Measures of Association

The chi-square test alerts you when there is a statistically significant relationship between two variables, but it is silent as to the strength or magnitude of that relationship. We know from the previous two examples, for instance, that gender and education are related to attitudes toward capital punishment, but we do not know the magnitudes of these associations: They could be strong, moderate, or weak. This question is an important one because a trivial relationship—even if statistically significant in a technical sense—is not of much substantive or practical importance. Robust relationships are more meaningful. To illustrate this, suppose an evaluation of a gang-prevention program for youth was declared a success after researchers found a statistically significant difference in gang membership rates among youth who did and did not participate in the program. Digging deeper, however, you learn that 9% of the youth who went through the program ended up joining gangs, compared to 12% of those who did not participate. While any program that keeps kids out of gangs is laudable, a reduction of three percentage points can hardly be considered a resounding success. We would probably want to continue searching for a more effective way to prevent gang involvement. Measures of association offer insight into the magnitude of the differences between groups so that we can figure out how strong the overlap is.