......Page 33
1.5 Statistical procedures for the Poisson distribution......Page 36
1.6 The multinomial distribution......Page 38
1.7 Sir Ronald Fisher's conditioning result......Page 40
1.8 More general sampling models......Page 41
1.9 Generalising the binomial distribution......Page 43
1.10 The discrete exponential family of distributions......Page 46
1.11 Generalising the multinomial distribution......Page 50
Exercises......Page 51
2.1 Conditional probability and independence......Page 56
2.2 Independence of rows and columns......Page 57
2.3 Investigating independence, given observational data......Page 58
2.4 Edwards' theorem......Page 62
2.5 Log-contrasts and the multinomial distribution......Page 65
2.6 The log-measure-of-association test......Page 66
2.7 The product binomial model......Page 69
2.8 The independent Poisson model......Page 72
2.9 Fisher's exact test......Page 77
2.10 Power properties of our test procedures......Page 79
Exercises......Page 80
3.1 Probability theory......Page 86
3.2 The Cornish pixie/Irish leprechaun example......Page 88
3.3 Interpretation of Simpson's paradox......Page 90
3.4 The three-directional approach......Page 92
3.5 Measure of association analysis for 23 tables......Page 96
3.6 Medical example......Page 99
3.7 Testing equality for two 2 x 2 tables......Page 101
Exercises......Page 103
4.1 Experimental design......Page 106
4.2 Statistical results (phase 3) of study......Page 109
4.3 Further validation of results......Page 112
Exercises......Page 114
5.1 Introductory example (no totals fixed}......Page 116
5.2 Methodological developments (no totals fixed)......Page 119
5.3 Numerical example (a four-corners model)......Page 123
5.4 Methodological developments (overall total fixed)......Page 124
5.5 Business school example (overall total fixed)......Page 126
5.6 Methodological developments (row totals fixed)......Page 127
5.7 Advertising example (row totals fixed)......Page 129
5.8 Testing for equality of unconditional cell probabilities......Page 131
5.9 Analysis of Berkeley admissions data......Page 132
Exercises......Page 135
6.1 Hypertension, obesity, and alcohol consumption......Page 140
6.2 The Bristol cervical screening data......Page 146
6.3 The multiple sclerosis data......Page 149
6.4 The Dundee dental health data......Page 150
Exercises......Page 151
7.1 Fixed zeroes and missing observations......Page 152
7.2 Incomplete tables......Page 154
7.3 Perfectly fitting further cells......Page 155
7.4 Complete tables......Page 156
7.5 Further data sets......Page 157
Exercises......Page 158
8.1 Review of general methodology......Page 160
8.2 Analysing your data using Splus......Page 166
8.3 Analysis of the mice exposure data......Page 168
8.4 Analysis of space shuttle failure data......Page 169
8.5 Further data sets......Page 170
Exercises......Page 171
9.1 Regression models for Poisson data......Page 174
9.2 The California earthquake data......Page 176
9.3 A generalisation of logistic regression......Page 177
9.4 Logistic regression for matched case-control studies......Page 181
Exercises......Page 183
10.1 Continuous random variables......Page 186
10.2 Logistic discrimination analysis......Page 187
10.3 Testing the slope and quadratic term......Page 190
10.4 Extensions......Page 191
10.5 Three-way contingency tables......Page 193
Exercises......Page 194
References......Page 196
Index......Page 202