Below is a very interesting graphic that takes some focus and analysis. It illustrates the impact that income and educational legacy has on the BA graduation rates of students who are full-time and start at a four-year public institution.
The three sets of columns focus on the educational legacy of a student's parents: high school diploma, some college (but no degree), and a BA. This essentially controls for parental legacy allowing us to see the impact of income. The varied colored bars illustrate the four income quartiles (dependent students).
For students whose parents earned a high school diploma, note the differential in BA attainment from lowest quartile to third quartile (low N did not allow for the highest quartile, meaning that most people in that demographic had more than a high school diploma). The more affluent students doubled the BA attainment rate of those from the first quartile (73 versus 35 percent). Looking at the third set of bars, for those whose parents had a BA, note that income still matters greatly. Affluent students graduated at an 86 percent rate, compared to 59 percent for low-income students. As can clearly be seen, each quartile upward in income returns with a higher graduation rate.
Looking across the three sets of columns, we also notice that the graduation rate also increase by educational legacy. Note that low-income students whose parents had a BA graduated at a higher rate than third quartile income students whose parents had only some college. However, third-quartile students whose parents only had a high school diploma did much better than those third quartile students whose parents had some college. That would seem to be an anomaly of some type.
Regardless, this graphic, and the associated table, illustrates the impact of income and educational legacy, with a possibly conclusion that money matters more than legacy.