Abstract
Population invariance in equating exists when the relationship between two scales is the same for two or more subpopulations of examinees and hence the function used to equate the scales is not dependent on subpopulations. A lack of equating invariance (i.e., equating dependence) leads to a situation whereby examinees having the same score on one scale, but belonging to different subpopulations, have different expected test scores on the corresponding equated scale. This situation results in an expected advantage for one or more subpopulations of examinees and hence is a concern for fairness in assessment and disaggregated accountability. Little is known about the causes of equating dependence, and the purpose of this study is to locate a source of this problem. It is hypothesized that differential item functioning manifested in the anchor items of an assessment will have an effect on population invariance of equating. Findings show that when differential item functioning varies across forms in a differential manner across subpopulations, population invariance of equating can be compromised. Under these conditions, an increase in equating dependence is associated with increases in magnitudes of the differential item functioning and, to a lesser degree, increases in the frequency of anchor items with differential item functioning. These effects can be problematic in conditions of both unidirectional and bidirectional differential item functioning, and can pose problems for subpopulations that have equal or different mean ability levels.