**Update: **Mike has written another post clarifying the intuitions behind his math.

The spectacular Mike Caulfield casts a skeptical eye on the Course Signals data:

Only a portion of Purdue’s classes are Course Signals classes, so the chance any course a freshman takes is a Course Signals course can be expressed as a percentage, say 25%. In an overly dramatic simplification of this model, a freshman who takes four classes the first semester and drops out has a has about a 16% chance of having taken two Course Signals courses (as always, beware my math here, but I think I’m right). Meanwhile they have a 74% chance of having taken 1 or fewer, and a 42% chance of having taken exactly one.

What about about a student who does *not* drop out first semester, and takes a full load of five courses each semester? Well, the chance of that student having two or more Course Signals courses is 75%. That’s right — just by taking a full load of classes and not dropping out first semester you’re likely to be tagged as a CS 2+ student.

In other words, each class you take is like an additional coin flip. A lot of what Course Signals “analysis” is measuring is how many classes students are taking.

Are there predictions this model makes that we can test? Absolutely. As we saw in the above example, at a 25% CS adoption rate, the median dropout has a 42% chance of having taken exactly one CS course. So it’s quite normal for a dropout to have had a CS course. But early on in the program the adoption rate would have much lower. What are the odds of a first semester dropout having a CS course in those early pilots? For the sake of argument let’s say adoption at that point was 5%. In that case, the chance our 4-course semester drop out would have exactly one CS course drops from 42% to 17%. In other words, as adoption grows having had one course in CS will cease to be a useful predictor of first to second-year persistence.

Is that what we see? Assuming adoption grew between 2007 and 2009, that’s *exactly* what we see.

I’d like to see somebody at Purdue (or Ellucian) respond to the questions that Mike raises. Matt Pistilli, are you listening?

[…] to the first of these posts, I suggested that a response from the Purdue researchers would be helpful. (It still would be.) Now Al Essa, […]