Imagine a family considering where their whip-smart, high-achieving teenager might attend college. They look up some elite universities’ tuition prices and discover that many exceed the parents’ combined income of $40,000 a year! Reeling from sticker shock, the family resolves to focus instead only on apparently cheaper educational options. Two recent analyses of college affordability suggest that could be a serious misjudgment.

Last year, researchers Sisi Wei and Annie Waldman at ProPublica crunched U.S. Department of Education data to calculate the amount of debt accumulated by the typical four-year university student from a lower-income background. Washington Monthly magazine released a related analysis last month examining the “net price” of attending national universities for families making less than $75,000 a year. The methods of calculating university affordability and the period of data examined differ a bit between the two analyses, but the results overlap in a potentially surprising way.

Institutions of higher learning such as the University of North Texas and the University of Texas at El Paso rank highly using both affordability methodologies. Given that they provide a quality four-year education while setting annual out-of-state tuition and fees below $10,000 and in-state rates even lower, their excellent rankings are entirely understandable. But how could anyone describe as highly affordable institutions such as the University of Pennsylvania, with its eye-watering $43,838 tuition rate?

The oddity of university affordability for the non-rich is that the wealthiest schools can be the cheapest to attend. A subset of universities with large endowments pour extensive funds into financial aid for lower- and middle-income families. For example, my employer, Stanford University, advertises a $45,195 rate for annual tuition and $13,631 for room on board, but students from families with incomes below $65,000 pay nothing for either. The other private universities ranked as highly affordable have similar approaches to financial aid.

Advertised tuition prices should thus be interpreted akin to the charges listed on a health-care billing statement, meaning they bear little relationship to what many people actually pay. A university with a high tuition rate on paper can be highly affordable or completely out of reach for a given family, depending on the institution’s financial-aid policies. The virtue of affordability studies is that they can help families of modest means recognize that their children have more educational opportunities available than they realize.

Keith Humphreys is a professor of psychiatry at Stanford University.