Notwithstanding heterogeneity (characteristic differences) among state averages, greater representative sample sizes help identify the underlying educational score distribution.
I agree and was thinking that this data is hard to interpret without knowing a great deal more about the selection bias occurring in the very low participation states. In Iowa for example only 3% of the kids take the ACT. I asked my son who recently took the test, if it seemed like the kids from his school were all in the gifted program. He said that many were, but there was also another group that included kids headed to college on athletic scholarships. It would be interesting to learn more about this group.
Thanks much Earl Kilgore. There is certainly a variety of heterogeneity in the sample data, which is why the blog note generally calls for a more representative samples. Still, the overall scores have a targeted center value for all students nationally, who take the exam.
There appears to be two major issues interacting in this case, and we don't further tease out the rationale behind these differences. The first interaction is that the "low participation" states have slightly smaller overall populations. Some mark the 70% participation level, to divide low participation states from high participation states. Statistical analysis here however would reveal that the separation is more significant closer to 40%. There are 26 states with less than 40% participation rate, and 3 of those states are top 10 by population.
The second interaction is in the inherent state differences based on the types of students who take the exam, their preparation and motivation, test taking skills, luck, and whatever other factors are mixed in as well. The standard deviation of the average scores, between all the states is 43. And the high participation states have a median SAT reading score of 492, with a standard deviation of 18. But the low participation states have a median score of 572, with a standard deviation of 24.
I agree and was thinking that this data is hard to interpret without knowing a great deal more about the selection bias occurring in the very low participation states. In Iowa for example only 3% of the kids take the ACT. I asked my son who recently took the test, if it seemed like the kids from his school were all in the gifted program. He said that many were, but there was also another group that included kids headed to college on athletic scholarships. It would be interesting to learn more about this group.
ReplyDeleteThanks much Earl Kilgore. There is certainly a variety of heterogeneity in the sample data, which is why the blog note generally calls for a more representative samples. Still, the overall scores have a targeted center value for all students nationally, who take the exam.
DeleteThere appears to be two major issues interacting in this case, and we don't further tease out the rationale behind these differences. The first interaction is that the "low participation" states have slightly smaller overall populations. Some mark the 70% participation level, to divide low participation states from high participation states. Statistical analysis here however would reveal that the separation is more significant closer to 40%. There are 26 states with less than 40% participation rate, and 3 of those states are top 10 by population.
The second interaction is in the inherent state differences based on the types of students who take the exam, their preparation and motivation, test taking skills, luck, and whatever other factors are mixed in as well. The standard deviation of the average scores, between all the states is 43. And the high participation states have a median SAT reading score of 492, with a standard deviation of 18. But the low participation states have a median score of 572, with a standard deviation of 24.