Non-linear Psychometric Thresholds for Physics and Mathematics
Stephen D.H. Hsu, James Schombert
We analyze 5 years of student records at the University of Oregon to estimate the probability of success (as deﬁned by superior undergraduate record; sufficient for admission to graduate school) in Physics and Mathematics as a function of SAT-M score. We ﬁnd evidence of a non-linear threshold: below SAT-M score of roughly 600, the probability of success is very low. Interestingly, no similar threshold exists in other majors, such as Sociology, History, English or Biology, whether on SAT combined, SAT-R or SAT-M. Our ﬁndings have signiﬁcant implications for the demographic makeup of graduate populations in mathematically intensive subjects, given the current distribution of SAT-M scores.
There is clearly something different about the physics and math GPA vs SAT distributions compared to all of the other majors we looked at (see figure 1 in the paper). In the other majors (history, sociology, etc.) it appears that hard work can compensate for low SAT score. But that is not the case in math and physics.
One interesting question is whether the apparent cognitive threshold is a linear or non-linear effect. Our data suggests that the probability of doing well in any particular quarter of introductory physics may be linear with SAT-M, but the probability of having a high cumulative GPA in physics or math is very non-linear in SAT-M. See figure below: the red line is the upper bound at 95% confidence level on the probability of getting an A in a particular quarter of introductory physics, and the blue line is an upper bound on the probability of earning a cumulative GPA of at least 3.5 or so.
Fig. 4.— Probability charts for SAT Math versus grades in Physics classes. For each SAT bin, the number of A-type grades (n) is listed along with the total number of grades per bin (N). The red line displays the 95% probability P(95%) and the blue symbols display an upper bound on the probability that a student will achieve 8 or more A’s out of 16 courses (typically necessary for an upper division GPA of 3.5.) Click image for better version.