Applying a measurement instrument developed in a specific country to other countries raise a critical and important question of interest in especially cross-cultural studies. Confirmatory factor analysis (CFA) is the most preferred and used method to examine the cross-cultural applicability of measurement tools. Although CFA is a sophisticated technique to investigate various equivalence types (structural, metric, scalar and alike.), it has some limitations. In light of the classical test theory, when a measurement tool is not invariant between countries, what factors contribute to the error variance become unclear. Also, CFA reveals little as to how dimensionality of the relevant measurement tool affects measurement invariance. Hence, a fundamental focus of this study is to examine the measurement comparability or cross-cultural applicability for different countries on an international assessment using generalizability theory (G-theory) in educational science studies. With multi-faceted design, the contribution of dimensionality to error variance is examined, as well. For illustration purposes, eight scales from PISA 2012 student questionnaire dataset related to attitudes towards mathematics are used. The study is based on data from Türkiye, Finland and USA. The unbalanced multi-faceted designs are performed using G String IV. In conclusion, almost all results supported all research expectations. From the estimations of the G-theory, it can be rightly deduced cross-nationally applicability of the attitudes towards mathematics scales from these research findings.