# How to show statistical significance of me playing for my team

I'm trying to prove that my presence on my college football team has a statistically significant effect (for the better). To make things easier I'm ignoring draws.

I have data on the wins and losses of matches with and without me playing for the team, and the dates of each match (though I'm fairly confident the dates are not important).

Without me: P: 27, W: 17, L: 10, With me: P: 12, W: 8, L: 4

I am trying to figure out what the best statistical test to show significance is. As it stands I currently think that treating my team without me as a coin with probability of heads (winning) and tails (losing) being equal to win / loss percentages of my team (17/27 and 10/27 respectively). I then plan on asking what the chance of getting the win / loss record with me on the team - 5 wins in 7 games i.e. getting 5 heads from 7 coin flips.

Is this approach a. sound, and b. the most appropriate?

• Have you thought of using chi-squared or Fisher's exact test? Dec 27, 2017 at 11:51
• The problem with your approach is that (if I got it correctly) you assume the winning probability without you to be exactly 17/27 where in reality, the true probability might be a bit higher or lower, just by chance. Dec 27, 2017 at 12:32

You can present your data as a contingency table and do a chi-squared test. Using R:

chisq.test(cbind(c(17, 10), c(8, 4)))

Pearson's Chi-squared test with Yates' continuity correction

data:  cbind(c(17, 10), c(8, 4))
X-squared = 6.1124e-31, df = 1, p-value = 1

Warning message:
In chisq.test(cbind(c(17, 10), c(8, 4))) :
Chi-squared approximation may be incorrect


The last sentence above might look worrying, but in this case, just look at the chi-squared observed value itself, practically zero. So there is little doubt, your team seems to do well also without you.