Statistical science fiction
Running in the rain


Nyt_tuitionfree2 In celebrating the recent trend by "elite" colleges to lowering the cost of education, the Times printed this chart, the top part of which is shown here.

The three colors represent different levels of aid.  Blue means "grants replace loans"; red means "free tuition"; yellow means "parents pay nothing".  The colleges are grouped by the minimum qualifying income for the blue category.

The whole effect is of a knit.  We shall call this the "knit chart".

I believe a simple data table will do the job nicely.  If any reader has other ideas, please show us your work!

A few points to note about the original:

  • Ordering by the minimum income to qualify for "grants replace loans" is arbitrary, as is alphabetizing colleges within each group
  • Qualifying "at any income level" should be shown on the left of "$40,000 or below" rather than to the right of $100,000.  The current order is such that qualifying level increases with income from left to right, except from $100,000 to "any income", where it falls off a cliff.
  • Qualifying at any income level is better shown as a separate column on the right disconnected from the income scale.  The current configuration devalues the effort spent in making a proper income scale.
  • Too many lines of equal length, and too few yellow and red lines to make the knit chart effective
  • Should the graph cater to parents interested in seeing what aid they qualify for given their income level?  Or should the graph highlight the breadth of aid available at individual colleges?

Reference: "The (Yes) Low Cost of Higher Ed", New York Times, April 20 2008.

PS. The original point about the "any income level" was incorrect as pointed out by Chris below.  I have replaced that with a different issue.

PPS. Matias' version (see comments) is a superb demonstration of the power of data tables, well-applied.   It is clean and simple, and addresses both the questions pointed out in the last bullet point.  The only thing sacrificed was the visual representation of the relative size of the income requirements, which I agree is the least valuable part of the original.  As usual, many thanks to our readers for coming up with great ideas!



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I agree with many of the issues that you highlight with the chart, but I can't see why 'at any income level' should be to the left of $40,000.

Isn't the family income one needs to qualify the amount stated or below? Therefore, qualification is hardest on the left hand side ($40,000 or below), and gets easier as you go right on the chart. This places 'at any income level' in the correct position.

Marty Alchin

I would agree with Chris on the income level issue. Consider a family with an income of $120,000. This is too high to qualify for anything other than the "any income level" colleges. Should a $120,000 income be placed below a $40,000 income, or above $100,000? Seems pretty obvious to me.

Of course, it's only obvious after logically thinking it through. The fact remains that it's a subtlety that would likely be lost on most of the parents trying to make sense of the chart.


Hey, I made my version of the table this chart should have been. You can see it at

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