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Taking Risks, Reaping the Benefits"Quantitative Decisions" describes what we do, but it's hard to make that clear in the abstract. We all know what a doctor does, or an accountant, or a bricklayer. But a decision supporter? What does he or she do? An example is better than a description and I can think of no better one than the pile of sand blast grit a client had to dispose of several years ago. This pile, if classified as "special waste," would cost $500K more than if it were disposed of as "clean fill." This is not much for a large corporation, but it is enough to deserve a moment's thought. The problem was that the grit left over from cleaning this former dry dock contained some metals, including lead, which is considered hazardous in small quantities. Environmental regulations therefore require testing some grit samples by "TCLP." This procedure washes the grit in acid and measures the metals that are dissolved. The TCLP lead concentrations for three out of five samples were above the special waste standard (and the other two concentrations were close). On the face of it, this was an easy decision: the grit obviously did not meet environmental standards. We did not look at it that way, though. We performed a specialized but quick statistical analysis of the data. The analysis included simulating the results of (hypothetical) additional samples. Our summary of the situation:
Our advice: on balance, it is worthwhile to obtain more samples, even though the odds are heavily against success. The basis for this advice is statistical expectation. Our client had, in effect, an opportunity to gamble. ("Invest" is a nicer word, but the effect is the same.) The bet is $10,000. The potential payoff is $500,000. The odds are that he would lose the game, but he had a seven percent chance of winning. Would you play this game? Many people would not: they cannot afford to lose $10,000. A large corporation or indeed anyone who is faced routinely with such decisions thinks about it differently, though. Imagine playing this game 100 times. In 93 of those plays, you lose the $10,000. In the other seven, you lose the $10,000 but win back $500,000. The total loss is a million dollars, but the total payoff is 7 * $500,000 = $3.5 million. The net gain is $2.5 million: $25,000 per game. That is its statistical expectation. Our client elected to play and he won. In his situation he invested $10,000 and received a $500,000 return within two weeks. In other cases our clients took similar gambles and lost. That is the nature of the game. Playing it once really is a gamble. Playing it many times is a sure thing. (This is the simple principle behind the success of casinos.) It gets better, though: we knew more than the statistical results told us. For instance, most environmental sampling is biased. Very few consultants (and it is almost always an environmental consultant that obtains samples) follow procedures that guarantee lack of bias. (This one's report said they sampled "in general conformance with accepted procedures." When pressed, they admitted they took the samples where it was easy to get them.) In general, the direction of the bias is not predictable. As a rule, though, consultants have learned to take samples where there is the greatest chance of finding contamination. That makes sense and is good, but in some circumstances--such as when an environmental medium is generally clean--it results in an unfair portrayal of reality. We suspected this bias was operating in the grit sample data. It made our client's decision to obtain more samples even easier. It should now be obvious where the "quantitative" and the "decisions" come from in our name. But it might not be so obvious how important a role the quantitative element played in this case:
If you make high-stakes decisions, shouldn't you be using a quantitative approach too?
This figure shows 15 locations randomly selected by computer superimposed on a faxed map of the sandblast grit pile. Geographic information systems technology lets us apply and match appropriate technologies (fax and statistical software in this case) to get the job done efficiently and well.
William A. Huber, Ph.D. |
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