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FACTOR ANALYSIS

Factor analysis is based on the simple and compelling idea that if things we observe are correlated with each other, they must have some underlying variable in common. Factor analysis refers to a set of techniques for identifying and interpreting those underlying variables.

For example, people in the United States who are in favor of gun control are likely (but not guaranteed) to be in favor of: (1) a woman’s right to an abortion, (2) participation by the U.S. military in overseas peacekeeping missions of the United Nations, and (3) affirmative action in college admissions. People who are against gun control are likely to favor: (1) restrictions on abortion, (2) less involvement of the United States in UN peacekeeping missions, and (3) curbs on affirmative action.

Of course, people are free to mix and match their opinions on any of these issues, but overall, there is a strong association of opinions across these issues. Factor analysis assumes that this association is the result of an underlying, hypothetical variable, a general attitude orientation. We can use a set of statistical techniques to identify both the existence and the content of this underlying variable. Naming the variable is a strictly qualitative exercise.

Many studies have demonstrated the existence of an underlying value orientation usually called ‘‘liberal versus conservative.” Liberals and conservatives exhibit packages of attitudes about things like personal freedom (as with the right to own a hand gun or the right to an abortion), about foreign policy (as with involvement in peacekeeping missions), and about domestic policies (as with affirmative action).

This idea of multidimensional supervariables that underlie a set of observations was first articulated in 1904 by Charles E. Spearman (he for whom Spearman’s rank-order correlation coefficient is named—see chapter 21). Spearman noticed that the scores of students on various exams (classics, French, English, math, etc.) were correlated. He suggested that the exam scores were correlated with each other because they were all correlated with an underlying factor, which he labeled g, for general intelligence.

The single-factor theory of intelligence has been repudiated and defended over the years and continues to be the focus of scholarly and political debate, but the idea of factors—multidimensional variables—that underlie and give rise to a set of correlated events is one of the most important developments in all the social sciences.

The data for factor analysis are often attitude items, like the kind you see in Likert scales, but can just as well be about artifacts (movies, songs, buildings, cars, brands of beer . . .), people (movie stars, politicians, fashion models, criminals, classical musicians . . .), or even countries. Factor analysis is used across the social sciences in data reduction—to explore large data sets with dozens or even hundreds of variables in order to extract a few variables that tell a big story.

In political science, for example, Lieske (1993) partitioned the 3,164 counties in the United States into 10 distinctive regional subcultures by looking for common, underlying factors in the correlations among 45 racial, ethnic, religious, and social structural variables. In social psychology, Stein et al. (1991) used factor analysis to test the influence of ethnicity, socioeconomic status, and various anxieties as barriers to the use of mammography among white, African American, and Hispanic women. Factor analysis confirmed the influence of five kinds of anxiety: fear of radiation, fear of pain, embarrassment about breast exams, anxiety about what might be found, and concerns about cost.

 
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