The measurement invariance checker compares the nested models of a multigroup CFA (configural, metric, scalar and strict) exactly as they come out of lavaan or AMOS: it computes Δχ² with its exact p (chi-square CDF via the incomplete gamma function, verified against pchisq in R), ΔCFI, ΔRMSEA and ΔSRMR, applies the Chen (2007) and Cheung and Rensvold (2002) criteria, and writes the APA 7 table and the results paragraph. Worked example: a 9-item scale administered to 412 men and 389 women; configural χ²(54) = 128.40, CFI = .967, RMSEA = .058; metric Δχ²(8) = 11.20, p = .191, ΔCFI = −.002 (holds); scalar Δχ²(8) = 12.30, p = .138, ΔCFI = −.002, ΔSRMR = +.002 (holds); strict Δχ²(9) = 56.40, p < .001, ΔCFI = −.021, ΔSRMR = +.013 (not supported). Invariance holds up to the scalar level: the means of men and women can be compared.
What level do you need to compare means across groups? Scalar: without equal intercepts, a mean difference may come from the instrument rather than the construct. Does a significant Δχ² kill invariance? Not on its own: it inherits the sample-size sensitivity of χ², which is why the decision uses ΔCFI ≤ .010 together with ΔRMSEA ≤ .015 and ΔSRMR ≤ .030 for metric or ≤ .010 for scalar and strict invariance (Chen, 2007).
Check that your scale measures the same thing in each group before comparing means: Δχ² with its p, ΔCFI, ΔRMSEA and ΔSRMR under Chen (2007) criteria.
If you use it in your thesis or in a paper, cite it so that readers of your Methods section know how the calculation was done.
Ciudad-Fernández, V. (2026). Measurement invariance checker [Web application]. Ciudad Science. Retrieved October 14, 2026, from https://analisisdedatospsicologia.com/en/tools/measurement-invariance-checker
For your Methods section: Measurement invariance across groups was assessed by comparing nested models through the change in fit indices (Cheung & Rensvold, 2002; Chen, 2007), using the Ciudad Science measurement invariance checker (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026invarianza,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Measurement invariance checker}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/tools/measurement-invariance-checker},
urldate = {2026-10-14},
note = {Accessed 2026-10-14},
}