Bikinis and Drivel

"Statistics are like a bikini. What they reveal is suggestive, but what they conceal is vital."

Aaron Levinstein.

It occasionally amuses me to surf mathematical websites for interesting problems. Statistical ones are a minefield of misdirection and I quite liked this one.

A company is expanding and has 455 new jobs, 70 white collar, the rest blue. For the white collar jobs there were 200 male and 200 female applicants. 15% of the men and 20% of the women were hired. For the blue collar jobs 400 men and 100 women applied. 75% of the men and 85% of the female applicants were hired.

In summary:

An official alleging discrimination noticed that many more men than women were hired. The company responded by pointing out that a greater percentage of women were hired in both blue and white collar categories , thus if anything there was positive discrimination in favour of women. The official then produced his own statistics. A female had a 58% chance of denial compared with a 45% chance for a man. Both sets of results taken collectively are counterintuitive, so who is right? The answer is, of course, both.

Would anybody with a logical turn of mind like to point out the flaw in the reasoning?

Creating policy based on statistics like this is doomed to failure, whether the policy is concerned with how many new settlements to build in East Jerusalem or which school is ‘better’ based upon league tables.