Inferential conditions in the statistical detection of measurement bias

Measurement bias in an observed variable Y as a measure of an unobserved variable W exists when the relationship of Y to W varies among populations of interest. Bias is often studied by examining population differences in the relationship of Y to a second observed measure Z that serves as a substitute for W. Whether the results of such studies have implications for measurement bias is addressed by first defining two forms of invariance- one corresponding to the relationship of Y to the unmeasured W, and one corresponding to the relationship of Y to the observed Z. General theoretical conditions are provided that justify the inference of one form of invariance from the other. The implications of these conditions for bias detection in two broad areas of application are discussed: differential item functioning and predictive bias in employment and educational settings. It is concluded that the conditions for inference are restrictive, and that bias investigations that rely strictly on observed measures are not, in general, diagnostic of measurement bias or the lack of bias. Some alternative approaches to bias detection are discussed. Index terms: differential item functioning, invariance, item bias, item response theory, measurement bias, predictive bias