# Is chi-square meaningful for such a small data set?

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:

1. Win the first, win the second
2. Win the first, lose the second
3. Lose the first, win the second
4. 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?

• I think McNemar's test will be more appropriate as it has a clear "within-subject" aspect. – usεr11852 Jan 27 at 20:31
• Could you explain what you mean by "the team" playing the second game? If I understand Lacrosse correctly, it takes two teams to play and--barring ties (which seem to be rare, given their nonexistence in your dataset)--one of them will lose the second and one of them will win the second. It therefore seems impossible for there to be any disadvantage. Moreover, how is it possible that you have 141+121=262 games in which the first was won and only 130+152=252 in which the first was lost? Either your numbers are wrong or their descriptions aren't what they seem to mean. – whuber Jan 27 at 21:06
• The numbers only need to add up when the other teams also played two days on a single weekends. It might be possible that there is, on a particular weekend only a single team that plays two days. E.g. team 1 plays against team 2 on one day and against team 3 on another day, but team 2 and 3 do not play two times. – Martijn Weterings Jan 27 at 21:39
• Clarification: I'm looking at occasions where a team (call it team A) plays two games in a single weekend. Say game 1 is against team B and game 2 is against team C. I'm just looking at the results for team A. You are correct, there are no ties. – Graeme Perrow Jan 27 at 22:08
• If I am calculating the statistic I get: $$\frac {5^2+15^2+6^2+16^2}{136} \approx 4$$ which is not so likely for 1 degree of freedom. But this may be expected since it is not strange for a good/bad team to win/loose several games in a row. You will need to compare the weekend games in a more advanced scheme, for instance compare with the distribution of two games in a row for non-two-in-a-weekend games (giving you 2×2×2=8 numbers instead of 4), or better compare with results of the teams. – Martijn Weterings Jan 27 at 22:09