# Chances of going to college based on parent’s income

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INCOME PERCENTILES AND INCOMES PAINT DIFFERENT PICTURES

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 a parent moves up in the income distribution, the chance that their child goes to college 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?

Jake scraped some income percentile data from whatsmypercent.com and we eyeballed the probability data from the chart at the NY Times. This enabled us to look at the probability of going to college based on income, which tells somewhat of a different story. In these plots, the size of the each point corresponds to the number of people in it.

The change you get by adding $10,000 a family’s income matters considerably for those earning between $10,000 and $100,000 (which the vast majority of Americans do), and matters much less outside that range. At the same time, it’s considerably more difficult for lower income parents to increase their income by this amount.

Probability of going to college vs log income:

Probability of going to college vs income:

SPOILER ALERT – BELOW YOU WILL SEE THE ANSWER FROM THE NY TIMES

Probability of going to college vs income **percentile**:

R CODE FOR YOUR CODING PLEASURE

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