Categorical Data Analysis by Example (eBook)

Graham J. G. Upton (Autor)

eBook Download: EPUB

2016
John Wiley & Sons (Verlag)
978-1-119-30793-8 (ISBN)

Infos

Introduces the key concepts in the analysis of categoricaldata with illustrative examples and accompanying R code

This book is aimed at all those who wish to discover how to analyze categorical data without getting immersed in complicated mathematics and without needing to wade through a large amount of prose. It is aimed at researchers with their own data ready to be analyzed and at students who would like an approachable alternative view of the subject.

Each new topic in categorical data analysis is illustrated with an example that readers can apply to their own sets of data. In many cases, R code is given and excerpts from the resulting output are presented. In the context of log-linear models for cross-tabulations, two specialties of the house have been included: the use of cobweb diagrams to get visual information concerning significant interactions, and a procedure for detecting outlier category combinations. The R code used for these is available and may be freely adapted. In addition, this book:

• Uses an example to illustrate each new topic in categorical data

• Provides a clear explanation of an important subject

• Is understandable to most readers with minimal statistical and mathematical backgrounds

• Contains examples that are accompanied by R code and resulting output

• Includes starred sections that provide more background details for interested readers

Categorical Data Analysis by Example is a reference for students in statistics and researchers in other disciplines, especially the social sciences, who use categorical data. This book is also a reference for practitioners in market research, medicine, and other fields.

GRAHAM J. G. UPTON is formerly Professor of Applied Statistics, Department of Mathematical Sciences, University of Essex. Dr. Upton is author of The Analysis of Cross-tabulated Data (1978) and joint author of Spatial Data Analysis by Example (2 volumes, 1995), both published by Wiley. He is the lead author of The Oxford Dictionary of Statistics (OUP, 2014). His books have been translated into Japanese, Russian, and Welsh.

GRAHAM J. G. UPTON is formerly Professor of Applied Statistics, Department of Mathematical Sciences, University of Essex. Dr. Upton is author of The Analysis of Cross-tabulated Data (1978) and joint author of Spatial Data Analysis by Example (2 volumes, 1995), both published by Wiley. He is the lead author of The Oxford Dictionary of Statistics (OUP, 2014). His books have been translated into Japanese, Russian, and Welsh.

Rezensionen

"Concise introduction to dealing with
categorical data (with supporting R code)
which will help the general data scientist." (Raspberry Pi March 2017)

Textauszug

CHAPTER 1
Introduction

This chapter introduces basic statistical ideas and terminology in what the author hopes is a suitably concise fashion. Many readers will be able to turn to Chapter 2 without further ado!

1.1 What are categorical data?

Categorical data are the observed values of variables such as the color of a book, a person’s religion, gender, political preference, social class, etc. In short, any variable other than a continuous variable (such as length, weight, time, distance, etc.).

If the categories have no obvious order (e.g., Red, Yellow, White, Blue) then the variable is described as a nominal variable. If the categories have an obvious order (e.g., Small, Medium, Large) then the variable is described as an ordinal variable. In the latter case the categories may relate to an underlying continuous variable where the precise value is unrecorded, or where it simplifies matters to replace the measurement by the relevant category. For example, while an individual’s age may be known, it may suffice to record it as belonging to one of the categories “Under 18,” “Between 18 and 65,” “Over 65.”

If a variable has just two categories, then it is a binary variable and whether or not the categories are ordered has no effect on the ensuing analysis.

1.2 A typical data set

The basic data with which we are concerned are counts, also called frequencies. Such data occur naturally when we summarize the answers to questions in a survey such as that in Table 1.1.

Table 1.1 Hypothetical sports preference survey

Sports preference questionnaire

(A) Are you:- Male Female ?

(B) Are you:- Aged 45 or under Aged over 45 ?

(C) Do you:- Prefer golf to tennis Prefer tennis to golf ?

The people answering this (fictitious) survey will be classified by each of the three characteristics: gender, age, and sport preference. Suppose that the 400 replies were as given in Table 1.2 which shows that males prefer golf to tennis (142 out of 194 is 73%) whereas females prefer tennis to golf (161 out of 206 is 78%). However, there is a lot of other information available. For example:

Table 1.2 Results of sports preference survey

Category of response

Frequency

Male, aged 45 or under, prefers golf to tennis

64

Male, aged 45 or under, prefers tennis to golf

28

Male, aged over 45, prefers golf to tennis

78

Male, aged over 45, prefers tennis to golf

24

Female, aged 45 or under, prefers golf to tennis

22

Female, aged 45 or under, prefers tennis to golf

86

Female, aged over 45, prefers golf to tennis

23

Female, aged over 45, prefers tennis to golf

75

• There are more replies from females than males.
• There are more tennis lovers than golf lovers.
• Amongst males, the proportion preferring golf to tennis is greater amongst those aged over 45 (78/102 is 76%) than those aged 45 or under (64/92 is 70%).

This book is concerned with models that can reveal all of these subtleties simultaneously.

1.3 Visualization and cross-tabulation

While Table 1.2 certainly summarizes the results, it does so in a clumsily long-winded fashion. We need a more succinct alternative, which is provided in Table 1.3.

Table 1.3 Presentation of survey results by gender

Male

Female

Sport

45 and under

Over 45

Total

Sport

45 and under

Over 45

Total

Tennis

28

24

52

Tennis

86

75

161

Golf

64

78

142

Golf

22

23

45

Total

92

102

194

Total

108

98

206

A table of this type is referred to as a contingency table—in this case it is (in effect) a three-dimensional contingency table. The locations in the body of the table are referred to as the cells of the table. Note that the table can be presented in several different ways. One alternative is Table 1.4.

Table 1.4 Presentation of survey results by sport preference

Prefers tennis

Prefers golf

Gender

45 and under

Over 45

Total

Gender

45 and under

Over 45

Total

Female

86

75

161

Female

22

23

45

Male

28

24

52

Male

64

78

142

Total

114

99

213

Total

86

101

187

Figure 1.1 Illustration of results of sports preference survey.

In this example, the problem is that the page of a book is two-dimensional, whereas, with its three classifying variables, the data set is essentially three-dimensional, as Figure 1.1 indicates. Each face of the diagram contains information about the 2 × 2 category combinations for two variables for some particular category of the third variable.

With a small table and just three variables, a diagram is feasible, as Figure 1.1 illustrates. In general, however, there will be too many variables and too many categories for this to be a useful approach.

1.4 Samples, populations, and random variation

Suppose we repeat the survey of sport preferences, interviewing a second group of 100 individuals and obtaining the results summarized in Table 1.5.

Table 1.5 The results of a second survey

Prefers tennis

Prefers golf

Gender

45 and under

Over 45

Total

Gender

45 and under

Over 45

Total

Female

81

76

157

Female

16

24

40

Male

26

34

60

Male

62

81

143

Total

107

110

217

Total

78

105

183

As one would expect, the results are very similar to those from the first survey, but they are not identical. All the principal characteristics (for example, the preference of females for tennis and males for golf) are again present, but there are slight...

Produkt-Details

• Erscheint lt. Verlag: 24.10.2016
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Analysis • Book • categorical • categoricaldata • categorical data analysis • Code • Concepts • ConText • Data • Datenanalyse • Example • Examples • excerpts • Given • Illustrated • illustrative • Kategoriale Datenanalyse • Kategorielle Datenanalyse • Key • Loglinear • many • Models • New • Output • presented • Readers • Ready • Researchers • Statistical Software / R • Statistics • Statistics for Social Sciences • Statistik • Statistik in den Sozialwissenschaften • Statistiksoftware / R • students • topic
• ISBN-10: 1-119-30793-7 / 1119307937
• ISBN-13: 978-1-119-30793-8 / 9781119307938