Forbes tried to pull a fast-one, exploiting innumeracy to make a politically correct point.
In the article “Girls Rule” they presented a table, and I’ve extracted the meaty part below:
| . | . | STOCK PERFORMANCE | ||
| Rank | Name / Company / Industry | Change | Relative | Relative |
| 24 | Anne Lauvergeon / Areva / electrical prods | 394% | 360 | 448 |
| 63 | Marjorie Scardino / Pearson / publishing | 65 | 170 | 119 |
| 36 | Lynn Laverty Elsenhans / Sunoco / oil refining | -15 | 157 | 96 |
| 54 | Carol Meyrowitz / TJX Cos / apparel retailing | 60 | 152 | 184 |
| 57 | Andrea Jung / Avon Products / personal care prods | 102 | 150 | 240 |
| 89 | Shikha Sharma / Axis Bank / banking | 307 | 119 | 173 |
| 97 | Angela Ahrendts / Burberry Group / apparel | 94 | 116 | 217 |
| 52 | Guler Sabanci / Sabanci Holding / financial services | 141 | 113 | 71 |
| 92 | Chanda Kochhar / ICICI Bank / banking | 280 | 111 | 146 |
| 82 | Laura Sen / BJ's Wholesale club / discount retailing | 27 | 110 | 91 |
| 8 | Gail Kelly / Westpac / banking | -13 | 103 | 115 |
| 71 | Chua Sock Koong / Singapore Telecom / telecom | 49 | 103 | 100 |
| 26 | Patricia Woertz / Archer Daniels Midland / food | 5 | 102 | 119 |
| 20 | Ursula Burns / Xerox / electronic equipment | 59 | 102 | 123 |
| 77 | Nancy McKinstry / Wolters Kluwer / publishing | 35 | 101 | 112 |
| 12 | Angela Braly / Wellpoint / health care services | -30 | 99 | 89 |
| 32 | Maria Ramos / Absa Group / banking | 80 | 91 | 95 |
| 18 | Ellen Kullman / Dupont / chemicals | 1 | 90 | 114 |
| 2 | Irene Rosenfeld / Kraft Foods / food processing | -4 | 90 | 108 |
| 6 | Indra Nooyi / PepsiCo / soft drinks | 5 | 89 | 117 |
| 75 | Susan Ivey / Reynolds American / tobacco | -10 | 85 | 116 |
| 65 | Annika Falkengren / SEB / banking | -27 | 80 | 50 |
| 85 | Janet Robinson / New York Times Co. / publishing | -81 | 78 | 20 |
| 14 | Cynthia Carroll / Anglo American / metals & mining | -9 | 77 | 117 |
| 38 | Ana Patricia Botin / Banco Espanol de Credito / banking | -7 | 77 | 46 |
| 42 | Carol Bartz / Yahoo! / Internet services | 16 | 61 | 92 |
| Average | 115 | 128 | ||
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.
