In conducting a cross-cultural study with a quantitative method, the researchers need to effectively address the cultural and linguistic influence on the operation of the instrument (or scale) across population groups. Measurement invariance (MI) provides valuable information to this concern and is the key to many psychological and developmental research studies. It is tested by evaluating how well the specified model fits the observed data. Researchers had developed effective fit indices to evaluate MI. Most scholars utilized the chi-square test with some alternative fit indices (such as root mean square error of approximation (RMSEA), standardized root-mean-square residual (SRMR), comparative fit index (CFI), and others) to report MI. Researchers argue about the sensitivity of these fit indices, and whether these fit indices accurately reflect the MI level. The current study followed Khojasteh and Lo (2015)'s study to test the sensitivities of a series of fit indices, including ΔCFI, ΔRMSEA, ΔSRMR, ΔGamma, and Δχ2, under specified conditions with Monte Carlo simulation data. Experimental conditions included test length, number of factors, sample sizes, factor loadings, and the percentage of noninvariant items. Results showed that the ΔCFI and ΔGamma are most powerful in testing invariance and are less sensitive to the sample size and non-invariance (or lack of invariance, LOI) situations. There was inflation in Type I error in the 2 factors 8 variable models. ΔSRMR and ΔRMSEA are more powerful only when the sample size is 1,000. ΔSRMR is sensitive to sample size and level of LOI; hence, it is not recommended. The results are compared with previous simulation studies and provide significant implications to researchers who are applying measurement invariance procedures about what fit indices to adopt in their studies.


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Graduation Date





Sivo, Stephen


Doctor of Philosophy (Ph.D.)


College of Community Innovation and Education


Learning Sciences and Educational Research

Degree Program

Education; Methodology, Measurement and Analysis


CFE0009173; DP0026769





Release Date

August 2025

Length of Campus-only Access

3 years

Access Status

Doctoral Dissertation (Campus-only Access)

Restricted to the UCF community until August 2025; it will then be open access.