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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

Inferential Conditions in the Statistical Detection of Measurement Bias