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.
Millsap, Roger E.; Meredith, William.
Inferential conditions in the statistical detection of measurement bias.
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