<p>@silverturtle: Thanks for pointing that out. I should add a few points regarding that.</p>
<p>Yes, this study lacks a certain degree of dimension and is not purely causational simply because it only accounts for the SAT score on a student’s probability of admission (as significant as that factor may be) when other variables are present. Moreover, it is a perfectly valid assumption that there exists a positive correlation between high SAT scores and high achievement on other objective measures. In fact, it is even justifiable to speculate that there is a positive association between students with high SAT scores and students that have better qualifications overall. Even so, those facts still do not hold consequence for the finding that there is a stabilization or even a dip in one’s admission chances between the 93rd and 98th percentiles at Harvard and Princeton, respectively. A correlation would only strengthen the peculiarity or better delineate that a definite strategy exists in their admission behavior. </p>
<p>Yet this study suggests more of a reflection of admission behavior that systematically denies a continuity of admission probability for students do not quite exceed a certain measure of academic merit. It is a basic indicator that the opportunities of admission are greatest for those who demonstrate merit at a lower level and those who demonstrate the greatest degree of merit. The logic regarding the admission of students from the former group is that these students are not likely to obtain acceptances from universities that are perceived to be as or more desirable as the institution making the decision. Hence, the admission of lower-performing students (who likely will not be offered acceptances to the same extent as students who display more meritorious qualities) has a greater effect on increasing the matriculation rate at the given university which in turn increases the university’s yield and hence its selectivity and subsequent public desirability. In essence, the institution sacrifices quality for the sake of its own image. However, universities also compete for the top students since the standardized testing statistics (SAT scores in particular) are a direct reflection of the quality of the incoming class – more so than high school GPA and Subject Test scores since these are very rarely noted or considered when noting the academic quality of a university’s student body. </p>
<p>And yes, since there is, in theory, a linear correlation between SAT scores and other favorable qualifications, there would be an increase in an individual’s admission chances once a specific merit threshold is reached. However, it still does not account for an exponential increase in admission probability if these multiple objective factors additively contribute to a student’s overall academic merit. That is, if a linear correlation between the SAT and other academic measures exists, there should theoretically be a linear correlation in admission probability. But the results of this study simply suggest that these given universities begin to better increasingly favor merit at higher degrees of achievement. Namely, it is not simply a straightforward process that can be uniformly modeled mathematically for the full range of all applicants. </p>
<p>But based on the logical explanation for this admission behavior for the stabilization/regression of admission followed by exponential increase, it is logical that this same behavior would be exhibited even if additional qualifications were somehow factored into the study. But, in this case, the SAT was simply used as a representative measure of a student’s merit since it is intuitively plain that a higher score represents more favorable qualifications in other areas of a student’s application.</p>