Provost Dukes Love gave a presentation (pdf) on “Access and Affordability in Higher Education” at the Alumni Leadership weekend in May. Thanks to popular demand, we will spend this week going through some highlights. Background reading: this 2016 overview of similar material from the previous provost, Will Dudley ’89, and our 2017 series about the Equality of Opportunity project. Day 3.

1) This is the ugliest graphic I have ever seen in a Williams presentation. Eph (honorary degree in 2000) Edward Tufte would say:

• Be consistent with your x-axes across the presentation. This (using academic years like 2016/17) is the third different choice you have made. Best is probably using “2018” to mean values for the 2017/2018 academic year. Also, there is no need to show every year. Doing so is too busy. Every 5th year, plus the start and end years, would be fine.
• Don’t show regression models and summary statistics. How many people in your audience will know what R2 = 0.9138 means? Will you have time to explain it? Should you spend your/their valuable time trying to teach your audience about linear models?
• If you insist on showing nonsense, then at least show a sensible number of significant digits for your nonsense. R2 = 0.91 would be more sensible, perhaps even R2 = 0.9.
• Think harder about the substance of what you are trying to convey. Would even a statistically sophisticated reader care about the exact values of R2, much less for the values of the intercept from your linear regression? No! Your main (only?) point is about the slopes. And that is an interesting point! Including all the other statistical arcana hides the interesting facts you have discovered.
• The purple/gold bars at either side of the graphic are very hard to interpret. I realize that you can explain them on the fly, but the need for explanation is often the sign of poor graphics.

2) Your key point is that Williams sticker price has gone up about 4 times faster than median income but only half as fast as 95th percentile income. Good stuff! And worth thinking about. This is why the regression lines are interesting, not because of the intercept for the R2‘s. But the exact coefficient values don’t really matter. All that you (and your audience) care about are relative magnitudes. So, perhaps better would be to just show a line graph of these two ratios directly. Graph the ratio of family income (median and 95th) to the Williams sticker price. That would make clear that former in falling very fast, i.e., that the cost of Williams has gone from a smallish portion of median family income to almost equal to it. (The ratio has fallen from about 3 to close to 1.) The ratio has also fallen for the 95th percentile but, in this case, the drop has been much less, from about 6 to 3. (You could also present this in percentage terms: The cost of Williams has gone from 30% (15%) of the median (95th percentile) family income up to 95% (26%).

3) Indeed, the best method would be to have two slides. The first shows the raw line graphs, so that people can see the actual numbers. You say a few words about how, yes, the price of Williams has increased. (Make a joke about the class of 1988’s class song with refrain “Sixty thou to live with cows,” the punch line being that this was the 4 year cost 30 years ago.) But the only people who pay full freight have seen their incomes increase as well. (Also make a few remarks about stagnation for the median family.) Then, next slide, show the ratios. People like more slides rather than fewer.

4) Math quiz for attentive readers: If family incomes at the 95th percentile have gone up twice as fast as the Williams sticker price, then how could the sticker price as a percentage of 95th percentile family income also increased from 15% to 26%?

5) All these numbers reinforce my claim that Williams pricing strategy, like that of other elite schools, is sensible. We are selling a luxury good to rich people. They are not deterred by price. In fact, they often (and not incorrectly!) view price as a signal of quality. We should continue to raise prices at a fast rate while, simultaneously, offering extensive financial aid to non-rich admitted students. Relevant New York Times analysis here. Worth spending time on?