What is the chance of a kid going to college based on parent’s income?
The amazing team at the New York Times have a “You Draw It” feature in The Upshot in which readers try their hands at drawing a graph. The graph should show the probability of a child going to college based on their parents’ percentile in the income distribution.
As a cool added feature, after people took their guesses, they could see, in shades of red, the other guesses people had taken and compare it to the actual graph.
SPOILER ALERT: You can see the true answer at the bottom of this post. If you want to try your hand at guessing, click through to the NY Times and guess before proceeding.
One way to interpret this relationship is that for every percentile increase in parental income, the probability of college enrollment increases by a constant amount, which might seem somewhat surprising. Even the NY Times editors were surprised by this linear relationship, and the data they collected showed that other people were, too.
Jake Hofman and I wondered “what if people didn’t take the X-axis literally, what if they thought about it as something like log income or income (instead of percentile in the income distribution)?” Percentiles are tricky. They’re buckets with equal numbers of people, but those people can have very different incomes. What would the graph look like if the X-axis were income? Would this relationship be more intuitive to readers?