Social security, illegal immigrants and Iraqi civilians killed -- these are just three of many topical issues giving rise to misleading, dubious or uncertain numbers. Clarifying these numbers is important, because which statistics are quoted and stressed helps frame an issue and often determines people's reactions and positions. Here are three numerical/political short stories.
During and since the election campaign, I've read many news stories and watched many TV snippets dealing with President Bush's proposal to partially privatize Social Security. Usually in print and almost always on television, the proposal is said to call for 2 percent of Social Security taxes to be diverted into private accounts. Usually, few other details are provided and the reader/listener, whatever his attitude on the issue, probably comes away with the impression that even if passed, this change would be a tentative, very slow transition that shouldn't cause too much of a problem.
Looking a little further, however, one can find a few stories noting that the 6.2 percent of the average American's taxable income that goes to Social Security taxes will be cut to 4.2 percent. That's a 2 percentage point cut -- not a 2 percent cut, but a 32 percent cut! This will leave a huge hole in Social Security revenues for present retirees.
Why isn't the proposal fairly described as calling for a 32 percent cut in individuals' contributions? I suspect it's because most reporters don't feel confident enough of their basic arithmetic to so describe it.
Another statistic in the news is the number of illegal immigrants coming across the U.S.-Mexican border. A Time magazine story cited an estimate of 3 million illegal aliens annually crossing into the U.S., and this enormous figure has been uncritically accepted by many news and TV networks.
The origin of this number is interesting. Border agents say they apprehend approximately 1 million people annually, but estimate that three times as many people manage to make it across the border. Since three times 1 million is 3 million, an alarmist statistic is born. Ben Winograd, a freelance journalist in Arizona who has studied the issue, has noted problems with both the numbers 1 million and three.
First, 1 million apprehensions does not mean 1 million distinct individuals. It's well known that many people try over and over again to enter the U.S. and are apprehended over and over again. And the factor of three mentioned by border agents is just conjecture. How does one estimate how many people are not apprehended when these latter are, almost by definition, largely invisible? Whatever the real statistic, the 3 million figure has by now attained a life of its own.
The number of Iraqi civilians killed since the war began has also recently been in the news. Published last month in the British journal Lancet, research conducted in Iraq by Les Roberts of the Johns Hopkins Bloomberg School of Public Health and his associates attempts to estimate this number. To do so, the researchers surveyed the civilian war deaths in 33 clusters of 30 households each. The clusters were randomly selected from across the country. Projecting these neighborhoods' higher death rate since the war onto the country as a whole, they argued that the number of civilians killed since the war is approximately 100,000, more specifically 101,000 plus or minus 93,000; i.e, somewhere between 8,000 and 194,000. Most of these civilian deaths, the study maintains, have been caused by American air attacks.
There are reasons to be skeptical (but not dismissive) of the 100,000 figure. One, of course, is that the interval is quite large reflecting the sample size and study design. Given the conditions in Iraq, the samples were not only small, but sometimes not quite random either. When one selected neighborhood cluster couldn't be visited, say because of blocked roads, another was substituted. (Fallujah was excluded as being clearly unrepresentative.) Furthermore, some of the study's assumptions were less than certain. The 100,000 figure depends crucially on a comparison of the death rate before and after the invasion, and there have been claims that the researchers pegged the pre-invasion rate too low. The number also depends on truthful reporting by the distraught families involved since a death certificate was often not available.
Even if the number of civilians killed is not as large as the Lancet study suggests, the number is no doubt bigger than the figure reported by Iraq Body Count. IBC is a group of British researchers who compile as extensive a list of Iraqi civilians killed as they can from published reports, hospital records, and morgue reports. They doublecheck and otherwise fully document the names and associated details of those killed, but miss those whose names don't make it into the papers or onto hospital or morgue lists. Their list contains approximately 15,000 names.
So what's the real number? Despite the brave efforts of the Lancet researchers, my guess, and it's only that, is that the number is somewhat more than the IBC's confirmed total, but considerably less than the Lancet figure of 100,000. Interestingly, the number of civilians said to have been killed by Saddam Hussein during his long reign is usually put at 300,000, and this number too is probably overstated, since only a small fraction of these have appeared in mass graves.
There are many more numbers to deconstruct, most of them much less depressing than the last example, but doing so is strenous work, and I'll need to take some vitamin E to keep going. Oops, that's another story -- and another number.
-- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including "Innumeracy" and "A Mathematician Plays the Stock Market." His Who's Counting? column on ABCNEWS.com appears the first weekend of every month.