I realized I forgot to provide evidence from the paper that the range of ACT within colleges is smaller than the range of GDP.
From p.207 of the paper:
“Thus, ACT scores are related to college graduation, in part, because students with higher scores are more likely to attend the kinds of colleges where students are more likely to graduate...”
(I think they obviously have this backwards, for the most part. Seems to me more likely that the higher graduation rates of those “kinds of colleges” are the ones that choose students with the higher ACT scores.)
From p. 206:
“Many schools do not have students with very high ACT scores, and a number of schools do not have students with very low ACT scores [which explains why some colleges do not have students from the full ACT range, even though they do have students from the full GPA range].”
In other words: students DO sort themselves into schools based on ACT score more than they do by GPA.
Correction to above: the quote from p. 206 refers to high schools, not colleges.
For colleges, I found a page here that lists 25th and 75th ACT percentiles. Some pairs of schools have no overlap at all; for instance, Ohio State’s middle interval is (27, 31), while Vanderbilt is (32, 35). The average for college enrolees, per this study, was 20.1, with an SD of 4.33. So Vanderbilt’s 25th percentile is almost +3 SD.
For GPA … the 25th percentile for Vanderbilt is 3.75. The mean in this study was 2.72, with an SD of 0.65. So the 25th percentile for GPA was only around +1.6 SD.
For ACE at Vanderbilt, the 75th percentile is 0.92 SD higher than the 25th. If the same was true for GPA, the 75th percentile would have to be 4.34, which is clearly impossible, since the upper limit is 4.00.
So that supports the idea that for a given school, ACE has a narrower range than GPA.
I realized I forgot to provide evidence from the paper that the range of ACT within colleges is smaller than the range of GDP.
From p.207 of the paper:
“Thus, ACT scores are related to college graduation, in part, because students with higher scores are more likely to attend the kinds of colleges where students are more likely to graduate...”
(I think they obviously have this backwards, for the most part. Seems to me more likely that the higher graduation rates of those “kinds of colleges” are the ones that choose students with the higher ACT scores.)
From p. 206:
“Many schools do not have students with very high ACT scores, and a number of schools do not have students with very low ACT scores [which explains why some colleges do not have students from the full ACT range, even though they do have students from the full GPA range].”
In other words: students DO sort themselves into schools based on ACT score more than they do by GPA.
Correction to above: the quote from p. 206 refers to high schools, not colleges.
For colleges, I found a page here that lists 25th and 75th ACT percentiles. Some pairs of schools have no overlap at all; for instance, Ohio State’s middle interval is (27, 31), while Vanderbilt is (32, 35). The average for college enrolees, per this study, was 20.1, with an SD of 4.33. So Vanderbilt’s 25th percentile is almost +3 SD.
For GPA … the 25th percentile for Vanderbilt is 3.75. The mean in this study was 2.72, with an SD of 0.65. So the 25th percentile for GPA was only around +1.6 SD.
For ACE at Vanderbilt, the 75th percentile is 0.92 SD higher than the 25th. If the same was true for GPA, the 75th percentile would have to be 4.34, which is clearly impossible, since the upper limit is 4.00.
So that supports the idea that for a given school, ACE has a narrower range than GPA.