Measures are comparable if and only if measurement equivalence has been demonstrated. Although comparability and equivalence of measures are sometimes used interchangeably, we advocate a subtle but important difference in meaning. Comparability implies that measures from one group can be compared with measures from another group. It is a property of the measures, which is given or not. In particular, comparability presumes valid measures within each group compared. Measurement equivalence, by contrast, refers to the way measures are derived and estimated. It is intrinsically tied to the underlying theory of measurement. Thus, measurement equivalence cannot be dealt with in isolation. Its assessment has to be incorporated into the theoretical framework of measurement. Measurement equivalence is closely connected to construct validity for it refers to the way manifest indicators are related to the latent variable, within a particular culture and across different cultures. From this it follows that equivalence cannot, or should not, be treated as a separate issue but as a constitutive element of validity. A discussion of measurement equivalence without addressing validity would be incomplete.

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