Statistically, via this calculator:
http://vassarstats.net/propdiff_ind.html
Our 32/418 vs the Mancs' 13/418 has only a probability of occuring by chance 0.36% of the time. That sounds pretty significant. But due to the number of comparisons, you must adjust this using a correction. Normal significance level is 5%, so you divide that number by the number of comparisons (in this case roughly 18+17+16...(this assumes all the teams in the PL are the same), and so that's the triangular number of 18, which is 171 (this is called a Bonferroni correction, IIRC). Thus, in order for statistical significance, the chance that any one team has a significantly higher occurence of home red cards than another is 5%/171 = 0.036%. This is roughly one tenth the likelihood calculated by the chi-squared test (what I assume is on the back-end of this calculator), meaning we're no longer significant.
Just due to the large number of comparisons and the relatively small number of red cards, we cannot conclude that the difference in red cards between Everton and ManU cannot simply occur by chance. Had it been significant, that still doesn't mean that refs are to blame, it could be substantially affected by manager or playing style, especially considering that roughly half those matches for Everton and nearly all for ManU are under one manager.
For experiment's sake, had our value of red cards been 38 and theirs remain the same, the difference would then be significant. Or if ours remained the same and theirs dropped to 9, they would also be significantly different.
I'm not sure why I did this, but hey, it's Friday. It's mostly correct, though statistics is not my specific area of expertise. Enjoy the weekend and COYB!
Materazzi, played about 30 games and sent off 4 times. nob head
