Alright I got some new data today, i gathered the ilvls from 200 alliance players and 222 horde players and ran the bootstrapping hypothesis test again. The sample mean ilvl for the horde was 197.3 and 198.5 for alliance. (earlier data was from May so it makes sense that it went up). I got a P-value of 0.55 so i was unable to show that the mean ilvl for horde/alliance are different.
I calculated some other interesting stats with the new data all using 95% confidence.
The proportion of players at or below 184 ilvl (I define that as undergeared) is
0.19 ± 0.055 \ 19% ± 5.5% for alliance
0.21 ± 0.054 \ 21% ± 5.4% for horde
The proportion of players at or above 220 (I define that as very geared) is
0.13 ± 0.048 \ 13% ± 4.8% for alliance
0.07 ± 0.034 \ 7% ± 3.4% for horde
The mean ilvl was
198 ± 2.8 for alliance
197.3 ± 2.4 for horde
As you can see all of the confidence intervals overlap between the two factions so if the statistics are different between the two it’s probably a small difference. I didn’t take note of how many mercs i saw but i could find a proportion for that too if I had data.