Reliability, Validity, and Measurement Invariance of Attitudinal and Social Norm Factors in Math

Soung Hwa Walker


The purpose of the present study was to provide a deeper understanding of multidimensional aspects of attitudes and social norms in educational contexts. Specifically, the current investigation aimed to (1) examine reliability and validity of factorial structure of math attitudes (Affective, Behavioral, and Cognitive factors) and perceived math social norms (Parent, Peer, and Teacher factors) and (2) test whether measurement of all factors would be invariant across national groups. Three nationally representative sample data (USA, Hong Kong, and Singapore; N = 15,019) were obtained from the 2012 Programme of International Student Assessment (PISA) database. High values in Cronbach’s Alpha, Composite Reliability scores, and factor loadings indicated strong internal consistency and convergent validity of all factors. Estimated correlations among latent factors were ranged from small to moderate in value (rs = .21 - .51, ps < .001) and each square root of average variance extracted turned out to be greater than all bivariate correlations (.71 - .85), which supported clear discriminant validity. Furthermore, the results of Multigroup Confirmatory Factor Analysis (MGCFA) yielded that measurement of the six factors was equivalent across national groups at the level of strong (scalar) factorial invariance. Implications for math education and future research are discussed.

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