This all started from this map from GOOD magazine. It went viral on Twitter, which puzzled the data vis community. Moritz Stefaner notably asked others for advice and input, and Andy Kirk, then Enrico Bertini answered in some detail.
I won't go into great detail on why I didn't like the original map much, it has been amply criticized as is. So, what's a better way to answer this question?
Are the richest Americans the best educated?
Wealth vs. School performance
IMO, it doesn't make a lot of sense to talk of the richest Americans at the county level. There are huge inequalities even in the better-off counties, so all schools in a county don't have the same resources, and obviously, all families don't have the same means. Those remarks also apply to academic achievement.
So it's more relevant to examine that at the individual level. The dataset I am using is an extract from OECD PISA 2009 study, where close to 450,000 15-years-olds have been given a standardized test where their reading, maths and science skills were assessed. Here, we are looking at the 5233 American kids only. The scores of the test go from 200 to 800.
In addition to the test questions, students must fill a very detailed questionnaire about their family, their habits, and other factors that could influence their results. From some of these answers a wealth index can be computed, based on the availability of various items or equipments in their home.
This visualization shows the correlation between the two. As the shape of the trend line and that of the cloud of points assess, there is a correlation but it's pretty weak. I've added the possibility to color the dots by the answers to some of the questions asked. Here's how to read that. If the colors are scattered all over the place, it means that this question is not very relevant. If the top half of the chart is different than the bottom half (as in : how many books do you have), it means that the question is important. If the left half is different than the right half, it means: this question has a strong impact on the wealth, not so much on the performance (as in: how many cars are there in your home).
I've only used a small subset of all the questions.