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The measurement invariance is an essential assumption in the use of scale scores. Only when instrument is measuring the same trait across groups will the scores be acceptable and results be interpretable. The goodness-of-fit index of ΔCFI proposed by Cheung and Rensvold (2002) has been the gold standard criterion. The purpose of the present study was to expand previous study and set up additional goodness-of-fit comparison tools in testing measurement invariance. Simulation study was conducted to examine the performance of (a) ΔCFI under the lack of measurement invariance, as well as (b) the difference in Tucker-Lewis Index (TLI), which has adjusted for degrees of freedom, and (c) the Satorra-Bentler scaled chi-square difference test (TRd) under the condition of non-normality.