How Measurement Error in Dichotomous Predictors Affects the Analysis of Continuous Criteria

Suppose you are comparing a continuous outcome across two groups, and the average value of that outcome genuinely differs from one group to the other. If the variable you use to assign people to groups is itself measured with error, meaning some cases get sorted into the wrong group, then whatever effect size you estimate will be off.

The problem parallels what happens in the classical errors-in-variables model that applies to continuous predictors. There, noise in the predictor pulls the estimated relationship toward zero. The same thing occurs when the predictor is a two-category (dichotomous) grouping variable: the true difference between the groups ends up being underestimated.

Christof Schuster works through the mechanics of this and provides a correction. Once certain features of the measurement error are known, for instance how reliably cases are classified, the biased estimate can be adjusted back toward the true effect size.

The treatment stays within a regression framework and keeps the focus narrow: measurement error in predictors, the reliability of a dichotomous predictor, and what both mean for interpreting group differences in a continuous criterion.