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Analysis of Nominal Data (Quantitative Applications in the Social Sciences)

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This is one of the entries in the Sage series, "Quantitative Applications oin the Social Sciences." The subject of this slim volume (just 82 pages long)? Analyzing nominal data. Nominal data are at the lowest end of the level of measurement. These are categorical variables, where the different categories have no numerical relationship to one another (e.g., religion, major in college, etc.). Only specific kinds of statistical techniques are appropriate for such variables. This book does a serviceable job discussing the essence of nominal data, measures of association (relationship between two variables)--including the odds ratio, the contingency coefficient, lambda, etc., and multivariate techniques (e.g., log linear models).

Not the easiest reading book, but a resource for those willing to wade through the text.(

I first read H.T. Reynolds' Analysis of Nominal Data when I was regularly teaching an introductory statistics course to upperclassmen and graduate students. Since most students find statistical reasoning to be counter-intuitive, I was always on the lookout for something brief and straightforward to use as ancillary reading. It was my hope that this additional material would reinforce fundamental concepts in a simple and accessible way. The concepts I had in mind were the usual ones, such as statistical independence, statistical association, measures of association, strength of association, statistical significance, tests of significance, statistical power, making inferences from sample to population, and so on. Very basic material, but hard for most of us to grasp on first encounter.

Reynolds' inexpensive little eighty page paperback was initially appealing because the author writes clearly and succinctly and addresses basic issues. Though the first couple of chapters presuppose familiarity with notational conventions, I imagined that I could cover these in class before making reading assignments. I thought it was a virtue of the text that Reynold's introduces Chi-squared using double summation notation early on, and I was not troubled by his use of the log likelihood version of Chi-squared because his account was straightforward and easy to follow. Moreover, students eventually have to learn to work with natural logs since they are essential to testing the ubiquitous measure of association Pearson's r for statistical significance when tables tailored to this purpose are not available, as is often the case.

However, as I got further into Reynolds' book, it became quite clear that, given my objectives, it contained a good deal of surplus content. By that I mean that so much attention was devoted to the peculiarities of nominal or categorical data presented in tabular form and the idiosyncrasies of measures commonly applied to its analysis, that students were sure to get bogged down. Issues such as rules for making tables more informative through partitioning and types of perfect association, as well as conditions under which some measures such as the Contingency Coefficient C and Tschuprow's T are not normed are of interest to analysts working with contingency tables, but they are not readily generalizable to analyses not limited to crosstabs and nominal level data. I concluded that using the Analysis of Nominal Data as ancillary reading was a bad idea.

Nevertheless, this unfavorable assessment of Reynolds' book as a teaching tool for beginning students should not be taken to mean that his book is not valuable. If you find yourself in an applied social science setting, say deep in the bowels of a large state bureaucracy, presented with data that does not lend itself to the application of more informative techniques, the Analysis of Nominal Data can be quite useful. It introduces a variety of measures of association, some of which have intuitively appealing interpretations while others do not. If circumstances constrain you to use one of the less intuitively appealing measures, Reynolds book will at least enable you to explain why and to give a rough and ready interpretation based on the measure's properties.

You'll also be able to ransack more complex contingency tables for additional information, much of which can be presented simply by using percentages or proportions. You will, moreover, be alert to the presence of row and column totals (marginal frequencies) which artificially constrain or otherwise distort the numerical values of the measures you compute.

Furthermore, you'll be able to test measures of association for statistical significance, something that even the most statistically uninformed consumers of your analyses will have heard about. And you'll also be able to explain to your audience why a statistically significant association need not be an important one. In a limited way, moreover, and given adequate data, you'll be able to understand and apply statistical control.

Perhaps most important, you'll be much less likely to be taken unawares when, as is common with applied work done by well-meaning people who are untrained in data analysis, someone presents you his or her own cross-tabs, which you will be able to interpret and evaluate as to their statistical adequacy.

It is useful that Reynolds introduces readers to odds, odds ratios, and log odds. (Reynold's failure to provide an interpretation for the odds ratio is, well, odd.) Anyhow, these measures are essential to understanding multivariate treatments of nominal level data using loglinear analysis discussed in more advanced tests such as Hutcheson and Sofroniou's The Multivariate Social Scientist. Loglinear analysis is such a distinctive procedure, however, that with or without Reynold's very brief introduction it takes a good deal of effort for most readers to understand and apply.

Folks who have spent a good part of their adult lives in research institutions may dismiss the material in Reynolds' book as hopelessly obsolete, especially now that loglinear analysis is available in user-friendly software such as SPSS. However, anyone who has worked with public or private organizations that have a responsibility for producing quantitative analyses of evaluative import knows that there is still a need for measures such as those discussed by Reynolds. We may judge it unfortunate that these kinds of measures and ways of thinking about data have still not completely given way to more powerful procedures. Nevertheless, this is the case, so we may as well do the best we can with what we've got.

Finally, it's true that Reynolds failure to include a table of critical values of Chi-squared creates minor but annoying hassles for his readers. It is also the case that Reynolds sometimes goes beyond succinctness and presents material in such a condensed form that it takes an awful lot of thought to grasp. However, if you stick with this material it can be mastered without too much grief and aggravation. Whether or not it's worth the effort depends on the circumstances in which you find yourself.