It shouldn’t take a rocket scientist to recognize from the PCT that the Rays are a better team than the Orioles. And GB should show that. It doesn’t. Instead, it shows them as even.
There are a couple of ways to calculate GB, but the way I learned back in the early 70’s is to 1) subtract the bottom team’s wins from the top team’s wins, 2) subtract the top team’s losses from the bottom team’s losses, 3) add up those two figures and divide by 2. In this case you’d get 2 as the GB of the Orioles. This is not what USAToday shows.
The point of GB is to measure the minimum number of games for the bottom team to “catch” the top team. In this case, if the teams play 2 games each, and the Rays lose both, and the Orioles win both, they’ll each have the same record of 68-56.
* I really don’t pay much attention to this, but I noticed it on Monday in the local paper’s reprint, and it’s still there on Tuesday in the USAToday website.
Mix # 1 for waffles required 3/2 cups of mix, 3/4 cup of water, 3 tablespoons of water, and 1 egg.
But, I have only 3/4 cups of the mix, so the egg is going to be a problem.
Mix # 2 from a second box required 2 cups of mix, 3/4 cup of water, and 1/3 cup of oil, but no eggs.
I don’t want to try and come up with half an egg, and it’s clear from the first recipe that it’s substituting an egg for some oil. But how much?
A quick trip to the internet shows that 1/4 cup of oil can be substituted for 1 egg.
So, I measure out a half batch of Mix # 1: 3/4 cup of mix, 3/8 cup of water, 3/2 tablespoons of oil, and 1 egg.
Knowing there’s 1/2 egg extra in there, I substitute the extra 1/2 egg for 1/8 cup of oil in the second recipe. I’m making a half-batch of that too, so I use: 1 cup of mix, 3/8 cup of water, and 1/6 cup of oil minus the 1/8 cup of oil I’m getting from the egg.
To simplify, you note that the denominators 6 and 8 are common factors of 24. Then 1/6 cup is the same as 4/24 cup, and 1/8 cup is the same as 3/24 cup. So what I needed was 4/24 minus 3/24 equals 1/24 cup of oil.
A cup has 8 ounces. There’s two tablespoons in an ounce, so that’s 16 tablespoons in a cup. There’s 3 teaspoons in a tablespoon, so that’s 48 teaspoons in a cup. And 1/24 of a cup is then 48/24, or exactly 2 teaspoons. That’s how much extra oil I needed to add.*
I added that oil, whisked both half-batches together, started pouring onto the new waffle iron I got for Christmas, and the kids were happy with the waffles.
Tim Worstall is probably going to comment back that he just would’ve gone out for breakfast, but he’s not as geeky as me.
* The beauty of the customary system of weights and measures is that it is based on multiples of 2’s and 3’s, making the sort of arithmetic I used much more straightforward for someone with a basic grasp of fractions than using a calculator.
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.
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