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The primary aim of this study was to conduct a cross‐cultural comparison of the level of critical thinking of Danish and Spanish psychology students (N = 788) attending innately different bachelor‐level courses; personality psychology and introductory statistics/research methods. Several instruments are available for the assessment of critical thinking (CTh), but most are, however, unsuitable for use in large surveys with many constructs, due to length or single‐person administration formats. One brief and much‐used scale is the CTh scale in the Motivated Strategies for Learning Questionnaire (MSLQ), used in this study. To ensure unbiased comparisons across countries and courses, our secondary aim was to investigate the content validity, as well as the psychometric properties, of the CTh scale to ensure the most accurate and unbiased comparison. For this purpose, Rasch and graphical loglinear Rasch models were used. After reducing the number of items due to content validity issues, the CTh scale fitted Rasch models within each national sample, and was measurement invariant relative to age group, gender, course and university. In the cross‐cultural item analysis, two items functioned differentially relative to nationality, and the scale fitted a graphical loglinear Rasch model. CTh scores related to introductory statistics/research methods courses differed significantly from scores related to personality psychology, for Danish students only. [ABSTRACT FROM AUTHOR]