Monday, August 24, 2009

And the Facts Mean? (Part 4)

The EEOC has set an 80% standard for hiring and promotion. If a company hires 50% of the white people who apply, it must hire at least 80% of that or 40% of the minorities who apply. Failure to do so is considered prima facie evidence of discrimination. That rule might be useful in determining which companies bear investigation, but it is a terrible method of determining who is actually discriminating.

I've already discussed the fact that different groups have different characteristics. Some minorities, especially in the inner cities, have a culture that discourages education. Why should a company be forced to hire any certain number of them if the job requires cognitive skills? However there are also statistical problems with that rule.

Suppose for example 10% of the people living in a town are black and 90% white. A company in that town has four people doing a certain job. Now 10% of those four employees would be 0.4 people and 80% of that is 0.32 people. It is rather difficult to hire a fraction of a person. If they have one Black among the four employees, then 25% of the people there would be black, far in excess of the 10% of the population that Blacks represent.

Even if the company has 40 people doing that job, statisticians would tell us that it is unreasonable to expect exactly four of them to be black and 36 white. In fact statistically it would not be at all surprising if there were anywhere from zero to eight Blacks among those 40 workers. If you have the time, you can demonstrate this to yourself if you can find a few marbles of different colors. Put 9 of one color and one of a different color in a box and shake it up. If you don't have marbles you can use something else, maybe coins with a coin from a particular year representing the minority. You could even put a dot of fingernail polish on the minority coin.

This experiment is to simulate hiring at random, with the marbles representing the applicants. The nine majority color marbles represent the 90% white population in the town and the odd marble (or coin of a particular date) represents the 10% black population. Now without looking, randomly draw one marble from the box and record what color it is. Replace the marble, shake the box and draw again. Repeat this 40 times to simulate hiring 40 random people. How many times did you draw the odd marble? Probably not exactly four times.

Now repeat the above experiment at least ten times, each time recording how many times you drew the odd marble. Most likely once or twice you will draw the odd marble only once or not at all. Once or twice you will draw it 6 to 8 times out of the 40. Most of the time you will draw it three, four or five times out of the 40 tries. However even only drawing it three times fails the EEOC test of 80%, that means you only “hired the minority” 75% of the times that the minority “applied” for your job opening. Would you like to be exposed to charges of discrimination for the times you drew zero, one, two or even three minority marbles?

If you took the time to do this experiment what you have seen is normal statistical fluctuations. You can see something similar by tossing a coin ten times as I described in a previous blog. The most likely result is five heads and five tails. However there are many other possible results. Each of those other results is less likely than the five heads and five tails, but there are more of those possibilities so together they outweigh the probability of equal heads and tails. In fact the probability of getting exactly five heads and five tails is less than 25%.*

“But wait,” you say. “Don’t large companies hire more than 40 people, even more than 400?” Yes they do, but each work area usually has a much smaller number of people. Furthermore, even for larger numbers we would expect some deviation from the most expected value. The larger the number in the group, the less deviation we would expect percentage-wise, but there will be some. On top of that, as we go up the corporate ladder to more lucrative jobs, the number of employees gets smaller. A company may have 10,000 employees but will probably only have fifty or so in top management and fewer than ten at the vice presidential level or higher.

To say that a company is guilty of discrimination on the basis of statistics alone is to ignore those statistical fluctuations, as well as the fact that we cannot expect people of different backgrounds to have identical qualifications. Such a declaration of guilt ignores science. While statistical differences may raise questions, we should insist on actual evidence of biased actions before claiming that anyone or any company is guilty.

Now on somewhat of a personal note: I’ve been publishing five blogs per week and have enjoyed it. However there are also other things I would like to do, including complete a novel I started some time ago. To free up time for those projects I plan to cut back, initially to only three blogs per week. They will probably to be published on Monday, Wednesday and Friday. I’ll see how that goes and hopefully I won’t have to cut down to twice per week.

*For the mathematically inclined, the probability of getting exactly m heads out of n coin tosses is

P = (0.5)^n [n!/{(n-m)! m!}]

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