To know everything about anything, do the work

PERSPECTIVE

By George Templeton
Payson

Numbers Game

The great British physicist Lord Kelvin claimed that measurement and quantification were perquisite for deep understanding. He did not tell us that numbers can fool us. Fool me once, shame on you. Fool me twice, shame on me.

There is no such thing as computer error. The human is always responsible for using numbers. They are just tools like a hammer or pliers. It is no more correct to say that figures lie than to say that hammers lie. People can misinterpret data, or hit themselves on the thumb.

A businessman heard that four out of five businesses fail within the first year. His previous four had all failed. Now this, his fifth, according to the statistic, would be successful. What he did not consider was that he was describing a future, and if he had learned from the previous four failures his chances of success would increase. On the other hand, his four failed businesses might all have occurred because of the same character flaw in which case the fifth business would also quite likely fail.

A priori probability has its roots in games of chance. It assumes that there are truths that can be known apart from human experience. For example, we think of tossing a coin as a way of making a blind choice. Because a tossed penny can come up heads or tails, the probability of “heads” is one-half.

A posteriori probability’s knowledge comes from experience. You can’t know everything about anything when you experience nothing! You have to do the work. By tossing a penny a large number of times we observe that it comes out heads approximately one-half the time. We conclude that the probability of heads is one-half. Though unlikely, we might see 25 heads in a row even though the outcome of the penny toss is a random process governed entirely by chance. There are no guarantees, only probabilities.

A mathematician drowned in a river that was typically 1 foot deep. The significant fact was not the average depth but rather that there were some deep pools. The ad for the latest pill mentions that it has not been shown to be helpful for the disease that most people take it for, but average numbers are given for how it treats possible contributing causes. The ad is pages long, and was written for us by lawyers and marketing; not by scientists for doctors as it should be. Those rare side effects could happen to you.

Studies show…. Or marketing claims? John measured the fuel economy of the new truck. He said it got 14 mpg. Fred claimed 15.3 mpg. Who is right? What is at issue here is the reliability of the estimate. When we have only two numbers we have to choose according to Fred’s decimal point or John’s reputation. Food calories and any other single number rating suffer from the possibility that the measurement might not repeat. At least two numbers are required to give a result and a measure of its reliability. We asked John and Fred to repeat their measurements five times. This gave different numbers so each person averaged his data. John said 15.6 mpg and Fred 15.14 mpg. When the data was examined it was noted that Fred’s data points were much closer together. The tighter grouping of Fred’s data might lead us to prefer his rating. However, John was not about to take this lying down so he made 500 measurements and came up with 15.326 mpg. Some credit must be given to John for all the work he did. Interestingly, if we make a graph of John’s data plotting the frequency of occurrence versus mpg we approximate the familiar bell shaped curve that our teachers used to grade us by. Order emerges from disorder! Unfortunately there is no “correct” answer, only a “best” answer.

Consider plotting home prices versus time to calculate a rate of change. A computer can draw a straight line that does not go exactly through the data points but minimizes the deviation of data points from the line and gives a confidence interval. For the given data the line is the best estimator of prices, but the price of a home at a date shown on the plot could be far removed from the line. The greater the required confidence, the wider the interval becomes and the more data, the narrower it becomes. Studies lacking this information are practically meaningless. Even though the computer calculates a confidence interval, it is almost never quoted to the public. Why do you suppose that is?

Are we justified in thinking that prices are changing with time? This is the slope of the straight line. Could the data simply have happened by chance? The computer tells us about this. However, time does not cause prices and Medicaid does not cause sickness. There is no such thing as a crystal ball that shows the future. The computer predicts the future only when nothing changes.

Some think that time, having no objective reality, stops when nothing changes! Interestingly, statisticians have evolved an alternative view of reality where there can be many more dimensions than our senses can comprehend. Complex environments such as human behavior, the weather, and the economy are full of surprises making forecasting unreliable.

It all depends on how you look at things. The context determines how we interpret data. Data sometimes looks different when analyzed by subgroups such as different kinds of taxes, neighborhoods, people, time interval, type of loan, route traveled, etc. Opinion polls derived from leading questions with choices that miss the essence of the issue are biased. Even special attention can influence the outcome of a study.

That something is uncertain or cannot be proven does not mean that it is false. But uncertainty cuts both ways. Global warming could be much less or more than expected as could be the consequences of a debt default by America. As dirty Harry / Clint Eastwood said, “Do you feel lucky”?

Some ads give only the monthly payment but what is the total cost? We expect to have it now and don’t have the patience and self-discipline to wait until it is earned. The total cost and the future obligation to pay one’s debts hardly matters.

Numbers seem easy to understand until closely inspected. What is assumed to be a significant variable may not be, or it may interact with other variables so it is not “pure”. So it is with the debt ceiling, and taxes. Balancing the budget is not a simple matter like putting off the purchase of a new car or wide screen TV. It requires deep knowledge in economics, statistics, accounting, and concrete consequences. Because we can’t know all this we rely on our elected officials. But sometimes they fool us and advocate simple rigid solutions that are incomplete.

Sometimes politicians are less than accurate. They “move” beheadings and other heinous crimes across the border feeding the rumor mill. Inflated numbers magnify a problem contributing to hysteria, envy, and fear. The scribbling on the bathroom wall of a major store that prides itself on having Spanish speaking clerks reads “Gut shoot them at the border” and testifies to how the loose lips of our leaders are sowing hatred.

Are these numbers accurate? Five hundred thousand immigrants “invade” across the Arizona border every year. The national guard apprehended 7,000 in 6 months which works out to 14,000 in a year meaning they missed 36 for every one caught. But another 500,000 arrive at the airport initially with papers that they allow to expire. Then the number grows to about 1,000,000. This is more than three times larger than the Normandy landing, the largest amphibious invasion in world history. At this extreme rate more than 10 years are needed to reach the often quoted number of 11 million illegal immigrants in America. Why did it take so long for the present concern to be expressed? Didn’t we know that this was happening all along? Are these numbers politically expedient?

Telling the truth is not solely a matter of moral character. It is also a measure of correct appreciation of real situations and of serious reflection upon them.