# Inequality As a Summary Measure for the Effect of a Nominal Independent Variable

## Introduction

### Abstract

Many of the topics most central to sociological study involve nominal groupings. Race-ethnicity, religious affiliation, relationship status, sexual orientation, occupational sector, and political party are but a few examples. There are many cases in which a summary of a nominal variable’s effect as a holistic construct is needed and useful for interpretation. For example, has the role of religion in everyday life declined over the last 40 years? Fundamentally, this question involves summarizing the effect of many religious categories at one time point (say, 1980) and at a subsequent time point (say, 2020), and comparing the two summaries. As another example, what amount of the racial-ethnic disparities in health are explained by SES? Here, summarizing the effect of race-ethnicity before and after accounting for SES factors is needed along with a test of the difference in the summaries. In this project, we propose a new summary measure of nominal independent variable’s effects. We build on multiple classic approaches that remain useful but limited in their application. We propose calculating absolute and mean inequality measures using marginal effects to summarize a nominal independent variable’s holistic effect. The added benefit of our method is both an intuitive effect size metric and an approach that can be applied across many both linear and nonlinear models.

### Example

For an example of the approach, see the slides and example code from our presentation at the 2024 Sociological Science conference:

### Citation

For now, please cite as:

Mize, Trenton D. and Bing Han. 2024. "Inequality As a Summary Measure for the Effect of Nominal Independent Variables." Paper presented at the Sociological Science conference, Duke University.

## Stata Command

A Stata command to automate the calculation of the inequality measures is coming soon and will be posted here.