Categorical Statistics for Communication Research

Bryan E. Denham

• Publisher: Wiley-Blackwell
• Year: 2016
• Print ISBN:
  9781118927090
  9781118927106
• Edition: 1
• eBook ISBN:
  9781118927076
• Topic: Social Sciences
• Subtopic: Social Science Research & Methodology
• Index: Social Sciences

Categorical Statistics for CommunicationResearch presents scholars with a discipline-specific guide to categorical data analysis. The text blends necessary background information and formulas for statistical procedures with data analyses illustrating techniques such as log- linear modeling and logistic regression analysis.

• Provides techniques for analyzing categorical data from a communication studies perspective
• Provides an accessible presentation of techniques for analyzing categorical data for communication scholars and other social scientists working at the advanced undergraduate and graduate teaching levels
• Illustrated with examples from different types of communication research such as health, political and sports communication and entertainment
• Includes exercises at the end of each chapter and a companion website containing exercise answers and chapter-by-chapter PowerPoint slides

1
Introduction to Categorical Statistics

This text focuses principally on the analysis of nominal and ordinal data. Nominal measures contain unordered categories while ordinal variables contain categories in a sequence; both types of measures appear frequently in communication research. At the nominal level, news texts may or may not mention specific issue attributes, and during election years, individuals may or may not view a debate, campaign for a candidate, or vote in a primary. Individuals may be male or female, and they may or may not have served in the military. In addition to these dichotomous measures, unordered polytomous variables include items such as race, religion, and marital status, each of which contains more than two categories. At the ordinal level, attitude statements frequently include five response options: Strongly Agree, Agree, Undecided, Disagree, and Strongly Disagree. Estimations of risk may range from No Risk to Great Risk, and individuals responding to policy decisions may range from Strongly Approve to Strongly Disapprove in their reactions.

Statistician Alan Agresti (1990) mentioned two additional types of categorical data: discrete interval and grouped interval. Discrete interval measures often contain a limited number of values, and because they take the form of integers – and integers only – they are not treated as continuous quantitative measures, which can take on any real value. As an example of discrete interval data, a college dean might record the number of people who earn a graduate degree in communication each year, with recipients constituting discrete units. Regarding grouped interval data, researchers sometimes combine continuous interval measures into ordered brackets, as in the case of income, where asking a survey respondent for a specific figure might be considered both invasive and unnecessary. As a second example, while news reports about a given subject might average 731 words, a researcher might be interested in the number of articles that appear in ordered increments of 250 words.

Historical Overview

In covering techniques for analyzing both ordered and unordered categorical variables, the current text recognizes that statisticians have differed in their assumptions and approaches to categorical data analysis. As Powers and Xie (2000) explained, one school of thought considers categorical data part of an underlying continuous distribution, while a second perspective considers categorical data inherently categorical. In historical terms, Agresti (1990) explained that Karl Pearson (1900), who developed the chi‐square goodness‐of‐fit test, assumed continuous distributions underlying categorical variables, while one of Pearson’s contemporaries, George Udny Yule (1900), believed that certain types of variables were inherently categorical and did not require assumptions of underlying distributions. Fienberg (2007) observed merit in both perspectives, noting that Pearson and Yule, along with R. A. Fisher (1922a, 1922b), played significant roles in building a foundation for the development of more advanced analytic techniques (see, for additional history, Fienberg and Rinaldo 2007, Plackett 1983). Interestingly, several decades would pass before statisticians developed advanced procedures for categorical data analysis. Most of the modeling techniques covered in the current text emerged after 1960, whereas statisticians had developed multivariate tests for continuous data decades earlier.

Seminal research in communication (e.g., Lazarsfeld, Berelson, and Gaudet 1948) demonstrates how social scientists analyzed and displayed categorical data. Lacking advanced statistical procedures, researchers typically presented data in the form of frequency charts and cross‐tabulations. As an example, Table 1.1 contains data gathered in the 1948 election year and published in Voting: A Study of Opinion Formation in a Presidential Election (Berelson, Lazarsfeld, and McPhee 1954, 243). The table contains both nominal and ordinal frequency measures and offers descriptive information in a limited but effective manner. Recognizing a pattern between exposure to mass media and level of interest in the presidential election, the authors reported demographic and psychographic information about 814 individuals in Elmira, New York. In the table, numbers appearing in parentheses indicate cell frequencies while figures outside the parentheses indicate the percentage of individuals in each cell who were exposed to media at “High and High‐Middle” levels (N = 432). This approach allowed readers, if so inclined, to calculate the number of respondents in each cell who scored “Low and Low‐Middle” on exposure indices (N = 382), all the while inspecting results across three levels of campaign interest. The use of percentages for “High and High‐Middle” media users allowed the authors to show statistical patterns that raw cell frequencies would have obscured. Examining the table, one observes that individuals exposed the most to mass media and interested the most in the election belonged to more organizations, had higher levels of education, and appeared in higher socioeconomic classes.

Table 1.1 Example of cross‐classifications containing nominal and ordinal measures

Percentage with High or High‐Middle Exposure (on Index)
	Level of Interest
Characteristics	Great Deal	Quite a Lot	Not Much at All
(a) Organization Membership:
Belongs to Two or More	82 (103)	68 (87)	39 (64)
Belongs to One	72 (71)	57 (74)	34 (68)
Belongs to None	62 (100)	47 (112)	24 (126)
(b) E...

Table of contents

• Cover
• Title Page
• Table of Contents
• Preface
• Acknowledgments
• About the Companion Website
• 1 Introduction to Categorical Statistics
• 2 Univariate Goodness of Fit and Contingency Tables in Two Dimensions
• 3 Contingency Tables in Three Dimensions
• 4 Log-linear Analysis
• 5 Logit Log-linear Analysis
• 6 Binary Logistic Regression
• 7 Multinomial Logistic Regression
• 8 Ordinal Logistic Regression
• 9 Probit Analysis
• 10 Poisson and Negative Binomial Regression
• 11 Interrater Agreement Measures for Nominal and Ordinal Data
• 12 Concluding Communication
• Appendix A: Chi-Square Table
• Appendix B: SPSS Code for Selected Procedures
• Index
• End User License Agreement