Innumeracy is like illiteracy, except with numbers. Many people are simply not good at understanding the scale of numbers that come up commonly in macroeconomics. And that probably effects policy choices …
Laura Sen / BJ's Wholesale club / discount retailing
Gail Kelly / Westpac / banking
Chua Sock Koong / Singapore Telecom / telecom
Patricia Woertz / Archer Daniels Midland / food
Ursula Burns / Xerox / electronic equipment
Nancy McKinstry / Wolters Kluwer / publishing
Angela Braly / Wellpoint / health care services
Maria Ramos / Absa Group / banking
Ellen Kullman / Dupont / chemicals
Irene Rosenfeld / Kraft Foods / food processing
Indra Nooyi / PepsiCo / soft drinks
Susan Ivey / Reynolds American / tobacco
Annika Falkengren / SEB / banking
Janet Robinson / New York Times Co. / publishing
Cynthia Carroll / Anglo American / metals & mining
Ana Patricia Botin / Banco Espanol de Credito / banking
Carol Bartz / Yahoo! / Internet services
So what could possibly be wrong? The data support the position that women CEO’s deliver better investment performance to investors. Don’t they?
The problem is the use of an average. The number 115 in the last row, indicating that female CEO’s beat their industry’s average return by 15% is fine.
But, it isn’t the number one should use to answer this question.
The reason is that the way the data is measured is bounded going down, and unbounded going up: no female CEO can do worse than –100, but conceivably they could do as well as positive infinity.
When you average numbers like that, you get a value that is not in what most people would consider the center of the data. This is why you probably don’t live in the average house: Bill Gates’ house skews the average.
What’s worse, is that the table actually contains the appropriate data to analyze, and then doesn’t use it. You don’t get much better evidence of political correctness than that.
With data like this, you should look at the median. This is easy to spot from the dark gray column: there are 26 female CEO’s, so the median is between the 13th and 14th values: 102.
Well … you can still say that female CEO’s outperform their industries.
But good practice suggests that you have to give some sort of interval estimate to make that claim. It’s standard with data like this to use the interquartile range which runs from 87 to 117. Since that range includes 100, it would be conventional to conclude that there is no evidence that female CEO’s outperform male ones.
This isn’t what Forbes says. Instead we have:
… There's a ringingly clear answer: Women deliver the goods on a far more consistent basis.
It gets worse:
These results were not skewed by a couple of supercharged gains, as 16 of the women bosses outgained their respective markets.
Ooh ooh – 16 out of 26 beat their industry. That’s like saying your baseball team is good because they won 16 of their first 26 games. It’s pretty simple to plug that into a first semester statistics text (they do make reporters take stats, don’t they) to find that you’d really need to find more like 19 of them beating their industry average to draw that conclusion.
The pity in all this is that I’ve had enough female bosses, and worked with enough brilliant female business students, that I’m pretty sure this assertion may be true.
I’m sure no economists were harmed in the construction of this article. How can I be sure?
The article puts together information on 4 different costs of the trip — time, money, pollution, and risk — so that they can be compared across the 2 trips, without putting them in the same units so that one could compare the total costs of the two trips.
The value of time is subjective, but the metric ought to be opportunity cost: how much would we have to pay you to be in a car for the trip when you’d rather be doing something else. I think this would range from $10-50 per hour for most people, and I think we’d get a bunch for $20/hour. It just isn’t that odious to sit in a car.
The value of the greenhouse gas emissions is even more subjective, since even our most objective sources can’t agree on ballpark numbers. One plausible assumption is how much the government might pay you not to incur those emissions. Here, the optimal carbon tax of Nordhaus comes in handy: $30/ton. A ton of carbon is what is carried around in 7330 pounds of carbon dioxide. That’s less than a dollar for either driving or flying. One wonders what would motivate the authors to even worry about that?*
The value of avoiding a fatal accident probably has the firmest numbers. Forensic economists can ballpark the value of a human life fairly well based on the risky choices we can’t be bothered to avoid. The typical result is in the mid 7 figures. Here, it makes sense to call it an even $8 million. Then we can say the cost of the risk of driving is about $27, while that of flying is $1.
Here’s the revamped table:
Greenhouse gas emissions
Chance of a fatal accident
Clearly, these are guesstimates, but we can probably safely conclude that the trip is 50% more expensive by car.
* Note that the much more pessimistic Stern Report used a value about $10 times as high, which again won’t matter much to the overall decision.
The Baltimore example is that over the period of the recent blizzards – when most potential victims were stationary, and not accessible to the police, the crime rate dropped.
For example, murders – of which there were 18 in the first 37 days of the year – dropped to 0 in 9 days.
Statistically, that’s close to impossible – akin to flipping 9 heads in a row (try it: you’ll get bored before you do it). That is, unless there is some interfering factor.
In this case, it was that potential murderers were not intersecting with potential victims over those 9 days.
This sort of natural experiment should make it fairly clear that crime is about interactions between criminals and other people, rather than root causes that might leave those criminals with … low self-esteem.
It also should make it clear that policing isn’t that much of crime preventive. I hate to point it out, and the police did too. They’d probably be the first to point out that they couldn’t patrol during the blizzards like they do on most days. Perhaps policing is better viewed as reactionary.
How hot? Try 26,000 degrees Fahrenheit (14,425 Celsius). That is hot enough to melt lead or iron.
Why, yes indeed, that is hot enough to melt lead. So’s a gas cooktop, dumb*ss.
Of course, 26,000° F, is hot enough to melt everything. In fact, since melting is a phase transition from liquid to gas, that temperature is hot enough to push just about any material through the next phase transition from gas to plasma.
The problem is that the typical person looking at this will focus on the size of the triangles – so their area should be important to the idea being conveyed. But it isn’t. So, the graph has a huge “lie factor”.
The areas of the blue triangles are arguably the largest in 3 out the four panels (and a close second in size in the third panel).
Let’s think about what this means for the panel on GDP. Severity, on the vertical axis, is the important variable. The current recession is the mildest of the three shown on this count. Duration, on the horizontal axis, is a far les important measure of the economy’s problems. Here, the current recession fairs much worse.
To put this in words: the current recession took a lot longer to get almost as bad (but not quite) as the other two.
I submit that the reporter wouldn’t have had much of a story if they’d written that sentence out and thought about what it meant.
But, put it in a graph, combine a primary variable with a secondary variable, and add shading, we get a triangle that rather blurts out that the current recession is the worst overall.
But that isn’t what’s being shown at all. Let me offer analogy.
This chart is sort of like measuring the braking of a speeding car. The reduction in speed is the severity variable: the faster you’re going the worse it is to have to slam on the brakes. The horizontal axis will still measure duration, but now of the braking: braking for a long time isn’t a good thing, but it isn’t quite as critical as how you fast you were going. What the graph is saying is that it is worse to be driving slower, and to take a longer time reducing your speed. Tell that to your passengers the next time you have to lock ‘em up.
The core problem with this graphic is the impulse to connect the dots and shade the interior. They hypotenuse of each of these triangles actually contains important information: how far we’ve fallen, and how steep is the slope we’re sliding down. But, if we’re only talking about that line segment, there’s no need to form a triangle (or even a basis to call that line segment the hypotenuse – you only think of it as a hypotenuse because the triangles are being spoon fed to your brain). So, problem 1 is connecting the right endpoint of that line segment back up to the horizontal axis. Think about it: you’d only do that in a math class if they told you the question was about a triangle – you wouldn’t do it for the heck of it. But, having done that, the author goes one better and shades the triangle they just pulled out of thin air. The scary thing is, they don’t even have a triangle yet because there really isn’t a good basis for using the horizontal axis to connect the points other than that it just happens to already be there!
Lastly, let’s talk a little bit about the psychology of recessions. Turn the clock back to say 2005 and imagine you knew a recession was coming with certainty, but could steer the economy to one of two kinds of recessions. The two kinds have equal severity, but one takes less time to develop, while the other one takes longer. Which would you choose? My guess is that it would be about an 80/20 split in favor of the more slowly developing recession.
Don’t believe me? Then ask yourself how people felt last September when this recession switched from a very slowly worsening one to a quickly worsening one. Do you remember anyone being relieved? I didn’t think so.
In sum, recessions are no fun, and this one is a doozy. But to improperly emphasize that with weak thinking qualifies as pessimism porn.
Caveat 1: this is a pretty bad recession, and these charts only show some of the worst recessions, so if we showed all of them the current one would not compare well.
Caveat 2: duration of recession is a problem, but it is secondary when compared to the reported severity, so combining them to show duration-severity actually diminishes the point the author is trying to make.
Caveat 3: because this recession started out mildly and then shifted into overdrive, the triangles aren’t an accurate depiction anyway. Instead, something like a scooped-out triangle or even a crescent would make for a more realistic (and smaller) blue shaded area.
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