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05-26-2013, 11:17 AM
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Originally Posted by FreddtFoyle View Post
Pearson's chi-squared test is not the appropriate test for this small sample size.

"If the estimated data in any given cell is below 5, then there is not enough data to perform a Chi-square test."

As you pointed out, the expected random outcome for University Cup wins since 1998 for Canada West would be 4.7, and 4.5 for AUS. Both less than 5. That's also two/thirds (66.7%) of our frequencies.
At least you're beginning to understand the issues. Do you have another test to propose, or do you just wish to reject the chi-square and rely on nothing?

The reason the chi-square struggles with low frequencies is the same reason that your argument falls apart: a lack of observations.

To put it in perspective, if you flipped a coin 6 times, and it came up heads 4 times, would you conclude that it is weighted to heads? What if you flipped it 60 times, and it came up heads 40 times?

A chi-square test needs enough observations. 16 is pretty close, and it would only be an issue if we're trying to decide between 90% certainty and 95% certainty. It's not that close.

Anyways, here are two other tests to run, each of which conclude that the AUS is not winning a disproportionate number of championships:
- logistic regression ... more complex, and I did this one too, and the result is the same
- Bayesian multinomial logistic regression ... fancier technique, more difficult to run, NO sensitivity to the limited number of observations, and the same result.

I honestly hadn't picked up on the troll comment. I had thought we were engaged in moderately intelligent dialogue. Thanks for proving me wrong.

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