When the city of New York recently threw a ticker-tape parade for the world champion Yankees, the mayor's office issued a release crowing that 3.5 million people had lined the mile-long route.
Even granting that the slimmest of folks showed up, they would still have had to line up 1,000 deep, an impossibility on Wilshire Boulevard let alone the cramped streets of lower Manhattan. Still, the 3.5 million statistic made front-page headlines and was repeated until it took on the aura of fact, just the way dubious Rose Parade crowd estimates have year in and year out.
While no one may have been harmed by this particular mathematical mismanagement, it is yet another case that demonstrates how we have become a statistically challenged society.
Statistics bludgeon us. They are out there everywhere, most often unencumbered by interpretation. Should I care about the Dow Jones 30, the S & P 500 or the Russell 2,000? Does anyone really understand the quarterback rating system, hockey plus-minus or earned run average? Why does body temperature go up with the consumer price index and down with the wind-chill index?
The ubiquity of statistics is often laid at the feet of computers, but the real problem is not the preponderance of stats, but that they float in the data murk without understanding or clear interpretation.
"People are being overwhelmed by quantitative information," said Robert Stine, a professor of statistics at the University of Pennsylvania's Wharton School. "They don't always get to hear the origin of the information and they don't listen for good interpretations."
Said Prof. Donald Ylvisaker, consultant to the UCLA Statistics Counseling Center, "The real problem is this: We have to shift from an age of information to one of intelligence. Anyone can put data out there. The problem is really to filter it out and interpret what it all means."
But it can be a real mess when the stats aren't up to snuff. "The list of shortcomings in U.S. economic data is depressingly long," Alan Greenspan, the chairman of the Federal Reserve Board, testified recently before Congress.
In fact, a study by Michael Waldman of Cornell University and Seonghwan Oh of Seoul National University showed that a series of pessimistic economic data compiled by the government in the first half of 1989 was significant in persuading businesses and consumers to cut their spending. Later on, the statistics were revised upward--more than 10% of government statistics reported are later changed, Waldman said--but by that time, the country had lost an estimated $10 billion in production.
Another common complaint among economists is that the consumer price index, the statistic that newscasters are talking about when they tell you about inflation, is just plain wrong. The general feeling among these economists is that because the index doesn't try to quantify efficiencies in production and increased quality of products, it continually overstates inflation by about 1%.
This all wouldn't matter if the index were just another number, but many folks look upon it as their favorite number. More than three-quarters of all corporations use the index to help figure out employee raises. The index is the major factor in figuring out Social Security payout rates. Thus, an incorrect index is self-fulfilling. Revisions may be coming soon from a federal panel appointed by the Senate.
Stine once worked on a project to figure out how much gasoline was used in the United States. He discovered that there were four sources of statistics, all seemingly accurate, that differed by 15% to 20%. "There were rational explanations for this: Some were by consumption, some were by production. But it gave you a way to interpret them," he said. "Unfortunately, the government now has only one number. There's no conflict now, but can you really believe the new number?"
Statistical sleight of hand figured in the recent election campaigns, when Democrats repeatedly accused Republicans of proposing to cut Medicare. Republicans complained bitterly that they merely proposed to cut the size of the increases the Democrats had proposed. Everybody understood the distinction, right?
But what about the weather? Surely, no stat could confuse that.
"The wind-chill index has confused people as to what the real temperature is," said Fred Godomski, the head of the Pennsylvania State University TV Meterology program. "You have two temperatures floating around in the winter. Actually, it's an attempt to impart more drama to the weather.
"And the UV Index, ugh!" Godomski said. "Dermatologists say any type of sun is bad for your skin. It's just a proliferation of babble, just data for no reason because we can report it."
Godomski said he has his students look at some old TV weather forecasts from 1957 to compare to the statistically overloaded ones today. "The single biggest difference, beyond the magnetic blackboards, is the rate at which information is imparted. Today it is at breakneck speed," he said. "It's a wonder the average viewer can extract the necessary information from a mere weather cast."
It's even a greater wonder anyone without a doctorate in math can get through the sportscast or sports pages. "Occasionally I find there are overzealous uses of statistics," said Steve Hirdt, executive vice president of the Elias Sports Bureau in New York, the official statisticians of the National Football League, the National Basketball Assn. and Major League Baseball and, thus, the producer of most of this billowing flow of numbers.
Hirdt and his number-runners are the folks who compile all those arcane baseball statistics--like how many times left-handed batters walk against right-handed relievers during night games in May.
"There are times when the use of certain statistics makes me cringe because I know people think those uses emanate from us," Hirdt said. "But, hey, this is America, and if we can't keep guns out of the hands of the wrong people, how can we do that with sports stats?"
A particular common misuse of sports statistics, Hirdt said, is improper attribution of cause and effect. He noted that in the Dallas Cowboys glory years, it was constantly repeated that when Tony Dorsett rushed for 100 yards, the Cowboys always won the game. "But if you step back from that, the reason he got so many yards is that the Cowboys were already ahead and were running the ball to run out the clock. It's like saying when people carry umbrellas, it starts to rain."
But rain statistics it does and we seem powerless to do anything about it.
There are the Nielsen ratings, for instance. Who won last year? Each network used the numbers differently. NBC said it won because it got the highest total prime-time Nielsen numbers. CBS claimed it won more nights than NBC. ABC claimed it was the winner because it got more young viewers, those who attract more advertisers. Meanwhile, the total of the three major networks was at an all-time low, so the cable networks claimed victory.
There is a general belief that standards for mathematical comprehension have declined. But, of course, it is hard to prove that through statistics. The Scholastic Aptitude Tests would have been a good year-by-year comparison, but last year, the Educational Testing Service, which administers the SATs, recalibrated the way it arrives at the English and math scores, so that new scores are higher than in the past. The theory was that scores were going down, so something had to prop them up, even though there is evidence that since more students at the lower end of the curve are taking the SATs, it would be natural for scores to go down.
American students' deficiencies in math and science have been well-documented in a number of studies. Just last week, a new international study ranked American middle schoolers 28th of 45 countries studied in math performance. Based on an analysis of 1,000 textbooks and teaching guides, another recent study by the National Science Foundation found that U.S. schools teach too many math and science concepts--and cover them too superficially.
Those who study statistics say there is crying need for improved math literacy.
"We have discussions around the university about having a requirement in quantitative reasoning--learning how to use numbers," UCLA's Ylvisaker said. "You have to sort these things out to go through life sensibly. The filter of the newspaper isn't enough because, frankly, newspapers tend to want us to see the sensational side of statistics."
Ylvisaker added that there is a general math phobia afoot. "People say, 'Oh, I was never good at math,' or, 'Numbers have always confused me,' " he said. Once people say that, Ylvisaker said, they release themselves from the responsibility of knowing what any set of numbers they see means.
By the same token, the poorly educated invest numbers with super significance they only sometimes merit. Words manipulate, these people imagine; numbers are trustworthy. And the more precise they seem, the more seriously we take them.
Remember the old ad for Ivory Snow? The product was "99 and 44/100% pure." Sounded pretty exact, but what did that mean? And would you drink water that was 99 and 44/100% pure and the rest strychnine?
"Somehow, when you put a numerical value on something, it takes on a new level of meaning," Stine said. "And once you quantify something, it sells your point of view better."
Take the Million Man March. Many agreed that it was a good thing: black men getting together for any number of spiritual and political reasons. Then the U.S. Park Service announced its estimate of how many people were actually on the Mall in Washington that afternoon. It was 400,000. An impressive number, to be sure, but short of the advertised number.
The leaders of the march threatened to sue, calling the number a "willful undercount." The hoo-ha over the number threatened to become more important than the spirit of the event. The Park Service decided the only prudent course was to get out of the crowd estimation business completely--but that one less statistic will hardly staunch the torrent.