Commentator Nation

One of the least significant, but most widely read news stories of last week was the family that got thrown off an airplane because their three year old daughter threw a temper tantrum. See, for example, http://www.msnbc.msn.com/id/16780734/.

I thought it was interesting surfing the web to read people’s reactions. Google tantrum +airplane, or tantrum+airline+brat for slanted results. The responses were overwhelmingly (and often vehemently) supportive of the airline. And maybe they’re right, and the airline acted appropriately – could well be – but , um, . . . is there really enough detail in the story to know how it really went down? To all the people who patted the airline on the back for not taking guff from the lousy parents who couldn’t control their obviously spoiled brat – any chance you might be jumping to conclusions here?

Actually, my favorite commenters are the ones who realize that the facts themselves don’t offer much to get indignant about, so they try to deconstruct clues in the narrative to build their case. Um … why? It’s that important to you to build a case on sketchy evidence that some strangers are bad parents? Why?

Look – I’ve had plenty of bad airplane experiences with other peoples’ kids. Kids crying, screaming, kids behind me kicking the seat for the whole flight, kids throwing food. Makes you want to slap the parents and ask what the heck their problem is. And maybe the parents in this case are completely to blame. Good chance they are. But how can anyone be sure given the meager facts?

What’s even funnier is that from what we can read, it’s the parents’ word versus the airline’s, and most people are blindly taking the airline’s side. Umm, how many among us have been screwed by an airline? Who hasn’t been lied to, or treated discourteously by an airline employee? But never mind, we’ll take their word for it since it touches one of our hot buttons.

Does Speed Kill?

I was around for the debates in the mid-80’s and late 90’s about raising the speed limit, from 55 to 65, and from 65 to 70 and up, respectively. The tradeoff seemed fairly simple to me: you get to drive faster, at greater risk, to yourself and the rest of the drivers out there. Which did we as a community prefer?

Of course, the debate didn’t turn out quite that way. There are a lot of people who argue that speed and safety are not correlated; occasionally citing statistics that as average speeds have increased, fatalities have dropped. Well, I haven’t really dug into the studies, and seen whether they correct for things like safer cars, safer highways, and a faster-moving-thinking population, but call me skeptical. My uninformed opinion is these people are playing psychological tricks on themselves. They want to drive fast, so they talk themselves into believing that they are being safer. It seems pretty clear to me that the faster you go, the less reaction time you have, and the greater the force of impact when you smash into something. Call me crazy, but that can’t be good for either the accident or the fatality rate.

I have, however, heard one argument for higher speed limits that was at least half-respectable. On long stretches of rural highways, faster speeds mean you can save hours on long trips, and that reduces the likelihood of fatigue, which significantly contributes to accidents. I’m not totally sure what to make of this argument – certainly fatigue is bad; it’s just not clear exactly what the right tradeoff is. But it’s certainly a reasonable thing to say.

Which led me to perform a thought experiment. Suppose the speed limit was set to be something ultra-conservative; say 30 mph. And for the sake of argument, suppose that compliance was pretty good, so people really did drive that speed. What would happen? My guess is that people would get so bored that they would start multi-tasking like crazy to the point where they barely kept any focus on the road. I mean, it’s already no big deal to see people hauling down the road at 70 mph while yakking on the cell phone, shaving, putting on makeup, eating, listening to music, talking to passengers or kids in the back seat, or some combination of the above. All that when a five second lapse in concentration can kill you (and does kill plenty of people each year). Heck, I’ve even seen people driving on Wadsworth while reading a newspaper. God only knows what people would be doing if you slowed them down to only doing 30? Watching movies? Playing World of Warcraft?

So what I’m saying is that I do actually see the point of Peltzman-like theories (see the previous post) that people can have a sort of internal “risk thermostat”, whereby they have some level of risk that they are comfortable with, and if you constrain them to be safe in one dimension then they will compensate in some way by taking risks in other areas.

All that being said, I still find it hard to believe that drivers have become less safe as seatbelt adoption has gone up. Most people I know don’t want to be in a major crash, period, whether they think they’ll live through it or not. I don’t see the fact that their chances of surviving a major crash have gone up means that they are all of a sudden more tolerant of smashing into things.

Interesting topic though. I should check into the insurance angle. After all, the same theory would predict that people who are insured should be riskier drivers, and that uninsured drivers are safer. Although that’s counterbalanced by the fact that many uninsured drivers are that way because they suck and can’t get insurance.

Econ 101 Notes I – The Peltzman Effect

I’m about six chapters into my Econ 101 book (Mankiw: Essentials of Economics). I’m really enjoying it; lots of interesting stuff.

In the first chapter, as an example of tradeoffs, Mankiw refers to a study by one Sam Peltzman in 1975 which claimed to show that mandatory seat-belt laws had no effect on the overall death rate since people responded to the safer environment with riskier driving.

I haven’t read the study, but I can’t help but thinking that it’s crap. I mean, I never knew anyone who decided they could drive more recklessly because they put on a seatbelt. Skimming the web for opinions reveals a variety of opinions; Leavitt (the Freakonomics guy) disagrees with Peltzman’s thesis here: http://www.freakonomics.com/blog/2006/12/09/the-difference-between-theoretically-possible-and-important. The general counterarguments I’ve seen are:

• The data is bad, and doesn’t account for demographic changes.
• Other data shows the opposite.
• Anecdotal/intuitive evidence, as in my initial take
• If you only wear a seatbelt because the law requires you to, then you probably see no safety benefit to it, so why would you all of a sudden start driving more dangerously? Conversely, if you thought that wearing a seatbelt made you safer, then you would wear one whether there was a law or not, so the law would not change your behavior.

Ok, so the anti-seatbelt argument is crap. But the scuffle does raise my worst fears about economics, which is that it’s basically politics with a veneer of statistics. You have your own feelings about seatbelts and/or regulations, and then you try to present the data to prove that you’re right. Great.

But this brings me to another traffic-safety debate that I think about periodically. Next up: does speed kill?

Record Mathematics, Part II

In my last post, I explained why record temperatures are no big deal. In short, this is because the recorded history is so small (~100 years), and there are so many categories (two or four for each day of the year). Of course, analyzing weather trends is big now, in the context of global warming, and obviously a warming trend would be reflected in more record highs and fewer record lows than you would expect if the trend was flat. My main point was that the expected number of records being set for even a flat trend is a lot higher than most people would have guessed.

I’m hardly an expert, I can see why proving that global warming is real can be so slippery: not enough recorded history and too much natural variation. I personally believe that global warming is something we should be more concerned about than we currently are, but that comes not from having looked at data to draw my own conclusions, or from personally experiencing the climate, but more from trusting the mass of scientists who do look at the data.

And not to beat up on the global warming crowd, but as long as I’m on the subject, check out this quote:

Six of the ten warmest U.S. winters on record have occurred in the past 15 years

from http://www.wunderground.com/blog/JeffMasters/comment.html?entrynum=609&tstamp=200701 (which has some interesting charts, by the way).

Sounds significant. Maybe it is , but note the appearance of the somewhat unusual number ‘15’. That always throws a red flag in my mind – what sort of mining has been done to produce the most dramatic statistic. I mean, if you didn’t know the end result, you would probably pick rounder numbers, like 10, 20, or even 25. Why 15?

The worst place to see records found from mining is in sports. I’ve noticed more and more in the last few years sportscasters talking about records like “that team is the first in the last 31 years to average 300 passing yards a game over a five game span while holding the opponent to under 85 rushing yards.” Not only is that a mouthful, but the large number of variables makes for a massive number of record categories. It’s completely unexceptional that some of them get broken each year. I tune those records out.

The Mathematics of Record Temperatures

Every now and then, the weather person on TV will announce that we saw a record high or low for the day. When I was a kid, that used to freak me out – scoring a temperature that was a record for the past century had to mean that an ice age or eternal summer was dawning.

Well, I grew out of that, and found more pressing things to worry about. But I find it interesting to ask the question of how often we can expect record temperatures to be set. The short answer is: a lot more frequently than you might expect. The math turns out to be quite simple, and that’s what I want to talk about here.

In Denver, records have been kept since 1872, or 135 years up to 2006. You can see the records here: http://www.crh.noaa.gov/den/cli/climo.php.

For the sake of argument, let’s assume that there have been no climate trends, that a year was just as likely to be warm or cold in the 1880’s as it does now. (Now that actually isn’t the case, but the trend has been small enough to not be very significant for our purposes.) So the record high, say, for a given day is equally likely to have occurred in any of the past 135 years. In 2007, we will have added one more year to the mix. So the probability that a given day in 2007 will set a record high will be 1/136. Now that’s a small number . . . but wait – there are 365 days in 2007. So the average number of record highs that we’ll see will be 365/136, or about 2.7.

Think about that for a moment. On average, there will be over two-and-a-half days of record high temperatures. And the same calculations work for record lows; adding them up shows that we’ll see on average over five record-setting days in the next year.

Let me hasten to say that those are just averages. For any individual year, the number of record-setting days can vary widely, especially because there is correlation involved.

The NOAA data that I linked to above also states the record minimum high and record maximum low. For example, the records for September 1 are:

• The record high was 97, in 1995


• The lowest high temperature recorded on that day was 65, in 1954


• The record low was 44, in 1962


• The highest low temperature recorded on that day was 57, in 1972

So there are two more categories of temperatures where records can be set. So now the average year will have 1 /136 * 365 * (4 categories) = 10.8 records set.

I went ahead and broke down the NOAA numbers on that site, to make a histogram of how many current records belong to each year. That's not quite the statistic that I wanted, which was the number of records set each year as they happened, but it's interesting enough. It turns out that every year since 1872 has at least two records currently standing. In 2006 there were 23 record-setting days; the “busiest” year was 1989, which has 27 records still standing. Half of the years hold between seven and twelve records.

One more question to ask: In my lifetime, how many record-setting days do I expect to experience? I was born in 1966, at which time there were roughly 95 years of recorded data. So for my first year of life, I would have expected to see 1/95 * 365 * 4 records. For the next year, it would be 1/96 * 365 * 4, and so on. If I live to eighty, the total would be 365 * 4 * (1/95 + 1/96 + … + 1/174). There’s no convenient formula for that sum (it’s roughly equal to log(174) – log(94)), but adding it up with a computer, it works out to 365 * 4 * .61 or about 895 days. Note that this number includes records that were set and later broken during my lifetime, so some days can be double-counted or more. Whatever; it’s a lot of records. And that’s not even counting additional categories like precipitation.

So, somewhat surprisingly, a record temperature is no big deal, and will continue to not be a big deal for many years to come. We just haven’t had enough recorded history of temperatures to make records rare.