Thursday, 20 December 2007
Well the Mitchell report is making lots of press, and enough names have been named to generate some interesting questions. An Article in the Milwaukee Journal Sentinel compares the results of 46 baseball players named in the report in the first two seasons they have allegedly used steroids, with some surprising results.
Of the nineteen pitchers named in the report, fourteen had better than career average performances in the first year after the suspected first-use date. Now that is pretty significant if we assume that the chances of a better than average year is 50-50, like a coin flip. If you flip a coin nineteen times, the probability you get 14 or more heads is about 3% or one in thirty. For the hitters, a similar effect occurred; nineteen improved out of twenty-seven players. As a coin flip simulation, that is even less likely. The probability is about 2 ½ % or about one in forty chances.
Now those results would make a great case for steroid use, but when we look at the second year, we find that only nine of the nineteen pitchers were above their career average, and only seventeen of the twenty-seven hitters were above average. The results for hitters is still positive, with about a 12% probability of chance, which is definitely not a strong statistical significance; but for the pitchers, less than half improved on their career average.
One world-class statistician, Professor Paul Velleman of Cornell, suggests that the result could just be the well-known placebo effect. Hitters and pitchers performed better in their first year because they assumed that steroids would make them perform better.
I wrote recently about Pete Rose, who was banned for life for gambling. I don’t remember any suggestion that he ever was suspected of trying to cheat as part of that. He just loved to gamble. Now we have a bunch of players who actually cheated in many people’s eyes and some of them will be going to the hall of fame. So what is the message we send to young athletes with this result? If we are confused, I bet they are too.
Friday, 14 December 2007
Ok, I know a couple of tricks for quick computation, and every once in a while a chance comes up in class to use one, and I multiply 78 x 72 in my head or square 125 and the kids tell me I'm brillant... I love the attention and having them think I am clever, but this guy...WOW... this is magic... Just watch
Sunday, 9 December 2007
December 9th, and there are only 22 days left in the year, which means 16 more days till Christmas. Lots of people involved with counting involved with this date. This is the day on which statistician Herman Hollerith installs his computing device at the United States War Department. Math and science students of my generation remember him for two other inventions he used to make his computing machine work, punched cards, called Hollerith cards, and the keypunch machine to put holes in them. The company he formed went on to become one of the largest counting compnies in the world, IBM. He got the idea from the mechanical looms of a Frenchman named Jocard.
Speaking of computers and the internet, it was on this day that the NLS, or the "oNLine System", was introduced, It was a revolutionary computer collaboration systemdesigned by Douglas Engelbart and the researchers at the Stanford Research Institute. It was this project that led to the invention of html, and the ubiquitous computer “mouse”.
Of course the statistics which was at the heart of the work done by Hollerith and the big IBM computers were indebted to the work of a great Russian mathematician who died on this day in 1894, Pafnuty Chebyshev (ok, I know there are 20 spellings of the name, sorry if this is not YOUR favorite). The Russian name has been translated as both Chebyshev and Tschebyshev, as well as several other spellings, which can lead to confusion. It is said that Besicovitch used to declare, “We use the letter T for the class of T-polynomials because it is the first letter of Chebyshev”, which he was also known to claim had no letter T. His famous inequality is rememebered, and mis-remembered by each successive year of introductory statistics students. But my favorite is a little ditty I learned in college:
Tchebyshef said it
So I'll say it again
There's always a prime
between N and 2N
From the age of computers, the need for programming and compilers became essential, and so we point out that this was also the day in 1906 that Grace Murray Hopper was born. The lady Admiral is remembered as the creator of Cobol, and even has a cruiser named after her, but the greatest influence she has on modern computing comes from a failure. One of the large Mark I computer/calculator she worked on failed to operate one day, and the cause of the disaster was traced to a dead moth on one of the computer relays. The bug can be seen in the log book where she pasted it in the Smithsonian Museum of American History. It is, so they say, the creation of the term “bug” for a computer malfunction.
Another mathematician born on this day is related to both counting and disasters. William Whiston was a British Mathematician born on this day in 1667. the year after the great fire of London. He was headed for the top, and rubbing elbows with the best for a while. He served as Newton’s deputy at Cambridge, where he was a fellow, and followed Newton in the prestigious Lucasian professorship. He was also one of the earliest proponents of the theory that comets had a periodic behavior, along with Halley.
His contribution to came in the form of a translation of the works of Josephus, the first century Jewish-Roman historian, who survived the Jewish-Roman war perhaps due to his mathematical talents. In his book The Jewish Wars Flavius tells that he was one out of 41 Jewish rebels trapped by the Romans. His companions preferred suicide to escape, so they decided to draw lots to see who would kill whom so that they could avoid both capture and the sin of suicide. The idea that they decided to form a cycle and to kill every third person and to proceed around the circle until no one was left is probably a myth. According to the problem Josephus wasn't excited by the idea of killing himself, so he calculated where he has to stand to survive the vicious circle. The general Josephus problem involves deciding how many people will stand around a circle and how many shall be passed over before the next one is killed and predicting the last to survive. You can find a java applet to “play” at death at that same link.
Comets were also part of the disaster in his life. He had become famous for his studies that stated that the Biblical flood had been caused by a comet, and gave support for other geological impacts of comets on the Earth. Whiston was removed from his position at Cambridge, and denied membership in the Royal Society for his “heretical” views. He took the “wrong” side in the battle between Arianism and the Trinitarian view, but his brilliance still made the public attend to his proclamations. When he predicted the end of the world by a collision with a comet in October 16th of 1736 the Archbishop of Canterbury had to issue a denial to calm the panic.
For those who are wondering, the world did NOT end on that date, at least not according to Wikipedia, and they would know. Not sure what calculations Whiston used to make his prediction, but maybe his computer had a “bug” in it too.
Friday, 7 December 2007
Well, report card time again... And along with grades comes the difficult task of trying to find a quick short comment that summarizes 9 weeks of a student's life into a single sentence; Always hard to do. It is a time of year that brings out the humor in teachers, and I got the following from a colleague who, I assure you, meant them only in jest.
OK, so most of my kids did well, and I didn't have to use anything even close to the comments below, but I did chuckle at several of them, and one or two actually made me think of students I had known. The source said they were actual comments sent out by New York City teachers, but I hope that is just one more of those urban legends that is totally false. Whatever the source, I hope you can enjoy them for the tongue-in-cheek, sometimes too close to true, humor that prompted them.
These are actual comments made on students' report cards by teachers in
the New York City public school system.
1. Since my last report, your child has reached rock bottom and has
started to dig.
2. I would not allow this student to breed.
3. Your child has delusions of adequacy.
4. Your son is depriving a village somewhere of an idiot.
5. Your son sets low personal standards and then consistently fails to
6. The student has a "full six-pack" but lacks the plastic thing to hold
it all together .
7. This child has been working with glue too much.
8. When your daughter's IQ reaches 50, she should sell.
9. The gates are down, the lights are flashing, but the train isn't
10. If this student were any more stupid, he'd have to be watered twice
11. It's impossible to believe the sperm that created this child beat
out 1,000,000 others.
12. The wheel is turning but the hamster is definitely dead.
OK, there must be a thousand of these 0ut there, so send me your additions to the list....
Thursday, 6 December 2007
For anyone interested, the NAEP just release the 2007 results for 12th graders, and the results indicate that the "child" they did not want to leave behind is farther behind than in 1992.
I have made some comments, and even tried to attribute some share (all) of the blame in that truest of American traditions (if we can't fix it, find someone to blame)...
If you want to read it for yourself, the document is at... http://nationsreportcard.gov/
Section headings for the 12th grade scores include titles like:
>>>Overall Performance in Reading Declines in Comparison to 1992
>>>Twelfth-graders in 2005 scored lower than in 1992, but their score was not significantly different compared to 2002.
Except for the highest-performing students (90th percentile), declines were seen at all levels of performance since 1992.
In particular, the gap between the students at the 90th percentile of the nation and the 10th percentile, grew from 84 points to 98 points. The 90th percentile achievement level was still the same as 1992, but the 10th percentile score dropped 14 points. Notice in the chart that students in the bottom 50% of the population continue to decline, and the lower the level, the greater the decline.
Trend in twelfth-grade NAEP reading percentile scores
In math, the new test made it impossible to compare with previous years, but looking at overall success as judged by the NAEP competence levels, the nation is more at risk in math than ever. While 73% of seniors met "basic' level standards in reading, and 35 percent were "proficient", in Math only 60 percent were at "basic" level, and only 23% were " proficient".
In both tests, while there were differences in scores from different regions, different income levels, different parental educational levels, and reading backgrounds, no factor so greatly predicted a lack of achievement in reading or learning math as race. Blacks and Hispanics still fall far below white and Asian students on both tests.
Only 6% of blacks and 8% of Hispanics reached the proficient level in math (25% -33%of national average achievement level) and 16% of blacks and 20% of Hispanics reaching that level in Reading. And while both whites and blacks had lower reading scores than in 1992, the "gap" has grown from 24 to 26 points.
The net impact of fifteen years of educational reform has been a stagnation or very mild decline of the best students and a faster decline of the lower ones. It is not just teachers whining that "Kids ain't what they used to be." The weakest 50% of the population of seniors today really do read more poorly than 15 years ago. Measurably worse, statistically significantly worse, and the cure seems to be killing them.
BTW.. scores in fourth grade continue to improve, and 8th grade is steady. So what has happened in high schools in the last fifteen years that is markedly different than the trends in elementary and middle schools. Teacher, how do you spell BLOCK?
NO event has so crippled student success in recent years in the areas of Math and foreign language as much as the block schedule. Teachers like it because it is less classes to prepare for. Student's like it because they get half as much homework (check the statistics, that is a conservative statement), and administrators like it because, as one clever principal told me in justifying his love of the block schedule, "this year our tardy rate dropped by 40%". When I tried to explain that the number of opportunities to be tardy had dropped by 50%, his eyes just glazed over.....