Math illiteracy affects judgment

I suspect that many people (most people?) would give the wrong answer or be at a loss for an answer.

Answers to real-life questions that involve probabilities greatly influence what products we buy, what companies we invest in and how the public's money is spent.

Consider a real-life 1950s example from the field of drug testing. In a particular community, 450 children were treated with a new polio vaccine and another 680 children were not treated -- in sampling lingo the 680 children were a control group. None of the 450 children who were treated came down with polio. Good news for the vaccine maker, right?

Nope! To the surprise of the researchers, none of the control group came down with polio either. What the researchers had neglected to consider was the very small probability of contracting polio under any circumstances. What appeared to be a large sample of 1,130 children actually was much too small to produce meaningful results.

Now back to the coin toss question. The answer is: Not a whole lot.

There is nearly one chance in five that a fairly balanced coin will yield seven or more heads in 10 tosses. On the other hand, if the coin had been tossed 100 times and 70 heads had appeared you could be pretty sure that the coin was unfair because the probability of 70 or more heads coming up would then be about four chances in 100,000. The point being that sample size matters more than most people suspect.

Consider another example of how innumeracy bedevils all of us. I frequently testify in civil lawsuits as an expert economist. What I have often found is a tendency for certain lawyers to count on the fact that not many jurors have enough understanding of numbers and probabilities to make informed decisions on certain matters. These lawyers count on the fact that many jurors are uncomfortable with numbers and statistics and that those jurors will tend to assign a higher probability to the subjective beliefs of credible plaintiffs than they do to conflicting statistical testimony from credible defense experts.

One widely publicized result is the extreme jury awards that have been given to plaintiffs in certain medical malpractice cases, awards that help to drive up the cost of malpractice insurance for the medical profession and thereby the costs of medical care for everyone. The point being that no matter how careful or well-trained or alert the physician or surgeon, there is always a significant risk of a bad outcome. In many cases that seems not to matter to a jury.

Here is another example. My experience tells me that more than one-half of the adult population judges decisions on the outcome and not on the probability of that decision having been the best, given the information available at the time. Many public-sector decisions must be made even when none of the choices are good. To condemn the decision-maker when a predictably bad outcome happens is a popular pastime frequently engaged in by politicians and camp followers of the opposite party.

And then there are the pharmaceutical companies that exploit public innumeracy when they stress that their product will reduce your chances of contracting some vicious disease by one-half. What they do not say is that the probability is reduced by a whopping two chances in 100,000.

The problem might never go away, but education has a role to play. So if you think that innumeracy is a problem and you need an argument on behalf of more teaching of mathematics and statistics in our schools and colleges, consider that offered here. If you do not think innumeracy is a problem, ask yourself why lottery players who always play six different numbers almost never play six consecutive numbers.

Acknowledgement: The polio example was taken from the book "How to Lie With Statistics" by Darrell Huff, (W.W. Norton & Co., New York, 1954 edition).

David M. Reaume holds a doctoral degree in economics. He lived and worked in Alaska for 22 years before moving to Washington state in 1999. His opinion column appears every month in the Anchorage Daily News.