“Examining the Existence of Cognitive Thresholds in Highly Quantitative College Courses”, You Zhou, Nathan R. Kuncel, Paul R. Sackett2024-03-26 (high IQ)⁠:

While the dominant finding indicates a monotonic relationship between cognitive ability and academic performance, some researchers have suggested the existence of cognitive thresholds for challenging coursework, such that a certain level of cognitive ability is required for reaching a satisfactory level of academic achievement. Given the importance of finding a threshold for understanding the relationship between cognitive ability and academic performance, and the limited studies on the topic, it is worth further investigating the possibility of cognitive thresholds.

Using a multi-institutional dataset and the necessary condition analysis (NCA), we attempted to replicate previous findings of cognitive thresholds on the major GPA of mathematics and physics-majored students, as well as the course grade of organic chemistry, to examine whether high SAT math scores constitute a necessary condition for obtaining satisfactory grades in these courses.

The results from the two studies do not indicate an absolute cognitive threshold point below which students are doomed to fail regardless of the amount of effort they devote into learning.

However, we did find that the chance of students with a low level of quantitative ability to succeed in highly quantitative courses is very small, which qualifies for the virtually necessary condition.

…Study 1 Results: …In terms of a simple descriptive analysis, a close inspection of the dataset indicates that only 2 math-major students (out of 628 math students) and 9 physics-major students (out of 528 physics students) who scored below 600 on SAT Math and obtained an in-major GPA higher than 3.5.

…Study 2 Results: …Table 1 indicates that although there does not seem to be a clear-cut threshold point for SAT math scores below which no student in the group could obtain a course grade of 4.0, the likelihood of students scoring less than 400 or 400–500 on SAT math to obtain a course grade higher than B+ is very small (SAT math score < 400: 1% obtained B+ and A−, 3% for A; SAT math score 400–500, 4% obtained B+, 2% obtained A−, and 6% obtained A), and it is evident from the table that it is increasingly less likely for students with a low SAT math score to obtain a high grade in organic chemistry.