Paul R. Yarnold
Optimal Data Analysis, LLC
Data are from a contingency table used to determine the relationship between years of schooling arbitrarily parsed into six ordered categories, and ethnic group measured on a categorical variable with seven levels. Although ordinal data are inappropriate for analysis via chi-square-based methods, log-linear analysis was used to investigate association between years of schooling and ethnic group. Because the independence model didn’t provide an acceptable representation of the data, it is clear that some form of association underlies the data. A three-dimensional log-linear-based solution was proposed: “In terms of the scores in the first dimension only, whites are closest to Chinese; blacks are closest to Vietnamese; and Hispanics are extreme outliers. Either the distance matrix…or a two-dimensional plot…can be used to locate the groups or measure distances in terms of educational distributions” (p. 103). All possible pairwise comparisons were conducted between ethnic groups using UniODA, and the results revealed a single dimension (years of schooling) perfectly described the statistical conclusions reached for 20 of 21 analyses. The single inconsistent finding had an associated miniscule effect size.