At the MOOC Research Initiative conference Jeff Selingo gave what I thought was a capable presentation of the current landscape of higher education. People might quibble with a point or two, but overall it was a relatively balanced, hysteria-free overview of a market which is not necessarily “broken”, but is poised to undergo some relatively dramatic changes in the coming decade or two.

One stat from that talk bothered me though, and seeing it pop up again on Twitter today pushed me to try to explain the problem:

You hear variations of this stat all the time, and there’s no doubt in my mind we are undergoing a transformation of our student body. But here’s the important piece of information I never hear attached to such stats — is it a stock or a flow?

You see, there’s a couple ways to measure a phenomenon like this, and they have their strengths and weaknesses, and sometimes can give very different views of the data. The first way — measure the stock — is the first approach of most people. Is thyroid cancer a growing problem in a America? Control for population, compare the number of people with thyroid cancer with the number 50 years ago, and there you go — sorted.

But is the number of people living with thyroid cancer what you care about? Or is the number of people contracting thyroid cancer what you care about?

Those things sound like they’d give very similar views, but they don’t. Thyroid cancer used to be a uniformly deadly disease. People who contracted it would usually die, and die relatively soon after a diagnosis, so at any given time there was only a small population of people who had thyroid cancer. With the introduction of radioactive iodine as a treatment, the prognosis for most people with thyroid cancer today is quite good. Since cancer is considered a chronic disease (a person who contracts thyroid cancer will always be considered to have it, even in remission) the number of people who now have thyroid cancer has gone through the roof, but as a result of our success, not failure.

That’s why epidemiology has two different measures — one is prevalence, our measure of the “stock”. Prevalence asks how many people at a given time have a condition. But they also use an “inflow” measure: incidence. Incidence measures how many people per year move into a condition. Which measure we use will depend on what we aim to do with the information, but it is almost always appropriate when given one number to ask for the other as well. If the numbers tell two very different stories it’s time to sit down and parse out why.

So what about this 80% of students are non-traditional? Is that a stock or a flow?

My guess is it’s a stock, more akin to measures of prevalence than incidence (Apologies to Jeff if I am not right here). And if it is, that’s an interesting statistic, but I’m not sure it’s the right one to use. Here’s a simplified model to show why. Imagine a world that graduates two people from high school every two years. One always goes to college full-time and gets out in just under four years (just under because they graduate in May, not September). The other student goes part time, and finishes in eight years. Here’s a visual representation of how that plays out over time:

The blue arrows represent the tenure of our full-time students in college, and the red arrows the time spent by our part-timers.

Now here’s a question. Go to year eight and run down through the students that line bisects. Count up the students that are either starting college or currently enrolled. You’ll notice that there are two four-year students currently enrolled and four eight-year students. Now tally up your percentages. In this case we reach the conclusion that 66% of students are non-traditional eight-year students, compared to the measly 33% of the population who are in four-year programs. The “new normal” right?

But measures of flow tell a different story. In each graduating class, 50% of students go traditional, and 50% non-traditional. And asked whether flow or stock best represents what is a normal student experience here, I’d have to say it’s the measure of flow (50%). The stock measure is just too prone to outflow effects.

Of course, these are made up numbers. It could go the other way as well — if part-timers don’t persist at the rate of full-timers, the effect would run the other way, significantly minimizing the number of students who choose to attend part-time. Or perhaps the two trends balance one another out. The smaller point is that this discussion needs better numbers if we are to get an accurate sense of what is going on. The larger point is when presented with stats on a stock, always seek out a corresponding flow, and vice versa. If they give you deficit, ask for debt. If they give you number of people imprisoned, ask for a count of yearly incarcerations. And so on. The interesting story is usually where different measures seem to disagree, and you can’t get that from a single view.