• SETH ON LANGUAGE 17.08.2011

    This is nothing new.

    Most agree that advertisers and political agenda holders will try to mislead us with statistics and emphasis. Indeed, the statement “You can use statistics to prove anything” has been around for years to capture our general frustration with the misuse of facts and figures. I think it should be noted, though, that numbers can only prove what is true, so in reality, they cannot prove anything you want – but, with clever emphasis (or non-scientific collecting of them), they can be used to imply flawed conclusions.

    For instance, a reporter who is assigned to do a story that demonstrates the (alleged) substandard play of the local sports team will take the team’s following list of results—


    —and, from one side of his mouth, say that the team is playing so poorly that it has only won two of its last ten games. But if the same scribe is asked to demonstrate that the team has fared well, then he or she will happily note, from the other side of their mouth, that the team has impressively only lost two of its last ten games.

    In reality, if viewed collectively, the statistics are perfectly clear that the team has fared exactly evenly (2 wins, 2 losses, 6 ties) in their last 10 games. The numbers did nothing wrong! The blame should be squared at the interpreter of those stats who cruelly abused their earnest willingness to help and emphasized only the part that seemed on the surface to support their conclusion.

    Thus, in defence of statistics—which, when compiled scientifically, are innocent figures, who just want to depict their environment as accurately as possible—I have collected over the past few weeks some examples of emphasis gone wrong:

    (A) “The 53 year-old grandfather of two”:

    In a recent feel-good story, a reporter was trying to emphasize the impressiveness of a man’s swim across some great distance—especially since he was older than the average practitioner of such an activity. Apparently, the man’s 53 years on their own didn’t sound old enough, so the journalist referred to him as a “53 year-old grandfather of two.” My understanding, though, is that there is no evidence to indicate that 53 year-old grandfathers of two are any older than 53 year-old grandfathers of one, who in turn have not been shown to be any older than 53 year-olds in general.

    (B) “We’ll cover the tax on your purchase”:

    It seems on the surface here that retailers are simply trying to capitalize on their customers’ general tax resentment, and so are saying, “I’m on your side: I’m going to cancel out the tax.” But, in fact, if they had simply given a discount equivalent to the tax rate, they would have saved the customer more money:

    If, for instance, an item cost $100 and the tax rate was 10%, then – before the discount, the total price of the purchase would have been $110. But the noble, anti-tax warrior is covering that total tax of $10, so the consumer only pays $100. In contrast, if the company had simply given a 10% discount on the purchase, the pre-tax price would have been $90, which – taxed at 10% – would be $99 total.

    Not a remarkable distinction in such a small purchase, but when I recently overheard a car company boasting that they would cover the tax for their beloved consumer, their tax-hating friendship seemed particularly expensive (on a $15,000 car, the distinction between “covering a 10% tax” and “giving a 10% discount” would be a distinction of $150, i.e. $1500 savings vs $1650).

    (C) “Three-time boxing champion”:

    In most sports, to be a three-time champion means that you have three times gone into a championship tournament and won. So the more-time champion you are, the better. In the boxing world, however, the “times” are calculated differently because, in that world, you stay the champion until someone defeats you. So, when you first win, you’re a one-time champion. If you lose your belt and regain it, then, you become a two-time champion. Thus, someone who never loses their championship will end their career as a one-time champ, while someone who loses it twice and regains it twice is a three-time champion. This is still impressive, but, unlike in other sports, being a three-time champion is not necessarily better than being a two-time champion.

    Nevertheless, when advertising the appearance of a champion boxer, promoters will universally capitalize on the phrase “3-time champion” as though it means the same superior result as it would in other sports.

    (D) “The lowest/highest paid X in the country”:

    Politicians enjoy defending or criticizing social facts in their own jurisdiction by comparing them to adjacent neighbourhoods. For instance, to prove that BC’s rate of X is too high or low, they’ll say, “BC has the third most/least X in the country” (as compared with the other nine provinces).

    Such a factoid presumes two things: (A) that there is a significant difference between the highest and lowest, and (B) that because X is the most, it must, by definition, be too high, and if it is the lowest, it must be too low. In fact, it may be that, even though Canada, let’s say, gives the most per capita of any country in North America to fighting curable diseases in Africa, a moral philosopher still has the right to argue that we should be giving more. Meanwhile, even though a certain population may be the worst paid in their profession in the country, that doesn’t necessarily mean that, ethically, they’re underpaid. Maybe Canada as a whole pays a lot for that profession, and so even the tenth-rated province may still pay pretty well. Similarly, Shakespeare’s “worst” play isn’t necessarily bad. It may still be better than most of us could write.

    (E) “50% percent more”:

    Anytime someone compares an increase only by percentage, it’s likely that they realize the numbers on their own aren’t impressive enough to compel us. If, for instance, the Canucks are penalized six times compared to with the rival team’s four times in a hockey game, the difference doesn’t sound particularly significant. But our beloved GM Mike Gillis would prefer to say, “We were penalized 50% more times than the opposition!” Wow, that sounds like a lot!

    Percentage comparisons, I’m sure, can be useful, but when they’re used without the numbers to justify them, I can’t help wondering what the presenter of them is trying to hide.

    (F) “People who do X, tend to…”:

    I recently heard an advert on TV for multi-grain cereals stating that those who eat multi-grain foods tend to weigh less. Clearly, the cereal seller is hoping that we will notice this correlation and assume causation: “It must be the multi-grains that are causing those people to weigh less, so, if I eat them, there’ll be less of me, too!” In fact, of course, it may simply be that the person who eats multi-grains tends to care about their health, and so tends to do other things for their health as well – such as exercising more often – which in turn may be the actual cause of their leanness.

    Obviously, this correlation vs causation distinction—as with all of my examples—is no great epiphany. We all know that advertisers, politicians, and interest groups manipulate the numbers for their greater good. Moreover, numbers themselves will rarely be perfect given that the collectors of statistics can so easily over-focus on particular groups or ask leading questions. But at least the statistics’ governing body—the scientific method—aims in good faith to cull such errors in collection. In contrast, the quoting, referencing and emphasizing of particular statistics without considering their context and complexity seems to be occurring without a police officer. So, for the sake of promoting the integrity of statistics in general, I think it’s worth pointing out these deceptions whenever we see them so that the well collected and well-defined facts can stand out as the sincere creatures that they are.

    Posted by SethBlog @ 8:33 AM

  • 2 Responses

    • meggles Says:

      Thanks for the post! It always bugs me when I see outrageous stats on TV and always look for the angle. My favourite, is when their definition of something is more inclusive than we are aware.

      ie “20% of people have gone to work naked.”* My definition is ‘no clothes’, but their definition might be no sleeves or no socks.

      (*note to Seth, this stats was made up by me. Please don’t go to work without any clothes.)

    • SethBlog Says:

      Thanks for the comment, Meggles: (A) because I agree whole cranially with your annoyance with HADS (Hidden Artificial Definition Stats), and (B) because now I feel more comfortable going naked to work now that I now that I’m among 20% of the population.

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