From USA Today

A recent article in USA Today discussed standardized testing in D.C. public schools. It mentioned that some high-performing schools have very high numbers of answers erased on tests (when you erase an answer on the Scantron sheet and put in a new one, the machine can detect the residue). The article claimed that this could be possible evidence that teachers tampered with the tests prior to submitting them for grading.

The following quote appeared:

"Noyes is one of 103 public schools here that have had erasure rates that surpassed D.C. averages at least once since 2008. That's more than half of D.C. schools."

This statement is not too surprising. If the distribution of erasure rates were symmetrical, then in any given year half of them will be above average. Since the schools above average will change from year to year (if only due to random variation), then over a 3-year period more than half of the schools will be above average in at least one of those years. (For instance, if the erasure rates are random and independent, then each year each school will have a 1/2 probability of being above average, so each school will have a 7/8 probability of being above average in at least one year.)

Aside from this sentence, the rest of the article was actually fairly good statistically. It mentioned that this particular school hasd erasure rates so far higher that it wasn't due to chance, and included a lengthy discussion of possible alternative explanations for the data.

Gaming Math - Problem 17

Recently, University of Illinois computer science professor Sheldon Jacobson has developed a mathematical model to predict the distribution of seeds in the Final Four of the NCAA basketball tournament. (The NCAA basketball tournament consists of 64 teams divided into 4 regions with 16 teams each. It is a single-elimination tournament, and within each region the teams are "seeded" from 1 to 16, with the teams in order from strongest to weakest. The team that wins in each region goes to the "Final Four".) There is a web site allowing you to explore the results of the model. A key finding, reported in media coverage about this web site, is that the most likely combination of seeds is not (1,1,1,1), but rather (1,1,2,3).

Problem 17: Seeds of Victory

According to the web site, the probability that all four 1-seeded teams will go to the Final Four is 1 in 31.82, while the probability that two 1-seeded teams, one 2-seeded teams, and one 3-seeded team will go to the Final Four is 1 in 14.05.

In the article, Jacobson made the following statement:

"But I can tell you that if you want to go purely with the odds, choose a Final Four with seeds 1, 1, 2, 3.”

For concreteness, suppose that you are asked to pick, for each region, which team is going to the Final Four, and you are only considered "successful" if you correctly pick all four regions. Assuming that the probabilities given by Jacobson's model are accurate, is it true that picking a (1,1,2,3) split is more likely to be successful than a (1,1,1,1) split?

The answer is here.

Job Search

So, last week I made my decision: I will be switching to a Masters degree program. This does mean that I won't get to do that internship at Lawrence Livermore, because the internship requires that you commit to staying in school through the Fall semester. This actually turns out to be okay because I will get to stay at school through August to finish up my thesis. There's a fair bit of work still left; I have to finish up all the remaining programming work, write documentation on all my code so that my replacement can figure out what's going on after I leave, and of course write the actual thesis. Also, I have started to look for full-time jobs for after school.

I went to the Engineering Career Services office and got my resume and cover letter looked at, and they basically had me rewrite the whole thing using the format described in the career guide, which made it look much better. I took the new resume and cover letter over to the Graduate College's career services office, and they told me that my resume and cover letter looked very good, and they only had a couple minor stylistic changes. I searched for jobs online and through job posting on bulletin boards in the Computer Science department. So far I have submitted resumes to 9 companies, and have gotten phone interview requests from 2 of them. One of them was MathWorks, which makes Matlab. Another was Palantir Technologies, which makes a data analysis and visualization platform (read the web site if you are interested). They wanted to interview me for a "Business Development" position, and I'm very interested in what that position entails. I'll report back when I see how the interviews go.

And one more thing. When I was in elementary school and people asked me what I wanted to be when I grew up, I would answer "math test-question editor", because I took lots of math tests like the Math Olympiad during that time and often I found the test questions ambiguous. During my online job search, I found an online job advertisement for a math test-question editor. But things have changed a lot in the past 15 years, and I decided not to apply for that job.

The results are in

I have two pieces of good news to report:

First, I passed my qual! I haven't got the “official” announcement yet but Jeff told me that the qual has been graded and I passed it.

Second, all the votes are in and I am now going to be an official member of House Valdemar in Belegarth. They are in the process of making the special tunic for me and I will have an official “initiation ritual” next Saturday, March 12.

EDIT: I typed "not" instead of "now" before.