On the lonely gypsum weed

[austin_dern]

I'm still out of academia, really, apart from doing some research and getting started on that second draft of the book. However, I got to wet my toes back in the good proper stuff again. You see, my mother teaches as an adjunct a course on experimental methods, for a psychology class, and while most of that is very low-mathematics there is the need to explain significance testing and the Gaussian distribution and that sort of thing. This is ordinarily the point in the class where her students freeze up, panic, talk about things like ``dyscalcula'', and wince at how they really can't skip this without being lost for the rest of the course.

So --- and she's done this before --- she invited me in to talk about the first step of these topics, the z-score. This is a way of converting raw scores in a sample to their equivalents on a standard bell curve, and while it's incredibly easy once you're comfortable with what mean and standard deviation are (the z score for a given x is x minus the mean, divided by the standard deviation), it's building those concepts that's the hard part, as isn't it always?

Thus it was that I spent an hour and a half going from my mother's given example of calculating the mean and standard deviation --- using the scores of their just-completed exam --- and showing what would happen if you added a constant to every term (the mean changes, the standard deviation does not), or multiply everything by a constant (the mean and standard deviation are multiplied by that constant), and how you can use this to rescale everything to the same distribution. We stopped before the nominal end of class, as students started to get restless and plainly distraught, but I could've gone on all day.

Trivia: The Allied offensive which captured Baghdad in March 1917 was code-named ``Yilderim'', meaning ``lightning''. Source: The First World War, Hew Strachan.

Currently Reading: Dear George: Advice And Answers From America's Leading Expert On Everything From A To B, George Burns. It's a pretty silly bunch of short questions and answers but, hey, he had 800 years of vaudeville, radio, and TV experience to draw on so it's pretty amusing.

Comments

[lexomatic.livejournal.com]

::: This is ordinarily the point in the class where her students freeze up, panic, ... and wince at how they really can't skip this without being lost for the rest of the course.

More importantly: If they can't hack the math, if they don't really feel the numbers, they should jump ship now for something more touchy-feely. In any statistics-heavey field, misunderstanding numbers means you're likely to do a disservice to your clients. "Many wizards don't know the first thing about logic," Hermione Granger sniffs disdainfully, and many doctors don't know enough stats to realize that the latest experimental results don't amount to much. (Hobbyhorse prompted by recent reading. Please carry on.)

(Engineers whose bridges collapse because they transposed their stress-strain matrices don't do well, professionally. Maybe medical professionals should be periodically recertified on math? "Given the nature of this test, how many additional patients will be helped? Per year? As a fraction of the patient-population?" And drivers should be recertified on rules of the road. Oh, right, you were trying to carry on, weren't you?)

::: what would happen if you added a constant to every term ... or multiply everything by a constant

Sounds like those would be easily demonstrable with pictures. And with example datasets (assuming the right statistical software). That's what I find myself doing with the time-series database at work whenever I need to see how a certain operation works ("aha, so the lag, growth and everything else is measured from the past up until the reference period").

::: Dear George: Advice And Answers From America's Leading Expert On Everything From A To B, George Burns. It's a pretty silly bunch of short questions and answers ...

I have not read this, but suspect fluff. I'd have more respect for the material (speaking in general terms) if the advice was first useful, and concise, and funny. This might require the complementary talents of more than a single humorist. Like, "Do not disturb sleeping dragons, for you are crunchy and good with ketchup" is amusing enough for three seconds, but is it really extensible to any kind of large predator the audience is actually apt to encounter?

[austin-dern.livejournal.com]

Eh, but, most of these students are not going into fields where they need a feel for the arithmetic. Most of them, actually, aren't going to use anything from this course; it meets some of the advanced-course requirements for their major and that's all.

Those who are going on to further study are mostly going to education and child development studies where they'll need to know, if on this series of tests the child rates below these scores that's evidence of a learning disability, if the rate is between these scores that signifies potentially something to watch, if the score is above this level the child may be gifted and so on, but where the numbers come from is not really more important than where the questions on the evaluation exams come from.

I suppose pictures and live-action playing with a spreadsheet or the equivalent might help getting across the ideas of what happens with translating or scaling scores pretty well. I just did it by taking the same raw scores and manipulating them a few different ways, going through all the steps, in the hopes the commonality of what we were doing would make the procedure less frightening. I think they were getting the hang of the common results pretty soon, based on how their responses to the ``what do you imagine would happen if ... ?'' questions before we actually calculated things.

Of course the George Burns book is fluff. He's a comic writing a comic book. Sample bits:

Dear George --
I heard that Michaelangelo didn't start painting the ceiling of the Sistine Chapel until he was 70 years old. Is this true, and why did he wait so long to do it?
--- Artistic Alvin.

Dear Art ---
I happen to know all about this, because I held the ladder for him. I knew Mike very well. And it's true, Michelangelo started painting the ceiling when he was 70 years old. he would have started sooner, but he felt it only needed one coat.

Or:

Dear George ---
If you had your choice, what would you have for your epitaph?
--- Inquisitive.

Dear In---
Who cares as long as I'm standing there reading it?
(That wasn't my original answer. My first answer was a shrimp cocktail. Then my secretary explained to me, ``An epitaph is not an appetizer. An epitaph is something that goes on a tombstone. How could you say a shrimp cocktail?'' I said, ``While I'm standing there reading my epitaph, I'd like to eat something.'')