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Cultural Measurement Equivalence

Joseph E. Trimble
Western Washington University

            Cultural measurement equivalence refers to the possibility that interpretations of psychological measurements, assessments, and observations are similar if not equal across different ethnocultural populations. In principle, most cross-cultural psychological researchers agree that an analysis of cultural measurement equivalence occurs through the following concepts: functional equivalence; conceptual equivalence; stimulus equivalence; linguistic equivalence; and metric equivalence. Although five types of cultural equivalence are used to describe the dimensions of the concept there may upwards of 50 or more types that can be ordered into interpretive and procedural summary categories. On the surface the meaning of cultural measurement equivalence is straightforward yet it has created considerable discussion and debate in the literature as researchers and scholars struggle to disentangle its deeper meanings and applications.

In cross-cultural psychology debates also abound on the influence of one’s world-view in understanding and interpreting standardized tests and psychosocial scales Moreover, many cross-cultural psychologists contend that comparing elements from different ethnocultural populations can lead to distortions of their worldviews. Given this contention, ethnocultural comparative research using psychological measures may be burdened with problems of “incomparability” and, thus, may lead researchers to draw conclusions about a finding that may not be valid or justified. Indeed, with some exceptions, most of the psychological tests and assessment scales used with different ethnocultural groups cited in the literature have not considered cultural measurement equivalence and item bias possibilities. To avoid these possibilities, attention must be given to the cultural measurement equivalence concept and item bias in measurement studies.

In constructing and using psychological instruments and assessment tools in cultural comparative or cultural-sensitive research, the investigator must give serious attention to equivalence matters. Embedded in the equivalence construct is the precept that comparisons between ethnocultural groups require that a common, if not identical, measurement and assessment processes exist; in essence, the principle holds that a universal process must be developed to demonstrate and assess ethnocultural group comparability. Consequently, in order to achieve functionality two or more behaviors must pre-exist as naturally occurring phenomena related or identical to a similar phenomena or circumstance; in essence, the behaviors serve a similar function for groups selected for study.

Conceptual and stimulus equivalence exist when the meaning of stimuli, concepts, methods, etc., are similar or identical for culturally or ethnically different respondents. Linguistic equivalence is similar although the emphasis is placed on the linguistic accuracy of item translations. Metric equivalence or scale equivalence, probably the most technical and the most difficult to evaluate, exists when the psychometric properties of data sets from different ethnocultural groups reveal the same or similar coherence or structure. Of the five equivalence types, metric or scalar has received the least amount of empirical attention, perhaps because it is the most technical and/or poorly understood. For the psychometrician it may be the most important concern. Before a measure can be used in ethnocultural comparative research, it must first meet standards within the ethnocultural groups; then and only then can it be used between two or more groups. For example, use of forced choice scale alternatives laid out in a linear manner may not fit with the cognitive and evaluative preferences of certain cultural groups; a Likert-type format may work for one group but not for another; thus, the researcher must find a common metric or scalar equivalence to pursue comparative measurement studies.

Cultural measurement equivalence is similar to item bias. Item bias deals with the similarity or dissimilarity of scale outcomes across ethnic and cultural groups and thus is concerned with validity-threatening factors. In drawing a distinction between the two constructs, cultural measurement specialists typically assert that item bias is associated with construct, instrument, and method bias; item bias differs from cultural measurement equivalence because the latter deals more with the outcomes than with the factors that influence validity. Item bias deals with item contaminating factors and equivalence isolates bias and score comparability.
Use of conventional scaling procedures in cultural comparative research has introduced a number of methodological problems, especially in the use of a structured response format. Mounting research evidence points to the following problems: 1). Researchers tacitly, and perhaps incorrectly, assume that the numeric intervals between choice alternatives on a continuum are equal and can be assigned an integer value; 2). The number of choice alternatives are presumed, also perhaps incorrectly, to represent the full range of categories that an individual would use to evaluate an item; 3). The dimensions of the scale items may not truly be comparable between cultural groups; and 4). The effects and the outcomes of the categorization process, difficult to define in any group, may be confounded by the possibility that not all cultural groups respond to stimuli in a linear manner.

In the past decade, a few cross-cultural researchers and psychometricians have put forth a variety of interesting statistical algorithms for assessing the presence of forms of cultural measurement equivalence and culturally bound item bias. To assess metric equivalence, for example, some researchers have analyzed the scales or instruments with principal components or factor analysis. If the structural dimensions of instruments resemble one another then, presumably, the scales are equivalent across groups. Strength of the factor-based scales for the respective groups serves as partial criteria. Factor solutions have been expanded to include congruence coefficients and related manipulations to isolate the nature of the equivalence. For example, a few researchers have used factor solutions to examine the metric equivalence of personality scales administered to Asian and non-Asian population sand found that the factor solutions did not differ; item composition and the factor meanings varied appreciably as is often the case.
Use of factor analysis in psychometric research and testing equivalence is not without criticism. Based on the growing debate, three critical points should be made: (1) Factor solutions rarely fit the data completely in cultural-comparative research due, for the most part, to non-random measurement and translation error and unspecified conceptual contributions to the obtained weights; (2) Factor solutions are suggestive; and (3) Data should be, at a minimum, at the interval level. Most scales and inventories use binary or ordinal level response categories with presumed equality of the numerical distances between the alternatives; distortions can exist thus eroding the strength of the correlation coefficients. But it’s possible that variables with limited categories are not compatible with factor analytic models because at minimum correlations often are used to define unstable constructs.

A few cross-cultural researchers recommend use of covariance structural modeling or variants of confirmatory factor analysis (CFA) to test for equivalence. There are limitations associated with the use of exploratory factor models; the advances in confirmatory factor modeling, however, appear to overcome them. For example, in testing for measurement equivalence a few researchers used CFA algorithms and found that many of the scales and corresponding items were unstable across different cultural groups.

Use of item response theory (IRT) to assess equivalence and bias has produced interesting findings. Use of IRT and corresponding differential item functioning analyses (DIF) can generate different item consistency outcomes where item bias is detected The lines of research show promise for using IRT to assess equivalence of measures, scales, and tests.

A growing number of researchers recommend a form of latent trait analysis, especially when the scale contains binary scores. The Rasch one-parameter model can be used however some researchers remind us that the model should be used with other analytic models that treat the data in a slightly different manner. Use of Rasch modeling to assess cultural equivalence has not been that extensive. A few studies using the approach, for example, found that: 1). Use of negatively worded items with culturally unique populations creates scale problems and item interpretation; 2). Item linguistic translation can create considerable variance in multinational focused scales; 3). Shorter versions of a scale can be constructed for use in cultural comparative research however the longer version can be used with one cultural group without making any item adjustments; 4); and 5). Gender status and self-defined ethnic group respondents influence scale invariance and item nonequivalence of short scales originally believed to be reliable.

SEE ALSO: Cultural diversity, Cross-cultural competence in school psychologist's services, Stereotyping, Worldview

Suggested Reading

Byrne, B. M., & Watkins, D. (2003). The issue of measurement invariance revisited. Journal of Cross-Cultural Psychology, 34(2), 155-175.

Dana, R. H. (Ed.). (2000). Handbook of cross-cultural and multicultural personality assessment. Mahwah, NJ: Lawrence Erlbaum Associates.

Gerber, B., Smith Jr., E. V., Girotti, M., Pelaez, L., Lawless, K., Smolin, L., et. al. (2002). Using Rasch measurement to investigate cross-form equivalence and clinical utility of Spanish and English versions of a diabetes questionnaire: A pilot study. Journal of Applied Measurement, 3(3), 243-271.

Helms, J. E. (1996). Toward a methodology for measuring and assessing racial as distinguished from ethnic identity. In G. R. Sodowsky & J. C. Impara (Eds.), Multicultural assessment in counseling and clinical psychology (pp. 143-192). Lincoln: Buros Institute of Mental Measurements at the University of Nebraska.

Suggested Resources

Institute for Objective Measurement ( http://www.rasch.org )
IOM's Web site offers information on a wide variety of measurement programs and services.

Joseph E. Trimble, PhD
Center for Cross-Cultural Research
Department of Psychology
Western Washington University

Reference citation: Trimble, J. E. (2007). Cultural measurement equivalence. In C. S. Clauss-Ehlers (Ed.),
Encyclopedia of cross-cultural school psychology. New York,: Springer.