They are all around us, those numbers that advocates put out to try to stir us to action, shocking figures that are meant to awaken us to our dire situation. "1 in 6 adults are alcoholics." "1 in 3 women will be raped." "Oil will run out in 25 to 30 years." "1 in 150 children suffers from autism." "Pollution kills 20 million a year." "Smoking kills 50 million a year." "1 in 6 cannot receive adequate health care." "46 million are without insurance." "The seas will be empty of fish by 1985." "The American Robin will be extinct by 1980." "Famine 1975."

Oops, a few of those were later rescinded.

But that last one points out an important facet many don't recognize. Yes, these numbers are shocking, but are they true? And if they are "true", in what sense? Are they "true" in the "2+2=4" sense or the true as in "I feel it to be so" sense? In short, where did these numbers originate and how reliable are those sources? It is surprising how few ever ask these basic questions, and even more surprising how few of those asking are from among the journalists who are paid to ask such questions.

This question has been in my thoughts since my teen years. Back then I was hardly a conservative activist. In fact, when I first noticed such suspect numbers I was somewhere between an apolitical, heavy drinking punk rocker teen and a long hair, still heavy drinking, Bakuninist-SaintSimonist anarcho-communist. But, even when I was addled by bad political philosophy and/or alcohol, I was still rather upset to find I had been the victim of deception. And so, when I started hearing numbers about deforestation, I began to question whether they made any sense.

I think it first struck me in the mid-1980's, but perhaps a bit alter. Whenever it did, I noticed that we had been hearing the same numbers since the mid-1970's about rain forest loss. Inf act, we had even seen some of the same advertisements and PSAs. So, I thought, if deforestation has been progressing at the same rate for a decade, how long before the rain forest is gone? And so I sat down with an atlas and a calculator, watched the PSA on TV, and figured out that, given the numbers then popular, the entire Brazilian rain forest should have been gone a few years before then. Inf act, at the rate they mentioned, all of South America should have been tree-free.

Of course, I soon came to realize the reason those numbers made no sense. (It helped that my girlfriend's father was an agricultural economist for the World Bank, who had worked in Brasilia, though I don't know if he would agree with everything I am about to say.) The part they forgot to mention was that many farms created through deforestation were created to cash in on Brazilian farm subsidies, then rapidly abandoned, reforested, and "re-deforested". So, while we "lost" X acres of forest, we also gained back Y acres to lose again. Similarly, many cases of deforestation were quick clear cutting for timber, which then grew back rapidly, again forest not so much "lost" as temporarily removed.

So, while the advertisements were technically truthful, in that we "lost" X acres a year, they omitted the important fact much was later reforested. In fact, their wording implied the opposite. Still, at least they used real numbers (for the most part*), and just omitted crucial details, sometimes perhaps implying the opposite of the truth. As such numbers go, that is about as close to honesty as you get.

Ever since I made that discovery, I have been fascinated by numerical deception. (Actually, maybe a little earlier, as I described in "Mathematical Deception".) You can see the many blog posts I wrote on the topic in the postscript to "Bad Economics Part 1". However, that just scratches the surface. As that old "lies, damn lies, and statistics" quote says, numbers are one of the best ways to deceive, as they give the mistaken impression of accuracy and precision, while often giving neither. Though, to be fair, most of the best numeric lies contain many elements of truth, they simply take the true data and manage to subtly skew it to say something quite different (eg. "Misusing Numbers "), as many of my opening quotes demonstrate.

For example, the "1 in 6" number for alcoholics. Though this number has enjoyed great popularity, it really has no backing at all. There are some studies of limited groups that give numbers all over the map, mostly depending on how one defines alcoholic, but the number most often used, as far as anyone can tell, has no basis at all, and was simply pulled out of thin air. Similarly, the "1 in 10" number for homosexuality is also a hard number to support. Outside of certain urban centers I am sure the number seems absolutely unbelievable, and even in homosexual centers, such as San Francisco and Baltimore, it is hard to believe 10% is exclusively homosexual, or even bisexual. (See "Myths of Homosexuality", "Passing Thought on PET Scans", "A Question About Biological Theories of Sexual Identity", "Biology as Justification", "Don't Liberals Notice the Contradictions?", "Follow Up".) Kinsey did lend his name to this number, but as Kinsey's studies have been shown to be rather untrustworthy, and this number even less supported than most of his claims, this is essentially yet another number pulled out of thin air.

Other numbers are a bit more grounded in reality. Though that is not always very meaningful. For example, the number of "jobs saved or created" does come form some real numbers, the estimates of unemployment and the real employment numbers. The problem is, the estimates for expected unemployment have very little factual basis, and, as those generating them want to emphasize the number of jobs "saved or created" they have an interest in making anticipated unemployment as high as possible, making these numbers quite suspect. (See "Heads I Win, Tails I Win...", "Anecdotal Evidence of Coming Inflation", "Fairy Population up 6%! Pixies Almost Double!", "Bad Economics Part 4", "WSJ Discovers Miscount in Total of Fairies and Dragons!")

Of course there are other numbers where those generating the shocking figures do not have direct control over the raw data, so they need to adopt a different methodology.

First, let us look at the many figures we see stating that "1 in 6" or "1 in 5" or "1 in 10" or "1 in 7" women will be raped in their lifetimes. The fact that these figures vary so much should tell us something. We do not see this variation when discussing murder, or burglary, or cancer, or any other misfortune. But when it comes to rape, the numbers seem suddenly very uncertain. And the reason is twofold. First, because with the loosening of the definition of rape during the period in which "date rape" entered the headlines, going from stranger rape and forcible intercourse to cases where someone says "no" in mid-stream, it became much more difficult to decide what was rape and what was regret**. However, the bigger factor, and the source of most of our confusion, is not definition, but political beliefs. You see, many who believe rape is a defining part of western culture, also believe it is dreadfully under-reported.  And so, they take the number of reported rapes from crime statistics and multiply it by 7 or 10 or some other large number to generate the figures we often hear.

But that is a problem. There just is no evidence that under-reporting is anywhere near as prevalent as they claim. Traditional sources already do assume there is some lack of reporting, and offer up various figures based on hospital admissions, withdrawn charges, psychological studies, and other sources. These numbers are themselves not entirely reliable guides, but at least they have some basis in reality. On the other hand, the larger, more political figures, often have little more to justify them than assumptions. However, as they are the assumptions of PhDs, and PhDs with the right political beliefs, they are given credence that mere guesses would not receive were they based on opposing political beliefs.

A similar case is found in the reports of civilian casualties in Iraq. As with rape numbers, the number of civilian casualties is all over the place, running from a few thousand to a million or more***. And, as with rape figures, that variation is clearly a sign that the numbers are based on very uncertain methodologies.

The one difference here is that those positing huge numbers do actually give their methodologies, or at least offer some sort of superficial gloss of their plans. The only problem being that often that description is either too vague to be adequately examined for flaws, or uses raw data which are unavailable for those trying to validate the method. Then again, not all offer such elaborate explanations. As with the rape numbers there are a goodly number of those pushing high numbers who admit they simply assume only a percentage of deaths would be reported, and so they simply inflate the military figures by an order of magnitude or two. (See  "Civilian Casualties", "A Question for those Deploring "Civilian Casualties"in Iraq", "Just Angry".)

Which brings us to our final group, the numbers which are accurate, and reliable, but whose meaning or significance is obscured, intentionally or otherwise, or which are used for a purpose for which they are inappropriate.

Both examples of this have been covered already at great length. Peak oil claims in "Rejecting "Peak Oil" and "Why Peak Oil is Laughable ". Claims about the uninsured in "There ARE NOT 46 Million Uninsured!", "A Most Dishonest Commercial", "Medical Reform, An Overview", "Bad Economics Part 2"and "How to Ration Without Rationing". Both rely upon totally accurate numbers, numbers upon which everyone agrees, but both also use those numbers in idiosyncratic ways to reach conclusions different from the ones those numbers would normally support.

For example, the peak oil theory is based upon the "known reserves" or "proven reserves" of oil. Those numbers are not in dispute. We may not know precisely how much oil is in each well, but within certain limits, we can say that the oil fields we have discovered could produce a certain amount of oil given today's technology. The problem is, peak oil sues this number to support a claim it does not.  Peak oil theories confuse known reserves with all possible reserves, and today's technology with the ultimate technology. It is akin to saying "everyone I know speaks English" and assuming that proves everyone speaks English. The known reserves are not all the oil there is, or else no one would do exploration. Likewise, the technology we use is not the final word. Every day "dry" wells are brought back into production by new technology. So, despite peak oil claims, known reserves have little or no relation to total oil that will ever be available.

The insurance figures are misused in a different manner. They are presented accurately, as the total number of uninsured individuals in the year 2004 (at least for the 46 million figure). However, the significance of that number is being blurred. Often it is implied that that means they were uninsured for the whole year, as well as uninsured involuntarily. Often it is also implied that not only did they lack insurance, but could not receive health care. The fact is, there were 46 million who did not have insurance AT SOME TIME in the year. So ti includes everyone who lost insurance for even a day in the year, even if insured for 364 days. Similarly, it includes millionaires who opted out of insurance, the young and healthy who opt to go without, and health savings plan users who choose to handle health costs in alternate ways. But that reality is usually ignored and the implication is that 46 million individuals could not see a doctor or go to the hospital when they were ill or injured, and that is simply untrue.

Now, none of this is meant to imply that all statistics are unreliable. There are many times when numeric evidence is perfectly appropriate. Inf act, in many of these cases, legitimate numbers would be useful. The problem is not the use of numbers, but the misuse of numbers. And the solution is not, as many would suggest, to distrust all statistics, but simply to ascertain the origin of the numbers you hear, and then, once you know where the numbers originated, to determine whether or not those origins are both valid and appropriate for the purpose at hand, and, finally, deciding whether the numbers really mean what the proponents claim.

Of course these are the tasks the media and academics should be performing for us, but as the media and academia have become advocates rather than the impartial arbiters they claim to be (see "The Failure of Peer Review", "Eco-Nonsense", "Bad Economics Part 1", "The Death of Impartial Media",  "The Impossibility of Unbiased Reporting", "Media Double Standards and a Proposed Solution", "Checking In With the Professionals"), it is no longer possible to rely upon them, and so, for the foreseeable future, it is up to each of us to ensure that the shocking numbers we hear so often real mean what some claim.

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* Some also stacked the deck a bit by choosing the highest daily figure and using "per day", implying ti was a yearly mean, not the highest single day value. It was technically honest as well, but very misleading.

** I do not mean to trivialize rape. I am as opposed as anyone to forced intercourse. I detest any acts of violence. On the other hand, even the most politicized advocate must admit there is a difference between forcible rape of a stranger and a man who ignores a tepid "no" offered by a naked woman in his bed who has previously offered 100 "yes"es. I realize one has every right to say no at any point, but as the conversation about sexual matters is often rather circumspect, sometimes playful, and often fraught with double meanings and innuendo, it is hard to say whether every "no" really means that. Only the most unimaginative, boring individual on earth could seriously believe every word offered in romantic banter is offered with the precision of contractual negotiations. (Then again, these are the robotic drones who want dating contracts, so maybe they are the most boring, unimaginative individuals on earth.) Anyway, my point is that moving from stranger rape and forcible rape of acquaintances to "date rape" and "no means no" changed the definition enough that the clarity of the old definition was lost.

*** Originally I was going to limit myself to the guesstimate of 100,000, as numbers any higher seemed like the lunatic fringe, and completely implausible. However, I found more and more sites giving some credence to numbers approaching 500,000 or more. So, it seems the lunatic fringe numbers are gaining acceptance.

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POSTSCRIPT

My earlier writings on misapplied data can be found in the postscript to "Bad Economics Part 1", "Misusing Numbers ", "The Devil is in the Definitions (And Assumptions)" and "Another Example".