the irish lass

CNN SINKS NAVY [Jim Robbins]
A person who was at Annapolis today sent me the following about the AP photo CNN ran on its web site of Midshipmen asleep in the auditorium before the President’s speech:
This is bias. The mids started arriving at 0630 in the auditorium. Most have barely gotten any sleep because it's Army-Navy week. Almost all the mids were using the down time to get some rest while they waited the several hours. They were clearly all awake by 9:30 as things started to happen and certain all were awake for the speech.
As everyone who has attended a service academy will tell you, there is nothing more cherished than rack time. But CNN does a disservice to the Naval Academy to imply the mids would sprawl out asleep in the presence of the Commander in Chief. I think CNN owes these fine young Americans an apology.

Terms of art. I've been hanging out with mathematicians again. I love the way they talk. Speaking of a young lady of abundant charms (not Ms. Aniston), a mathematician observed to me appreciatively that: "She is nontrivially attractive."

That ought to lead naturally to this month's brainteaser. Instead of a brainteaser this month, though, I'm going to indulge myself in a math grumble. Hey, it's my diary, I can do what I like. Here comes the math grumble, with a dash of politics for seasoning.

How many sigmas? That the No Child Left Behind Act is degenerating into a massive nationwide cheat-a-thon will not be surprising to anyone who has followed the fate of this law, perhaps the stupidest piece of legislation enacted during the George W. Bush presidency, or possibly ever. In a nutshell: States get benefits from the feds if they can show that the test results of their students are improving, but they get to write the tests themselves. So guess what they do? Right. Or, as my ten-year-old would say: Duh.

My own beef about the tests my kids get, both the state tests and the less formal in-school ones, is that I have very little idea how well they have done on them.

Nellie Derbyshire: "Hey, Dad! I got 98 on my math test today!"

JD: "Really? Out of a possible thousand?"

ND: "Da-a-ad! Come on! A hundred, of course."

JD: "Well done, sweetheart. You're relieved of chores for a day."

But I am quietly thinking to myself: How many sigmas is that?

Let me explain. If you give a test to a disparate bunch of people, some will get high scores, some will get low scores, some will come out in the middle. The collection of all the scores is called by statisticians a distribution. The distribution has certain properties, measured by other numbers called statistics that you can derive by chewing up the original numbers in various ways. The best-known statistic is the average, officially called the mean. If you gave the test to five students and they scored 69, 56, 47, 53, and 55, that would be a mean score of 56. If you test another group of five students, and they score 84, 32, 41, 59, and 65, that would also be a mean score of 56. To get the mean, you just add up all your numbers and divide the total by how many there are — in this case, five.

However, while both groups got the same mean, the second group's scores are more "spread out," less "bunched together" than the first group's. There is another statistic you can work out to measure the spread-out-ness of the scores. This is the standard deviation. It would take too long to explain how to get it, but it's not hard, and I refer you to Google for the details. The standard deviation of that first test group is 8.062; of the second, 20.43. Yep, the second is more spread out — bigger standard deviation. Standard deviation is usually denoted by a lower-case Greek letter sigma.

So what I really want to know about my kids' test results is: How many sigmas away from the mean are they, and in which direction? If my daughter was the person in that first group who scored 47, she would have scored 9 points below the mean; that is, 1.12 sigmas below the mean (9 divided by 8.062), or "negative 1.12" for short. If, on the other hand, she was the person who scored 84 in that second group, she would have a sigma of +1.37.

With big groups and reasonably well-designed tests the distribution is the famous "bell-shaped curve," properly known as the normal, or Gaussian, distribution. In that distribution it is always the case that around two-thirds of the scores (to be precise, a shade over 68.2689492137 percent) will fall between negative one sigma and positive one sigma, 94.45 percent between negative two and positive two, 99.73 percent between negative three and positive three, and so on. In fact, you always know where you are with the normal distribution. If my daughter were to come home and announce: "Dad, we had a math test, and I scored one point three five sigma!" why, then, I should know that my princess was easily in the top ten percent of her peers, was in fact at the 91.15th percentile. And I would be happy.

Why can't schoolteachers do this for us? It's just elementary arithmetic. You don't even need a math package; Microsoft Excel will do sigmas for you perfectly well. The answer, I suspect, is that the average (not mean, average) American schoolteacher in this day and age would rather submit to an appendectomy without anesthetic than grade a student as "negative" anything.