Wednesday, December 17, 2014

My Issues with the Broadbent Institute's Inequality Report


Apparently I have it in for think tanks or something. Every few months a think tank somewhere comes out with a report that means well, portrays a message with fundamentals I agree with, but manages to mess up some amount of the data handling in a way that gets me riled up.

This time it's the Broadbent Institute. They released a report on income inequality recently, and presented the data in a virtually identical format to an American video from two years ago. While I agree that income inequality is a big issue in Canada, and I'm sure that the average Canadian isn't clear with just how bad it is, I have a pretty big issue with the statistical rigor in their report.

This is a screenshot from their video:

Along the x-axis, they have different population percentiles in 10% chunks. The chunk on the far right represents the richest 10% of the population, the one to its left is the next 10% richest people, etc.

The problem with this chart is that it shows the 50-60th percentiles as being richer than the 60-70th and 70-80th. They're trying to tell us that the 5th richest group is richer than the fourth and third richest groups. 

What!? That doesn't make any sense by definition.

These values appear to come from this table in their report:

Somehow, Canadians apparently consistently think that the middle 20% of the population is supposed to have more money than the 2nd wealthiest 20%. That's not possible, and I can't believe that it got all the way into the report and the video without anyone hitting the emergency stop button. The income curve shown in the first figure ought to be a version of a Lorenz curve, and necessarily should increase from left to right. Even if that is the actual result from the survey, it shows that either the survey wasn't clear enough in its instructions, or that adequate controls weren't in place in the survey to ensure accurate results. 

When I brought this up to them on twitter, their response was:

Which is... silly. There's a logical distinction between a "strong middle class" and a "middle class that's stronger than the upper middle class." They've clearly decided to ignore this distinction.

Finally, a (more than average) nitpicky point. Take one more look at this graph (where the blue line was the original "ideal" values);

The blue line of ideal values has five data points in it, which is great, but they're nowhere near where they should be! Each point (or kink in the blue line) corresponds with a 20% chunk of data, so they might have shown the mid-point 10%, 30%, 50%, 70%, and 90% marks. But instead they've shown the 0%, 25%, 50%, 75%, and 100% marks. This implies that the 0th percentile Canadian (the absolute poorest person in Canada) ought to have the wealth value that the people surveyed thought belonged to the bottom 20% as a whole.

Anyway, the point of all this is that research into wealth inequality is really important, and doesn't deserve to be handled quite this badly. If you're going to be sharing this report, please do so with a grain of salt.

Monday, December 15, 2014

Winter Tires in Canada

Well there's snow on the ground and the temperature's pretty low, so we can pretty solidly declare that winter is upon us. And with wintry blizzards comes one of the great Canadian traditions: changing over your summer tires for winter tires.

If you're anything like me, you probably waited until just after the first major snowfall to remember to put them on. This often ends up with you driving around dangerously for a week waiting for your appointment, all the while dodging other summer-tire skidders. It's a fairly dangerous and unpredictable way to go about driving.

Recently I tried looking up recommendations for when to put on your tires and came to an interesting discovery: almost every single source recommends to put them on once the temperatures dip below 7 degrees Celsius. Everyone from the tire producers to the Tire and Rubber Association of Canada agrees with this fairly precise temperature recommendation.

Why? Turns out that summer tires are made of a different rubber that gets quite stiff below 7 degrees, and reduces the friction of the tires (the comparison that was used was that they approach the consistency of a hockey puck). Winter tires become more effective below 7C, even on dry clean pavement.

Not to scale. Probably.
If you're looking to drive as safely as possible (which you should, seeing as road injuries are the 9th leading cause of death worldwide), it might not be quite enough to just wait until the forecast predicts a temperature below 7, seeing as it often takes time to book an appointment and by that point it could be a bit late. Fortunately, Environment Canada has the daily temperature for various cities over the past several decades all neatly stored online.

So I decided to take a look. These are the average mean daily temperatures for Edmonton per day for the 30-year span between 1981-2010:

Since each day of the year has a decent variation to them, it's also possible to determine the expected probability that any given day will be below 7 degrees Celsius (using their averages and standard deviations). That might get you something like this:

Once you have this, it's fairly straightforward to choose when to put on your winter tires. If you were willing to accept a 50% risk of being ill-equipped for the weather, you'd be looking to put them on sometime around the beginning of October, and take them off around the beginning of May. That's vastly longer than I typically have mine on for, and I suspect that's the same for many people. In total, an Edmontonian ought to have their winter tires on by October 1st, and leave them on for 210 days (at least seven months of the year!).

Of course, a 50% risk of having the wrong tires might seem a bit high for some people. If you were only willing to accept a 10% risk, you'd be looking at 261 days of winter tires starting September 4.

So that's all well and good for Edmonton, but how about the rest of the country? I decided to look at 30 stations' worth of data spanning 1981-2010 (~330,000 data points) to try to develop a map for winter tires in Canada. These stations included all major cities and a few select points to accurately represent the geographical differences. This is what I got:

Unsurprisingly, the northern territories tended to need winter tires more than the southern provinces (quite frankly, it's not worth taking winter tires off if you live in Iqaluit). What might be surprising to some is that even the warmest parts of the country, that hardly ever see snow, ought to have proper winter tires on for at least a third of the year.

Another way to represent the data is to show the probability of being below 7C on any given day like this:

Where green means 0% chance of being below 7C, and red means 100%.

The vast majority of Canadian cities have a high risk of being below 7C sometime in October, and it's important to know when exactly that will be in order to be sure you're driving with the best equipment available. In fact, the above graph can be summarized as follows:

One final thing to note: only the province of Quebec has legal requirements for winter tires, with the exception of some British Columbia highways. These legal requirements fall way outside of the 7 degree recommendation though. It's all well and good to have laws for additional safety when operating motor vehicles, but if they fail to capture the designed temperature ranges of the actual tires, it seems like a bit of a missed opportunity.

Monday, December 8, 2014

2014-2015 ski season

In case you haven't noticed, it's snowed a bit recently in town. And any time it snows in Alberta, I get excited that it's likely been snowing up in the mountains. And that means skiing!

As of December 7, the website OnTheSnow shows that Marmot Basin (the closest ski hill to Edmonton) has a snow depth of 90 cm. That sounds rather decent, and certainly right at the end of November it got a massive dump - but how does that actually compare to normal? I decided to figure out.

Here is the cumulative snowfall of Marmot basin for every ski season since 2007-08:

Alright, so there's quite a bit of variation in there. Maybe a better way of looking at it is like this:

For these graphs, the grey zone represents the maximum and minimum values over the last seven seasons, the light grey line is the average, and the black line is this season so far.

So there's good news and bad news here. The good news is that there's actually quite a bit more snow this year so far than normal! In fact, there's about as much snow at Marmot right now as there typically is by about January first. All in all, maybe not a bad time to go there, in fact!

The bad news is that, apart from two huge dumps, there really hasn't been any action in Marmot. It was way below any of the previous seasons measured until two weeks ago. Marmot looks like it's in a good position now, but if it hadn't gotten luck at the end of November it would pretty much just be rocks. In fact, we can tell it *has* been lucky - Marmot Basin typically only gets two to three snowfalls exceeding 20 cm per day per season (actually 2.43 average), and has already had two this year. Lucky for it now, but it's hard to predict for the future of the season.

Marmot Basin is also relatively easy to predict - on average by the end of the season, its total snowfall has a coefficient of variation of 37.1%. It also has a reasonably early season, with 100 cm of snow fallen on average by December 31.

But how about other Alberta ski hills? Take Sunshine Village, for instance:

Sunshine has a similar situation to Marmot Basin. It's been lagging behind previous years until the end of November (though still within normal ranges), and is now pretty much back on track. Hard to say how that will hold up though. They don't typically reach 100 cm of snowfall until a bit earlier than Marmot (average December 18), and tend to be more predictable (coefficient of variation of 23.8%). They also get far more snow in total than Marmot Basin does...

Lake Louise enjoys a base of 100 cm on average by December 16, but is raucously tricky to predict (coefficient of variation at end of season of 44.3%). Lake Louise has had the same problem as Marmot Basin - it had far less snow than previous years up until a sudden burst rather recently, but it's been flat since. Hopefully that isn't terrible news for the season...

Nakiska's almost doing the best for this time of year out of any of the last 7 years! Good for it. They tend to have more variation at this time of year than other Alberta hills too, so it's actually a bit tougher to say if they'll have a good season or not. They tend not to get a 100 cm base until around January 23rd, and have very unpredictable seasons, with a coefficient of variation of total snowfall of 48.2%.

Norquay's a bit sad. They're well within previous years' ranges, but it's still not looking nice. They'll get their first 100 cm on average by February 10 (yikes), and have a variation in total snowfall around 37.6%. Some years they don't even get 100 cm of snow, though.

Castle Mountain's another sort of sad mountain with a later season (100 cm average by January 11th) and high variability between seasons (43.2%). Both Castle and Norquay seem to have missed the awesome snow dump that the rest of Alberta had, but are tending to stick a bit better into where they'd be expected at this point in the season.

So overall for mountains in Alberta, it's looking like now is a great time to go to Marmot, Sunshine, Lake Louise, or Nakiska. They're certainly at least all doing much better than average for this time of year, and will likely continue to be above average for the rest of December.


Earliest decent season: Lake Louise (December 16)
Highest average snowfall: Sunshine Village (486 cm by May)
Most predictable: Sunshine Village (23.8% variation by season)

The sad thing is... BC mountains do way better on almost all counts. Take for example Fernie:

(100 cm by Dec 22, average snowfall 705 cm, COV 25.8%)

Or Whistler:

(100 cm by November 24, average snowfall 796 cm, COV 27.7%).

Both mountains consistently and reliably get far more snow than anything in Alberta. While that may make them sound great on paper, they still haven't had the trend-bucking dump that Alberta mountains have had, and are currently lagging quite far behind their Alberta peers. So while I can't guarantee that they'd have particularly good December skiing this year, you certainly ought to be able to rely on them for quality skiing in the mid- to late-season!