Earlier this year @thelabandfield offered to take a look at the Long John Index stats from 2011 to 2013, and look for patterns! While they were pattern searching we asked, 'Who is Colder? Calgary, Edmonton, Regina, Saskatoon or Winnipeg?'
Here is the answer:
"I used the same method as when I compared Saskatoon and Regina (comparing the medians, detecting a difference when p < 0.05), but ramped up to compare more than 2 groups. This is called a Kruskal-Wallis test. To look at differences between individual cities, we have to look at the graph. So, do western cities have different long john indices? Yes! (p< 0.001). From the graph, we can see that Calgary < Edmonton = Regina < Saskatoon < Winnipeg (i.e., Calgary is the warmest, Winnipeg the coldest, and Regina and Edmonton are the same). Make sense?
Now, if we head east…
First, if we look at the plot (east.jpg), there doesn't seem to be much difference. And indeed, the Kruskal-Wallis test gives us p = 0.107 - that is, this pattern could be due to chance 10% of the time. Since we decided that 5% was out cut-off, we must conclude that there are no differences among eastern cities.
And here's a special BONUS STATISTICAL ANALYSIS!
What about the NORTH? I'm glad you asked.
The Kruskal-Wallis test comparing Iqaluit, Yellowknife, Whitehorse, Innuvik, and Alert shows a significant difference (p < 0.001). To the box plot! Not surprisingly, Alert is the coldest, followed by Inuvik. Iqaluit and Yellowknife appear to be on par, and Whitehorse is the warmest of the North."