Statistical Approaches for Nominal Data: Chi-Square Tests

Abstract

In the previous chapter, we considered statistical tests that involve (1) a single continuous numeric variable, the sample mean for which is tested against a hypothetical population value, and (2) a single continuous numeric variable in which we compare means across a two category nominal level grouping variable like sex. Sometimes, however, we are faced with two nominal level variables we think may be related, like marital status and region of the country. In other cases, we may have a pair of ordinal variables, or a combination of nominal and ordinal variables, we expect to be associated but perhaps not linearly. For example, we may be interested in the relationship between religious affiliation (e.g., Protestant, Catholic, Jewish, Other, None) and educational degree attainment (e.g., high school diploma, 2-year college degree, 4-year college degree, more than a 4-year degree).