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Given records for a team in 2 semesters Fall and Spring. We want to check if there is a relationship between the semester "Fall or Spring" and result "win or loss". Can chi-square test be used? Example of data

Fall , Spring 
win , loss  
win , loss
win , loss
win , win 
win, win
loss, loss
loss, win
loss, loss

Many thanks

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I think so. Make a 2x2 contingency table: Fall by rows, Spring by columns. Do the tabulations in each cell. The expected numbers, assuming independence, ought to be $.25N$, where $N$ is the number of pairs. Your critical $\chi^2$ should have 1 d.f.

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  • $\begingroup$ My concern is that the data is coming from 2 different semesters and the examples I saw about chi-square usually comes from 1 list and not 2 lists. $\endgroup$ – tnaser Apr 3 '13 at 2:15
  • $\begingroup$ @tnaser Of course it will come from different semesters if it's coming from different seasons. Being in 1 vs 2 lists isn't important. You could have just stored it differently (e.g., (Fall, win), (Sping, loss), ....). $\endgroup$ – Stumpy Joe Pete Apr 3 '13 at 2:20
  • $\begingroup$ @tnaser A bigger concern is that you already know the answer: There is certainly a relationship between season and win/loss rate. It might be so small as to not be interesting, but it's certainly not 0.00000...infinite zeros. This means that the result of "significance" depends largely on the size of your sample. With enough data, you will eventually detect a "significant" difference, even if it's not practically important. $\endgroup$ – Stumpy Joe Pete Apr 3 '13 at 2:22
  • $\begingroup$ Ok , just to be sure, after doing the 2 *2 table, if the p-value is < 0.05 , I can say there is a relationship between the semester and the result? is there a way to know which semester the team wins more other than just looking at the data? Something that can prove with significance? $\endgroup$ – tnaser Apr 3 '13 at 2:28
  • $\begingroup$ @tnaser: You conclude that the two variables are statistically dependent, correct. Then, if you want to dig deeper, form a test of proportions (a two sample proportion test), eg, $H_a: p_{\text{Fall Wins}} > p_{\text{Spring Wins}}$ $\endgroup$ – baudolino Apr 3 '13 at 2:31

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