Wednesday, April 21, 2021

FARMs status correlates with college enrollment


A report, here, issued late last month out of the Howard County Pubic School System in Maryland, shows that post-secondary outcomes are less favorable for students who are eligible for free or reduced-price meals.

More than 70 percent of HCPSS graduates who weren’t eligible for free or reduced-price meals (FARMs) and enrolled in college earned an associate’s degree or higher within six years, compared to about 45 percent of FARMs-eligible graduates from the classes of 2007 and 2008.

Some of the summary information like that is misleading. For example, looking at the proportion of graduates who completed an undergraduate degree within six years, which is a very different question from the one trumpeted in the headline, we see some differences in the college completion rate for FARMs students compared to their non-FARMs-eligible peers.

Class of … FARMs Eligible 6-year Completion Rate Population Size
2007 No 63.2 2,867
2008 No 60.7 3,102
2007 Yes 32.4 205
2008 Yes 25.1 194

The we read an article about these findings in the Baltimore Sun, with a headline “Howard County graduates with FARMS status less likely to attend college, report finds.” The first sentence of the article makes the claim, based on the report, that “From 2007 to 2013, graduates of Howard County public schools who received free or reduced meals were 20 percent less likely to attend college than other graduates.”

That’s a huge leap, and it underscores how poorly reporters—and apparently the Howard County Public School System statisticians—understand what these data mean. I only have to point out that no analysis of variance was reported on two very different populations, so I can’t even make any conclusions about how “likely” an event is to occur given another event or compare the two proportions.

But that’s the least of the problems with this report. The bigger problem is that the public, upon reading an article about the report, is likely to assume “causation” when no such conclusion is reached in the report. It is simply pointed out, in an admittedly wild statistical stretch of the underlying facts, that kids who are poor go to and finish college at lower rates than kids who aren’t poor.

The “reasons” or “causes” for this disparity are multiple and vary for each kid in the sample. The most significant root cause is likely to be poverty itself. Neither the report nor the article addresses this elephant in the room, so we dismiss the report summarily: it misses the boat about what schools can do to address this problem, and it’s not news that poor kids don’t go to or complete college as frequently as rich kids.

But we can learn something about conditional probability

Let A be the event that a graduate gets a college degree within six years of graduating and B be the event that a graduate was eligible for free and reduced-price meals while attending Howard County Public Schools. Then, assuming the probability of B is greater than 0, which it is,

P(A|B) = \frac{P(A \cap B)}{P(B)}

In lay terms, in theory, the likelihood that a FARMs-eligible kid from Howard County will graduate college within six years is equal to the likelihood that the child both is eligible for FARMs and completes college, divided by the likelihood that the child is eligible for FARMs.

For Howard County, we know the sizes of the circles, not the underlying cause.
A = College Completion, Bn = FARMs eligibility status (Voxitatis graphic)

What reporters like to think but Howard County’s report doesn’t say at all is that if kids are eligible for free and reduced-price meals, they’re less likely to complete college than kids who aren’t FARMs-eligible. That may or may not be true, but we just can’t conclude it from the data presented in the current report.

We know, for instance, that P(A|B), read “the probability of A given B,” is not zero and it’s not one. Some FARMs-eligible kids earn college degrees within six years, so it’s not zero; some FARMs-eligible kids (who enroll in college) don’t earn college degress within six years, so P(A|B) isn’t one, either. It looks more like B3 than either B2 or B4.

What we absolutely don’t know is why the conditional probability is what it is. Kids who enroll but don’t complete college do so for any number of reasons. Some just don’t have the money to keep paying tuition for four or more years. Those kids are more likely to be FARMs-eligible. Some find other interests that don’t require college. Some flunk out or are driven out by the possibility of non-completion. And the reasons go on and on.

Understanding how many students this affects is really such a small part of the issue as to drive it into insignificance. What we need to do is attack the real causes here and, more importantly, stop believing that data actually tells us what we need to know in this case.

Also, the data show an achievement gap—in college enrollment and completion—between affluent students and poor students. I have held for many years that nobody cares about achievement gap data. Every parent only has kids in one of the groups and each parent wants what is best for their child. They don’t not want the best thing for other people’s kids, but presenting achievement gap data does little to foster an understanding or set a tone of continuous improvement for any individual students, teacher, school, district, or state.

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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