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Invariance Testing


Invariance Testing in Psychology

Invariance testing is a statistical technique to assist researchers in determining the degree of comparability of a measure, which has been used with different groups.

When a measure has been modified, translated, or used with people in various cultures, invariance testing can help determine if the same construct is being measured by the changes to the original measure and how people in different groups may understand the items.

Invariance testing is important to ensure a measure functions in the same way (measures the same concept) in different groups.

Hypothetical Example: A 16-item measure of forgiveness may have been originally written in American English and tested with college samples. The items are translated into four different languages and administered in ten different locations. One thing a researcher can do is examine the psychometric properties in the different samples. They may also consider correlations with other measures.  Another strategy is to conduct factor analyses to see if the scale has the same number of factors as did the original and if the same items load on the factors as they did in the original version.

Research Example: Davis et al. (2016) 

  [Notice the phrase "understood in the same way" as a key feature of the concept, invariance testing.

Although previous studies have suggested that the MFQ subscales are associated with religiosity, basic research has not yet established whether the measure is understood in the same way by believing and nonbelieving individuals. The purpose of this study, therefore, was to examine whether the MFQ (and specifically the purity/sanctity subscale) is understood in the same way by these 2 groups. We predicted that the purity/sanctity subscale would not demonstrate strong (i.e., scalar) invariance. Across 2 samples, we found support for configural and metric invariance and problems with scalar invariance. These results suggest that between-groups differences observed in previous studies may be due to measurement artifacts. (Davis et al., 2016, Abstract).

Read more in Lugtig & Hox (2012).


Davis, D. E., Dooley, M. T., Hook, J. N., Choe, E., & McElroy, S. E. (2017). The purity/sanctity subscale of the Moral Foundations Questionnaire does not work similarly for religious versus non-religious individuals. Psychology of Religion and Spirituality, 9(1), 124–130.

Lugtig, P. Hox, J. (2012) A checklist for testing measurement invariance, European Journal of Developmental Psychology, 9:4, 486-492, DOI: 10.1080/17405629.2012.686740


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