Earlier today, the New York times published a wonderful visualization on how family income affects children’s college chances. The visualization uses a new you-draw-it-first paradigm, where the reader guesses the expected relationship / trend before being shown the actual data. I found the idea very cool. Go ahead and try it, I’ll wait. It’s easy to see why this is easily one of my favourite NY Times visualizations ever.
Except, they chose the wrong dataset to exhibit the you-draw-it-first paradigm.
After you proceed to draw your guess, you find out that the relationship between “Percent of children who attend college” and “Parents’ income percentile” turns out to be surprisingly1 linear. Apart from the article itself calling the result “astonishing”, the aggregate responses given by NY Times readers (as of my writing the post) looks like the shaded region in this2:
As it turns out, the linearity arises only because of a few tricks at play here:
- Income Rank in the US is distributed ~log(Dollar Income).
- The original paper, Chetty, Hendren, Kline, talks about the quality of college attended as well, which the NYTimes article leaves it out.
- The original paper defines attending college as the mere presence of one or more 1098-T filing for a child. This definition is very broad and includes everything from universities to vocational schools.
Let’s choose an x-axis we intuitively understand
Let’s really dig in and see if this is as unintuitive as the article makes it seem. First let’s collect centile income data from Raj Chetty’s Equality of Opportunity. Since raw data of college attendance and quality is not readily avaiable, let’s reconstruct them off of the graphs in the paper3.
To verify our data, let’s first plot College and Attendence vs Rank as the paper does:
Here’s the same chart drawn against actual Income Dollars as opposed to Income Rank on the horizontal axis:
This is immediately easier to relate to as the horizontal axis is far more intuitive. We all know how much a thousand dollars is (as opposed to an income centile), and how hard it is to get a $1000 raise as opposed to how hard it is to get one that will push us up by one percentile2.
What does a percentile amount to?
The article states, “Moving up a single percentile on the family-income distribution makes enrolling in college about 0.7 percentage points more likely”. That’s incredibly hard to wrap my head around. How much is a percentile in dollar terms? Again, quoting, “About $2,400 in annual income separates the bottom two dots, while nearly $1 million separates the top two”.
Asking the reader to guess the relationship against Income Rank as opposed to Income Dollars is the difference between asking users to draw f(x) against log(x) as opposed to x!
Using the right axes matter!
Are we measuring the right thing?
College quality and attending college only tell part of the story. What’s really important is how much these children make when they are older. Chetty, Hendren, Klein do collect and present how “Family Income of Child at age of 31” varies with Parent’s Income Rank. Here’s a Google Sheets rendition of their data:
Here’s the same data plotted against our preferred horizontal axis of Parent Income Dollars:
This graph is far easier to understand! In fact, it begin to tell a story. A story of a world where the challenges of pursuing a quality college4 education bottoms out with income, but at the same time, a world where the money one is likely to make is directly proportional to the financial resources one has growing up.
- The entirety of the charm of a you-draw-it-first charm presumably lies in a surprise such as this. With that considered, the surprise isn’t that surprising after all. ↩
- Yep, my intention was to draw an S curve - but my impatience got the better of me! ↩
- Extrapolation was easy since the paper mentions that college attendance is linear with rank, and college quality is quadratic. ↩
- By college, we really mean an educational institution that had to file a Form 1098-T. ↩