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[Correction Notice: An erratum for this article was reported in Vol 95 (5) of Journal of Applied Psychology (see record 2010-18410-004). There was an error in Formula 6 on page 731 for the pooled standard deviation of the ESSD index. The correct formula is given in the erratum. Related to this, in Table 8 on page 739, the ETSSD statistic should have been. 094 for the cross cultural comparison and. 001 for the Administration Format example.] Much progress has been made in the past 2 decades with respect to methods of identifying measurement invariance or a lack thereof. Until now, the focus of these efforts has been to establish criteria for statistical significance in items and scales that function differently across samples. The power associated with tests of differential functioning, as with all significance tests, is affected by sample size and other considerations. Additionally, statistical significance need not imply …