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Wednesday, October 3, 2007

Random Samples: Making an Ass of You and Me

I first heard the colloquial definition of assume from my middle school band teacher. He relayed it during one of his notoriously crimson-faced tirades as a part of his tireless crusade to get us to practice our instruments. The mere mention of the word ass brought a cacophony of pubescent snickers, as you might well imagine.

Twenty years later, I find myself enrolled in school once again. This time around, I'm not taking any fine arts, and my musical stylings are reserved for my shower head and the lonely walls of the Pottery Barn stockroom. Still, the trite but true words of Mr. Danner stick with me. Daily I am confronted with a seemingly innocuous request to assume. Assume a friction-less surface. Assume no air resistance. Assume a random sample.

Of course, for the purposes of class, I play along. I understand that in order to proceed, a beginner like myself, must temporarily set aside the more confounding components of mathematical problems. Yet I do not take these assumptions lightly, and they hover somewhere in my psyche underlined, in both italics and bold-face. I fear that many people become far too accustomed to these kinds of assumptions, never truly revisiting their ramifications at that later date. Even seasoned professionals fall victim to this permanent credulousness.

My physics teacher relayed the results of a now famous statistical experiment whose findings declared that cats stand a greater chance of survival falling from higher windows than from lower ones. My hand shot up with such velocity that it nearly dislocated my shoulder. You see, that study has a huge hole in it. The sample space isn't really random at all. It originally appeared in a 1987 issue of the Journal of the American Veterinary Medical Association and was authored by two doctors at the Animal Medical Center of Manhattan. They published based on a small sample of cases they had seen at their practice, all feline victims of high-rise free-fall. On the surface, it all seems on the up and up, until you consider the one gaping hole in their methodology. In order to be a random sample, the study must include all instances of the event in question, which is a cat falling out of a window and hitting the ground. Ask yourself this, if your precious Fluffy were to fall victim to accidental defenestration, and upon reaching the street level, you found myriad biological parts where your furry friend was hoped to be, would you scoop up the pieces and take them to the vet? No, and neither do most of the pet-owners in Manhattan. The 1987 study is based on the assumption of random sampling that did not actually occur.

As I have said, these school room assumptions are necessary steps to greater understanding in any and all STEM related fields. But we must never forget that they exist. Our future failures hinge upon them.


mackenab said...

I would add that the study is also flawed by the fact that many cats that fall from low windows and appear to be fine would not be taken to the vet, either. It is only cats in some middle ground between "fine" and "dead" that find their way to the vet.

Also, I will point out that much progress in research is obtained by going back and tweaking assumptions. If you take the "conventional wisdom" in most any STEM field, you will find that this wisdom is usually dependent on certain assumptions. Remove, or even weaken, those assumptions and you often wind up with very interesting results.

Oh, and I still remember the first time I ever saw Mr. Danner write ASSUME on the board and underline ASS, U, and ME.

Anonymous said...

"I fear that many people become far too accustomed to these kinds of assumptions, never truly revisiting their ramifications at that later date. Even seasoned professionals fall victim to this permanent credulousness."

i would go further: learning
"permanent credulousness"
is the very "seasoning"!
becoming a professional *means*
assimilating certain attitudes
so well that the very thought
that they might lead us into error
*can't even arise* (at least,
this is a big part of it ...
also, you have to get paid).

this has something to do, for instance,
with the debasement of terminology
like "critical thinking".
for a certain kind of pro,
it's *obviously* enough to *preach*
"critical thinking" while *demonstating*
the exact opposite: "i take this
on faith [and so should you]" ...
and all (this is the point)
without even noticing that this
is what's happened.

here's my (brief) review of disciplined minds
(size the window to column width).

thanks for the convention report, btw.
long live "pencils down"!

Anonymous said...

So true. All of Euclidean geometry was founded on the assumption that the fifth postulate was "true." Seasoned professionals fell victim to this famous assumption for over 2,000 years.

Pedagogical speaking, I wonder if the problem is not in conveying what an assumption is, "believing something based on authority or experience" but in teaching the student to recognize when something is NOT an assumption. This would be much trickier to do in science due to its empirical nature than in logic or math.

paul said...

i miss the days of listening to you provide the backing vocals to such timeless musicians as peter cetera, joe esposito, and mc hawking.

i hope the insane schedule is becoming more manageable with time.