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Another consequence could be that such a test would have a weaker association with numeracy than the open-ended CRT does (Liberali et al., ).In other words, construct nonequivalence would implicate different cognitive processes taking place in the different formats of the CRT.The Cognitive Reflection Test, measuring intuition inhibition and cognitive reflection, has become extremely popular because it reliably predicts reasoning performance, decision-making, and beliefs.Across studies, the response format of CRT items sometimes differs, based on the assumed construct equivalence of tests with open-ended versus multiple-choice items (the ).Limited process-oriented evidence has indicated that pronounced cognitive conflict was present when using a multiple-choice version of the CRT.The mouse trajectories of participants who responded correctly revealed that they were attracted to the incorrect intuitive response (Travers et al., ).

Open-ended questions are more difficult to solve than multiple-choice ones for stem-equivalent items (i.e., that differ only by listing multiple choices), because presenting options enables a different array of cognitive strategies leading to increased performance (Bonner, ).This is supported by the thinking-aloud evidence, in which performance on the CRT with the open-ended response format was partly explained by the lack of specific knowledge needed to solve the problem (Szaszi et al., ).Since the correct answer is already included in the multiple-choice version of the test, this particular format might therefore be easier.We tested the two hypotheses experimentally by assessing the performance in tests with different response formats and by comparing their predictive and construct validity.In a between-subjects experiment ( = 452), participants answered stem-equivalent CRT items in an open-ended, a two-option, or a four-option response format and then completed tasks on belief bias, denominator neglect, and paranormal beliefs (benchmark indicators of predictive validity), as well as on actively open-minded thinking and numeracy (benchmark indicators of construct validity).

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