## Sometimes, Facts Actually Matter

A month or two ago, I got into a colloquy on the blog about average ages of community college students.

An alert reader send me an email exchange he had with the AACC on this exact question. The AACC Fast Facts page for 2009 has the following to say about average ages of cc students:

Average age: 29

21 or younger: 47%

22 to 39: 40%

Obviously, that can't be right. If 47 percent of cc students are 21 or younger, how could the 50th percentile be 29? The numbers don't make sense.

In the email exchange, Kent Phillippe, Senior Research Associate at the AACC, noted that the '29' figure is both several years behind the rest of the data, and a 'mean,' rather than a median. In other words, it's pulled upward by a small number of much older students. As he put it, the median age is “probably around 22 or 23.”

The word “probably” is revealing. It suggests that they haven't bothered to figure it out.

If the 47th percentile is 21, I'll go out on a big ol' limb and postulate that the median age is 22. This squares with the numbers at my own college, where the mean age is 25 but the median is 21.

This may seem pedantic, but it's actually kind of important.

If the public image of community colleges is based on thirty-year-olds returning to college after getting laid off, but the reality of community colleges is an increasing influx of traditional-aged students with the goal of transfer, then we'd expect to see policy interventions that don't mesh with the facts on the ground. We'd expect to see, for example, lots of federal grant programs geared towards quick-fix job training for displaced workers, when the real growth is in 18 year olds who struggled in high school math or whose parents don't have the money for Faraway State. We'd expect to see policymakers focus on short-term certificate programs, when the real need is in remedial math.

Ayup.

I'm not usually a fan of persnickety statistical critiques, but this strikes me as fundamental. The official public voice of community colleges in America, for reasons I personally can't fathom, is promulgating profoundly misleading data on our behalf.

It may be simple sloppiness – someone made an arbitrary data-reporting decision years ago and nobody has bothered to revisit it. It's not a very satisfying explanation, but I've been in administration long enough to know that sometimes, that's how things happen. If that's the case, I hope someone there reads this and issues some public corrections post-haste.

Or there may be some sort of PR/political calculation. If cc's present ourselves as focused mostly on retraining displaced adult workers, then we don't look like we're competing with four-year colleges. Or maybe the 'retraining' angle seems likelier to pay off in workforce development grant money. I'm all for workforce development grants, but we get far more students going through the English department than we get through all of our workforce stuff put together, and we need money for that, too.

We train, yes, but we also educate. In fact, if anything, the direction is towards the education side. That's as it should be, given that the Great Recession has hit hardest those jobs that pay well but don't require much formal education. These days, even many vocational programs require significant amounts of gen ed. The distinction is blurring, even though much funding is predicated on a clear boundary between the two. The policy assumptions are badly trailing the realities on the ground.

Locally, the demographic trends among our students show the average age going down, the racial composition getting ever less white, and the gender gap shrinking as the male population is increasing. (The students are still predominantly female, but only in the shrinking 25-and-over group. The youngsters are almost evenly split.) Although the press seemingly never tires of telling the story of the laid off 35 year old, the real growth is in young minority males taking traditional college courses. To me, this is a HUGE story, well worth telling, and an opportunity to accomplish something of historic significance. Young minority males are showing up at college in unprecedented numbers. (As I noted recently, it's raining men over at Admissions.) If we can succeed in getting those young men through college and into the land of good jobs at higher rates than we have in the past, we will have accomplished something with real impact. I just don't know why we're doing it completely below the radar, or why the AACC persists in telling a story that distracts from what's actually happening. Getting the story right could help get some of the policies right. There's too much at stake to get this wrong. Tell the truth, fix the policies, and get the resources where they're needed. If we miss this moment, we'll pay for it for decades to come.

If half your students are 21 and under, but the mean is 25, then there must be a large number older than 30 to bring the mean up. I'm curious to know whether you have alot in the 30-35 group, or a more even spread of older students.

Either way, your distribution sounds asymmetrical. Could be bi-modal: lots of "youngsters", lots of thirty-somethings and not many in the middle. Could be skewed: lots of "youngsters" and then a tailing off of older students.

Your students are (based on the figures given) younger than the national, but the shape could well be the same.

To me, these figures demonstrate that CC's are meeting the needs of two distinctly different populations - as you've said before.

I'd be interested to know the trend in your figures - have either the mean or median changed recently?

Why, yes, sometimes facts actually matter (like "irrefutable math" from a few discussion threads back. In this case, not only facts, but precise use of technical language matter.
Sorry, but you (and the AACC) seem to be a bit sloppy in your own use of precise statistical terms.

In statistical terms, the word "Average" -- "Mean" so when you write "the '29' figure is both several years behind the rest of the data, and a 'mean,' rather than a median." you then cannot say "the mean age is 'probably around 22 or 23.'"

It doesn't take many students over the age of 40 to counter the number of students under the age of 20 to shift the "average" or the "Mean" value.

This is important, since the who statement of yours that kicked off the numbers kerfuffle, was that "For quite a while now, the average age of our students has been dropping."Might I sugggest the "telling" statistic is in the missing 13%. Assuming the AACC actually has "real" date, then one must ask "How old are those in the 40+ age group?" Is there a reason why they present data in three, unequally sized groups, rather than providing the (traditional) quartile, or quintile, presentations of data? Certainly the addition of 1 or 2 lines of information would not overly tax the AACC website.

So, let me be perfectly clear on this: when you use the statistical terms correctly, and precisely, the numbers actually DO make sense. It worries me, but doesn't surprise me, that at the Community College level people still routinely confuse the use of these terms. Failing to understand statistics is one of my greatest criticisms of students transferring out of the CC. I am just saddened that it happens to be the Administration.

(and for those intellectually curious, the original post/comment thread can be found at http://suburbdad.blogspot.com/2009/02/new-york-times-misses-point-in-related.html)

Anon 4:54 -- I corrected the typo. The rest of your comment is now moot, except as a suggestion (which I'd second, btw) that the AACC use quintiles.

I'd appreciate stuffing the ad hominems now.

Thank you.

DD:

One aspect of your observations struck a nerve (in re: students attending as prima facie transfer candidates).

We are seeing an increasing rise in "transfer" students who show up with an AA/AAS degree without a substantive chunk of the Texas State Core. Here in Texas, we make it easy: All students must have the following courses, and all universities will accpet those courses from the 2 year schools.

Yet- students are sold the "Get the AS/AAS, it's 'even better'" line of BS and then feel cheated that they have 18 or more units to go before they complete the requirements of their first two years.

I have a student right now who showed up, AAS degree in hand, who actually only completed the first semester of Texas State Core.

His choices are to 1) take the courses at Big State (comass heading) U; or 2) go back and take them at a (different) CC.

First, he said he was going to 3) sue the community college for fraud . . .

[Hooray! *Finally* we are implementing a policy of "stuffing" the ad-hominems! About time, frankly. As a frequent recipient of these attacks, I am curious to know how this will be enforced? Is snarkiness on the chopping block as well?]

I don't know what is worse, an entire organization that is clueless about the most basic of statistical techniques (and a PR flack who is incapable of explaining mean and median) or a commenter who cannot visualize the age distribution of students at a CC in contrast to that of a 4-year comprehensive.

Apart from dual enrolled students, there is a lower cutoff in age at 18. There is no upper cutoff. It HAS to be asymmetric. I'd describe it as a Maxwell-Boltzmann distribution for the CC. Look at a graph, from wiki, although our distribution is probably squarer at the bottom end.

Anyone with a modicum of math or science training would want to see the histograms, and how they (and their measures) change with time. How about it, DD?

YACP -
Someone should raise the question (with SACS?) regarding why an AA degree does not articulate with the state "core".

I would not expect an AAS to satisfy them, but an AA should.

I read and very much enjoy your writing. Doing so is part of my daily routine, so thank you.

I have never commented on your blog in the past but feel compelled to do so now.

I am a statistician, and I understand that mean, median and mode can be misleading and that singly they can each offer a different -- and possibly misleading -- estimate of the central tendency of a distribution of numbers. They do not describe that distribution's spread (as in standard deviation and the like) or its shape (e.g. skewness or kurtosis).

I understand that clearly presenting statistical information to a lay audience can be difficult for both the presenter and the audience. One person sees richness, depth, and nuance in a marvelous mosiac. The other often wants to step back and see only the big picture that all of the tiles comprise without really looking at the masterful way in which the tiles make up the composite. I've been on both sides of that one.

The problem I have with today's post is that you claim to have been misled by a statistic and suggest that whoever reported the statistic(s) is culpable. (I might almost add "maliciously culpable", but "ignorantly" or "incompetently" or "lazily" culpable are more benign and probably more accurate. You tell me.)

Suppose an English 101 student approached you about his grade on an assignment to write 5 pages on the themes of kinship and kingship in _Beowulf_. The student claims that he did not understand the assignment and claimed that your description of the assignment was too brief, too vague and therefore misleading (thus blaming you and your poorly defined assignment for the student's less-than-wanted grade). In your conversation with this student you discovered that he was reading at about a 5th grade level.

Was the student misled? Probably. Was it your fault? No, the student misunderstood the assignment not because it was poorly described but because the student could not read _Beowulf_ well enough to understand the themes and probably could not write well.

I guess I'm getting really frustrated by all of this "you didn't tell me so you're responsible for my ignorance" sort of stuff that has permeated education.

If you are a consumer of statistical information, then learn to consume with a discriminating palate. Or, sit down with a statistican and ask them to help you understand the statistics. Most of these people are approachable enough despite their stereotype, and your decisions will be much better in the long run (see Meehl, 1954).

Heck, I struggle with writing clear prose and communicating complicated ideas in word form. So, I read your blog in part because I think it is very well written and it helps me become a better writer. (No, your blog is not my only source, but it certainly contributes.)

DD, on a totally unrelated note, are you psyched about "Community"?

You've never pointed out my misspellings or various grammar errors so forgive me for commenting on your use of stats:

Obviously, that can't be right. If 47 percent of cc students are 21 or younger, how could the 50th percentile be 29? The numbers don't make sense.The 50th percentile idea would only work if this was a normal distribution - that is if you had an distribution of values through the whole range that peaked at the mean and tailed symmetrically on each end. That is not the case with your population so things like means percentiles and standard deviations have less meaning or worse, can be very misleading. The median would be helpful here but even that might be misleading if even slightly more than half your students fall outside the 18-22 range – which in the case of these students is likely the case (I’m assuming that at least 10% of the folks in the unreported range are more than 40).

If the 47th percentile is 21, I'll go out on a big ol' limb and postulate that the median age is 22.Again, the use of percentile here is misleading – I think the stat means that a little more than half of your students are in that age range, but it does not mean that they fall in a percentile, where 47% are below 21 and 53% are above.

For what it’s worth, I think that you are right about the story that’s being missed. We have been shifting more and more female at my campus, especially in the life sciences. Engineering is one of the last colleges that is majority male – it’s enough to make you want to offer special scholarships to men interested in biology (where 60% of our students at graduation are female.) We will see if that shifts things in biotech and the academy though – men still dominate in positions that have high pay and responsibility (I call this the Summers Effect).

Dear CCPhysicist

Fisrtly, in regard to ad-hominem attacks: can you visualise a commenter who doesn't live, work or teach in the US, and therefore may not have your innate knowledge of the differences between different educational establishments.

Secondly, and more pertinently: yes, the tail-off towards the upper end is obvious. However, I was inquiring about which of two possible forms of asymmetry might be present (and certainly not excluding other forms). The data given by Dean Dad could be explained by a peak at the young end, then tailing off, but also by a peak at the young end, a dip in the twenties, and a second peak in the thirties/forties. (The second form suggesting higher recruitment from students changing career-paths'discovering the need for additional training later in life).

I hope this makes clearer that I was asking for shape of the histogram, but without expecting a graph to be posted!

Touchy subject!

First, as to the point that everybody knows that 'average' means 'mean' -- in the world of specialists, maybe. In the world of politics, absolutely not. The 'fast facts' are clearly aimed at the latter, and so is my objection.

From a policy perspective, it doesn't much matter if the few outliers are 35 or 55. What matters is where the bulk of the students are, and 29 is a world apart from 22. The median matters in a way that the mean just doesn't.

(I'll also add that posting the mean right above information about the distribution, without labeling it, is misleading.)

Since the AACC fast facts don't go very deep, I'm left to my own campus to discern patterns. On my own campus, there's a steep dropoff above 24, and it continues all the way up. There's no second peak in the forties or fifties. Whether that holds nationally or is just a local quirk, I don't know.

My larger point, which I probably shouldn't have saved for the last paragraph, is that a number as misleading as 29 gives a materially false picture of what's going on on campus. Our students are getting younger, but the peculiar way the AACC frames the data obscures that. If policymakers rely on misleading data, they'll get the interventions wrong.

In the world of politics, "average" does not at all mean "mean;" it means "typical." It's why you shouldn't use it in a statistical context unless you know the two are roughly the same.

I'm amazed by any report that does not include a median on a population; averages are meaningless in most cases, since few human populations are normally distributed around a central point. It suggests a group of people who are not particularly interested in what's going on.

Sorry, John. I simply assume that everyone posting here is very familiar with the characteristics of the student body in the various parts of US higher ed, particularly CCs. But if not, watch the clip for "community" someone posted. That will get you up to speed about an American CC.

I was laughing out loud. Oh, man, and I thought "Big Bang Theory" hit close to home ... only we can't have a bottle of wine in the office.

William is on the mark, but that criticism (and mine) should really be directed at the distributor, not the consumer. I know much less than my statistics colleagues, who were talking about "mu" at lunch today, but more than most - and those data DD pointed to tell me very little. Quartiles would tell us more, and a histogram would tell us a lot more. However, they could be severely limited by the data they get fed - but that would be partly their fault.

Our college bins its age data very strangely, but I can tell you that our distribution has no pronounced second peak in the 10-year bins used at the high end. Maybe I'll make up a histogram from what I have. BTW, our average is about 24 and our median is 20. We are predominantly a transfer school.

Could someone please explain the difference between an AA degree and an AAS degree? Web searching does not give a definitive answer. Thanks!

I pulled together a rough histogram of our college's age distribution from one year in the past decade, and put it here on my blog.

Just as DD said in his comment, you can see a rapid falloff like he described for his college. (You have to imagine a smooth curve running through the square bin that is the data set I had available.) Our mean age is five years below the national one, reflecting our status as a "transfer" school.

AAS and AS degrees are unique to a CC. They are terminal two-year degrees that include a few general education courses but are made up mostly of "content". Depending on the specific degree, it is possible that much of the "content" will not transfer as college credit to a 4-year school. Indeed, as far as I know, only accredited AS degrees like Nursing have content courses consistent between different colleges. I have no idea how our AAS programs are put together.

Two examples regarding transfer of credit.

AS Nursing consists almost entirely of nursing classes equivalent to those in the last two years of an RN program at a university. They might have only a semester's worth of regular college credit, but they can enter an RN to BSRN program to pick up the two years or so of college work they don't have.

AAS Accounting is mostly accounting classes, many of which are not at the level of those in a university's business college. If they were lucky, they might transfer a year's worth of credit into a university. In contrast, an AA degree for a future business major contains only a couple of accounting classes. All the rest consists of general education classes and pre-reqs like basic economics and a calculus class specifically for business majors.

In our state, the public universities would not admit a student with an AAS degree. They would send them to us to fill in the gaps needed to complete an AA.

My apologies if my comments came across as ad hominem. I did not mean them that way. Perhaps this speaks to my marginal ability to compose clear prose. (I'm still a amazed every time that a manuscript of mine is actually accepted.)

My frustration is real, but you are hardly the intended target. I'm sure its something I should take up with a therapist, but being an as-yet untenured assistant professor already argues for that.

Again, my apology.

Will

Clarification:

I believe the pre-transfer student *can* receive an AA in General Studies by completing the Texas Core; the problem is, the CCs steer the kids away from that program and into the occupationally focused AS/AAS degrees.

Some don't even advertise the General Studies AA option at all . . .

Do CCs get some benefit I don't know about from steering students into non-core qualifying occupational degree programs?

I have heard many of them steer students into two-year degree programs in general to boost their completion rate stats. But why not just steer them into the core-compliant two year degrees?

To be clear:

AA = Associate in Arts degree

AS = Associate in Science degree

AAS = Associate in Applied Science degree

These are 2-year degrees earned at US community colleges and junior colleges.

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