One-sample t-test on count data

Cross Validated Asked by Zarya on November 16, 2021

I’m working with sports performance data (ice hockey). The question I’m trying to answer is: Does the number of duels player A won in a specific match differ significantly from the mean number of duels player A won last season?

A colleague of mine suggested to use a one-sample t-test with H0: u (specific match) = u0 (mean of last season). I don’t think this is appropriate because
a) the data is not continuous (count data)
b) the data not normally distributed
c) the number of duels won in one specific match is not a “sample mean” but just a single observation

Do you agree?

I don’t know which test to use instead. I think I would just fit a distribution to the data of last season (probably Poisson or Negative Binomial due to overdispersion) and then calculate the probability of player A winning x duels in a specific match – but this would be another way to assess his performance.

Do you have any other (maybe more sophisticated) suggestions?

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