I realized that I hadn’t looked at some simple stats on inequality in my sample in a while, and I hadn’t written about those either.
So here goes!
The first measure I look at is the Add Health Picture Vocabulary Test (ah_pvt), standardized by student age. It’s a measure of vocabulary, indicating both IQ/academic achievement. The median score is 100. The bottom 25% have scores below 90 while the top 25% have scores above 111.
I take the maximum value of mothers and fathers education level and then recode into three categories. 1 indicates students whose max parent education is high school. 2 is for students with a parent with some college education. 3 indicates the student had at least one parent with a college degree.
The scores increase for students with more highly-educated parents.
. table educ3, c(n ah_pvt mean ah_pvt median ah_pvt)
educ3 | N(ah_pvt) mean(ah_pvt) med(ah_pvt)
1 | 7,209 94 95
2 | 5,780 101 101
3 | 6,484 105 107
A score of 95 indicates the 35th percentile score, while 106 is at the 65th percentile. So going from having no parents with a college degree to one parent with a college degree means moving from the 35th to the 65th percentile.
The disparities are extreme at the top of the achievement scale. Of the students at the 90th percentile of achievement and above, only 15% have parents who did not attend college. Of the students below the 10th percentile, 65% have parents who did not attend college, while 16% have parents who did attend college.
The story is similar for GPA. Median GPA is 2.75, the bottom 25% is below 2.25, the top 25% are above 3.33.
. table educ3, c(n gpa mean gpa median gpa)
educ3 | N(gpa) mean(gpa) med(gpa)
1 | 7,350 2.566429 2.5
2 | 5,961 2.713485 2.75
3 | 6,742 2.982362 3
2.5 is at the 42 percentile, while 3 is at the 66th percentile. 50% of the students in the bottom 10th percentile have parents who did not attend college, while 16% have parents who attended college. 22% of the students in the top 90th percentile have parents who did not attend college, while 51% have parents who attended college. The reason that there are more low-SES students with high GPAs is likely because of between-school segregation, where low-SES students in majority low-SES schools are now at the top end of the achievement distribution and receive higher grades.