You know you really are a nerdy Math teacher when....

I decided that it was time for me to actually start ending my summer, so I went to work today. The school is empty and so I have the run of the place. I did, however, get a chance to see the scores of the 15 students that I taught in AP Statistics last year. I taught one section of the AP course for the first time here at Head-Royce and the other three sections were taught by my colleague Chris, who has been teaching the course for about five years. I know that I did not do as good a job as he did, but I still have to compare my students' scores to his. Scores are out of 5, 5 being the best.

Score_____My Section_____All Four Sections
1 __________4 _________________8
2 __________3 _________________9
3__________ 0 _________________10
4 __________6 _________________24
5__________ 2 _________________12

So, how does one analyze whether or not my students scored in a proportion that is within reason of the entire four sections? Run a Chi-squared goodness of fit test of course. DUH!

After having to go back and teach myself the calculation, it comes up that there is s 25% chance (pretty good) that my distribution of scores would happen by chance given the distribution of all four sections combined. In other words, given the four section distribution, if we randomly took 15 students from that pool, there is a 25% chance that my distribution could have occurred. At a 5% significance level (meaning if the chi-squared percentage turned out to be under 5% and I should therefore think that my teaching was WAY substandard), my students scores are well within reason. WHEW!