I write about stats for a lacrosse web site. Most teams play one game each week, but now and again a team will play two games in a weekend. I'm looking into whether they are more or less likely to win the second game of such a weekend, i.e. is a team playing the second game of a back-to-back at a disadvantage?
I've calculated the number of such weekends, and there have been 544 of them over the last 30 years. I've broken them down into four categories:
- Win the first, win the second
- Win the first, lose the second
- Lose the first, win the second
- Lose the first, lose the second
The numbers are 141, 121, 130, and 152 respectively. My null hypothesis is that there will not be any difference between this situation and any other, which means that the expected output would be 136, 136, 136, 136. I have (or Excel has) calculated the chi-square value (using CHISQ.TEST) as .263.
My conclusion is that this supports the null hypothesis, and so playing back to back games is no different than playing two games a week apart. Does this conclusion follow? Can I make such a conclusion from only four pieces of data? Is there a better way to test this hypothesis?