Wednesday, August 27, 2014

Population of Canada by Longitude

A couple of months ago a friend of mine on Facebook shared a post with me that graphed the population of Canada by latitude. They also challenged me to come up with a similar graph of Canada's population, but by longitude.

And I promptly forgot. Until now!

Like the original post mentions, finding geographical data that matches up with population data from Statistics Canada is quite tough, largely because the postal code data is intellectual property of Canada Post, and they don't much like sharing. I managed to find the 2011 Census data sorted by Forward Sortation Area (the first three digits of your postal code), and the geographical data for all postal codes (which was an unreasonably large file), and combine the two to get a fairly precise view of the data. To make sure what I had was close enough to the original graph, I redid his work by latitude first:

Close enough. Around the north some things get wacky because postal codes are so large and we likely used different ways to approximate the centers of each FSA, but I'm still reasonably satisfied with the result.

It's a fun graph, and deservedly the original got a nice amount of HuffPo press. It's pretty weird to think that about half of Canada lives below the northern suburbs of Montreal, and only 31% of the country lives above the 49th parallel section of the border.

Sure, Canada's tall, but lets talk about how wide it is. It's really wide. It stretches from 52°37'W at Cape Spear to 141°0'W at Boundary Peak, which covers nearly a quarter of the longitudinal values on earth. Yay us.

If we do the same analysis as the previous graph, but for Longitude, we get the following (you can click on the image to zoom and enhance, spy-movie style!):

So really, nothing too surprising. The majority of people tend to live somewhere between Toronto and Qu├ębec City, and in both British Columbia and Alberta the major cities tend to fall more or less along the same line north-south.

I was planning on combining both maps into a generic heatmap for Canada, but then I stumbled on this, and it's way cooler than anything I'd have been able to do, so I'll just share it with you instead. Try not to get too mesmerized...

Friday, August 15, 2014

The Great Oven Mitt Review of 2014

So I've got some cool friends.

A little background: when I first moved into my apartment (one year ago today exactly!), I only remembered to buy oven mitts at the last minute. I grabbed the quickest and cheapest one I could, which was a single oven glove appropriately called the "Ove' Glove." The night I moved in, we made pizzas and the Ove' Glove was the source of much entertainment and complaints, as it appeared to be a very good conductor of heat instead of an insulator. Whoops.

To remedy this, a two weeks ago at my birthday party my friend Cassandra decided it would be a great gag gift idea for everyone to bring oven mitts for me. As a result, I am now in possession of 16 oven mitts, ranging in colours, sizes, and materials.

So on this, the anniversary of me moving in, I've decided to work with these oven mitts the way that I know best: test them and write a report.

My set-up was pretty basic - I made a system to hold the oven mitt a fixed distance away from a medium-heat element, stuck a meat thermometer inside, and took heat measurements for up to ten minutes. A check without oven mitts showed that this setup subjected the oven mitts to a temperature of approximately 70 degrees.

Test Setup (highly technical)
 So without further ado, I present to you my rankings for oven mitts from worst to best. Starting with:

#9 Blue Mitts of Death

  • Brand: Dollar Store
  • Value: $3
I suppose at this point it's worth pointing out exactly how I'm ranking them. First and foremost, I'm looking at how long it takes the mitts to actually burn you. According to this source, 55 degrees is hot enough to give second-degree burns after 17 seconds. Holding onto a 70 degree heat source, this means you'd burn your hand in less than 5 minutes using this oven mitt. Sure, that's not how normal people use these, but hey - you gotta compare them somehow. Since these have the highest potential for burning, I rate them the worst.

#8 Pink, Flowery, and Painful

  • Brand: Dollar Store
  • Value: $2.50
Though these are by far the prettiest, they're also quite deadly. If my hand had been in them for the experiment, I would have gotten a burn about 5:20 into the test. Not nice. It's also worth pointing out that throughout all tests, these oven mitts got the closest to 70 degrees (67.6 after 10 minutes). Yikes!

#7 Black Cuisinart

  • Brand: Cuisinart
  • Value: $15.95
Hilariously, I got these as a Christmas present from my parents before any of these birthday shenanigans went down. Sadly, they're also apparently the type of oven mitt that likes to burn your hand off. Their redeeming factor is that they only increased in temperature 1.2 degrees within the first 30 seconds of the test, which is more than enough time for most oven extractions. Would likely have burned my hand about 5:40 into the test.

#6 Green Silicone

  • Brand: Ming Wo (?)
  • Value: $9.99
Man, these silicone ones look so fancy, but really like burning your hands to crisps. This is very similar to #7, in that it has one of the lowest heat gradients at first, but by 7 minutes into the test would have made you very unhappy. I'm sure there's some materials science point to be made here, but that would involve actual science.

#5 Languages of Pain

  • Brand: Dollar Store
  • Value: $2.50
Awesomely enough, I got two pair of these for my birthday. These were pretty decent for a language lesson, but woulda burned your hands at about 7:20 into the test. An excellent example of Dollar Store quality oven mitts holding their own against their expensive counterparts though...

Here are pretty graphs of the worst five oven mitts:

Again, the pink and blue oven mitts both had high initial rates of heat pickup, and ended up with the highest heats (the ranking order is a bit different from the graph because I tested the pink one on a colder day. I know, terribly unscientific of me...). The silicone mitts did much better for the first two minutes, but then took on heat at a similar rate to everyone else. Tsk tsk. 

The rest of the mitts happily didn't ever hit 55 degrees within their tests, so I'll rank them based on their total heat gain over the 10 minutes:

#4 The Ove' Glove

  • Brand: No clue
  • Value: $18.99
In a stunning come-from-behind near-podium finish, the Ove' Glove turns out to be a contender! And if you don't believe me, check out this totally awesome super cool consumer video (sarcasm). The Ove' Glove gained heat at an average rate of 2.95 degrees per minute - not shabby!

#3 The Alien

  • Brand: Dollar Store
  • Value: $2
Put this sucker on your hand and you've got great alien chestburster puppet! Alternatively, use it to take hot things out of an oven and not burn yourself. By far the best bang for the buck, somehow it combines the silicone and fabric and makes a decent oven mitt, gaining an average 2.82 degrees per minute.

#2 Better Barbeque

  • Brand: CTG Brands
  • Value: Weight in gold?
Wowza. This one is hefty, basically goes up to my elbow, and can hold its heat, only gaining an average of 2.66 degrees per minute. Very nice. These also won the contest for lowest heat pick-up in the first minute, and didn't even register a temperature change until 30 seconds into the test. 

#1 President's Choice

  • Brand: PC
  • Value: 7 unicorn hairs?
These guys were the bomb, only gaining 2.61 degrees per minute. They're also flexible enough to use regularly, unlike the silicone ones. 
Graph of the top 4 oven mitts:

Again, some very smooth curves here. The CTG oven mitt was by far the steadiest heat increase, but lost out to the PC mitt over the full length of the test. I know that my ranking has been more-or-less arbitrary this whole time, but I'm comfortable with declaring the CTG mitt to be my favorite (because really, who uses a mitt for 10 minutes at a time?).

Thanks again to everyone for pitching in on the oven mitt present. I hope I've used them in an appropriate manner! 

Wednesday, August 13, 2014

Mud Heroes Aren't Normal

Last weekend I went ahead and did something I never thought I'd do: the Mud Hero race down in Red Deer.

Mud Hero, for those of you who are blissfully unaware, is a crazy obstacle course/race/endurance sport/mud bath and spa/general day of chaos that follows in the ever-growing trend of mud runs for the athletically-inclined. There are dozens of similar events to this around Canada each summer, and the Mud Hero appears to be one of the most popular with over twelve thousand participants over the three days of heroing in Red Deer last weekend.

The event attracted people from all backgrounds and fitness levels, and has likely inspired wonderful stories of perseverance, raising money for charity, and teamwork through adversity. To all this, I say nonsense. The most interesting part of the Mud Hero is the statistics, and, much as though readers of this have likely figured out already, the inescapable conclusion that Mud Heroes just aren't normal.

In an attempt to ostensibly appear as much like a legitimate race as possible, all participants were given timing chips to track their racing - and all results are posted online for people to show to their friends and family and brag about just how slowly they trudged through the muck. Since this involves thousands of numbers, it's pretty easy to salivate over the possible statistics of said numbers. So I did. Here's a graph of everyone who ran on the last day of the Alberta Mud Hero:

Right off the bat that may look quite like a normally-distributed bell curve - there's certainly a lovely peak right around the middle, and it tends to taper off at either end. The reported average time for the course was 1:25:22 (85 minutes), and that seems to be reasonably around the middle of the peak.

It isn't just enough to assume that that's a normal distribution though - a normal distribution is a rather precisely defined curve that doesn't necessarily include all bell-like shapes. The results from Sunday's Mud Hero had a mean of 85.37 minutes and a standard deviation of 29.90 minutes - as these are the two parameters you need to develop a normal distribution curve, we can compare Sunday's results to the normal assumption and get the following:

That's not really all that close at all. These are two bell curves that have the same mean and standard deviation, but are not identical, leading to the fun conclusion that Mud Hero runners are not normal (well, normally-distributed at least). Mud Heroes tend to be positively skewed (the mean is higher than the median), and have shorter and bounded tails.

This isn't really all that surprising - in fact a normal distribution would have been surprising as there are necessarily cut-offs to the data (nobody can do the race faster than 0 minutes, for instance), and it was a relatively short race. Often people tend to view all bell-shaped curves as normally-distributed, even though there are an incredible amount and diversity of probability distributions out there.

So Mud Heroes aren't normal. What else can we learn from the data? Fortunately the results are broken down into genders, ages, and hometowns, so let's look at those!

First of all, gender:

Fascinatingly enough (for an event whose purpose is explicitly to get dirty), women outnumbered men 2 to 1! That's pretty awesome. A quick Analysis of Variance test shows that the men were statistically significantly faster than the women were this time around though, which I suppose is the trend in races like this. Shame...

Bam. Age graph. I'm not entirely sure why the men aren't as consistent as they age, but then again, who is? (marriage joke)

And finally, home city:

Turns out there's no reasonable statistical difference between participants from Red Deer, Calgary, and Edmonton. These box plots for their results suggest they have almost identical distributions for time, and an ANOVA test suggests that they can all be considered to be drawn from the same population. So really, even though the average time for Calgarian Heroes was two minutes faster than Edmontonian heroes, it's not significant enough for them to brag. So ha!

All in all though, Mud Hero was definitely a fun experience. If you're looking for a good excuse to get tired and muddy, I'd highly recommend it for next year!