Taking a Statistical Look at Prelims

Going from last year to this year, first looking at the 8th/9th place cutoff times, there are only two events this year that were faster than last year's cutoffs: the 200 free and the 100 back. (To do this, I took the average of the 8th and 9th place times in 2009 and compared them with the average of the 8th and 9th place times of 2010; 9th place in the 100 Free was actually .04 seconds faster this year compared with last year, but otherwise both the 8th and the 9th place times were faster in the year with the faster 8th/9th average).
OK, now for the real "statistical" part...
I decided to run some hypothesis tests to try to first determine if, in fact, there was a significant difference between the results from 2009 and the results from 2010. To do this, I went event by event and took the average time, in seconds, of the top 16 finishers at prelims, then used Microsoft Excel to run a 2-sample t-test based on those two means from 2009 and 2010 in each event. Using a significance level of α=0.10 (such that each tail represents an area of 0.05). From here, I found that the 200 Medley Relay, 200 IM, 50 Free, 100 Fly, and 100 Breast all showed significant differences between 2009 and 2010. Furthermore, all of these events showed that at the α=.05 significance level, the times from 2010 were slower than 2009. The rest of the events, while showing some difference in the average, did not show any significant difference, per the 2-sample t-test. So, on the whole, based on this analysis, I would say that the prelims' results show this year to be somewhat slower than last year. Then again, I don't think many would argue that last year was a particularly fast year, just by the intuitive sense of the times. If you have any questions about this analysis, or would like additional information or other statistical tests, let me know, I have the data well-organized enough that I can work with you on that. Have a great night, and good luck to the girls, whenever they swim.