When the mighty Sherlock Holmes wasn’t too busy torturing violins, dosing himself with opiates, or punching people off Swiss waterfalls, the world’s greatest detective would occasionally deign to share his investigative methods with the unenlightened. Indeed, in his very first short story he points out that, “It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.”
The 19th Century Scotsman, Andrew Lang, thought along similar lines, warning of those who use statistics "...as a drunken man uses lamp-posts - for support rather than for illumination”. In other words, there are far too many people who use statistics to comfort rather than challenge, and to confirm prejudices rather than question them. Such people are twisting the facts to suit the theory.
Little has changed in the last hundred years. Indeed, the mighty tool by which these very words reach you has made the situation rather worse. If sticking a pin in the metaphorical map of the internet is most likely to reward the curious with a disturbing dose of brain-searing pornography (if the web had a shuffle function, using it would burn out your eyes within the first month), then surely the runner-up slot can be claimed by the legion of feckless mouth-breathers who twist statistics to breaking point to justify their lunatic dogmas. Let's call it Rule 35: if you can imagine a position, then somewhere on the internet someone will be offering numbers they insist mean that that position has been "prooved by sciense!"
Naturally, this is something of a concern. There is something much worse than using statistics as a comfort blanket, though, and that's using it to deliberately garrotte the truth. A sprinkling of knowledge amongst ignorance can be dangerous. A sprinkling of honesty amongst lies can be deadly.
Columnist and author Jonah Goldberg is not the first such mass-murderer of statistical laws, nor is he the most adept at hiding the truth behind curtains of decimal points and percentage signs. On the other hand, his LA Times article from last Tuesday is truly remarkable in at least two respects: the malignancy of his apparent intent; and the breathtaking lack of interest he shows in even attempting to disguise his various sleights of hand.
First, we need context. This is indirectly about the “Ground Zero Mosque” controversy. For those who haven’t heard about this, let me summarise. A recent decision to grant planning permission for a Muslim community centre two blocks from the gaping hole in Manhattan where the Twin Towers once stood has started a tempestuous discussion as to where exactly Muslim Americans stand in the glorious patchwork of the United States population. Are they a) US citizens with the exact same rights, privileges and responsibilities as every other American, b) Islamofascist quislings waiting for the white family next door to drop their guard so as to slaughter them with scimitars in a halal-friendly fountain of infidel’s blood, or c) much akin to welcome house guests, who we’re really glad are here and everything, but who still have to take their shoes off and use the right towels because that’s just how we do things around here?
According to the polls, there are a truly dumbfounding number of people who don’t believe the answer is a) (the latest figure puts the percentage of Americans who have at least a “somewhat favourable” view of Islam at under 50%). That means there is significant business to be done in reassuring the majority of the population that they’d never be the kind of person who could secretly believe b). No, sir, they’re all about that c), right there. Never mind that the latter answer is just the same bigotry wearing a somewhat prettier hat, and that anyone who offers it as some kind of compromise is a cowardly hack; there will always be a lot of money to be made in giving rank ugliness a nice coat of shiny varnish.
The only way to understand Goldberg’s article (and believe me, it is absolutely the only way) is as part of this process. His is an ancient role, as old as propaganda itself: to persuade the man holding all the aces that his opponent has been dealt three times as many cards.
His argument begins, as these things so often do, with something that sounds reasonable as long as you don’t think about it too much:
“According to the FBI, hate crimes against Muslims increased by a staggering 1,600% in 2001. That sounds serious! But wait, the increase is a math mirage. There were 28 anti-Islamic incidents in 2000. That number climbed to 481 the year a bunch of Muslim terrorists murdered 3,000 Americans in the name of Islam on Sept. 11.
Now, that was a hate crime.”
I need to make something absolutely clear before we go any further: using statistics to argue one kind of hatred or tragedy is worse than another is an absolutely horrible thing to do. Indeed, trying to make those comparisons at all is something to be avoided if at all possible. How do we judge if over a century of slavery was worse than the six years of the Holocaust? Exactly how many incidents of naked anti-Muslim aggression would Goldberg consider equivalent to the destruction suffered on 9/11? These questions have no answers. Such man-made tragedies are both too profoundly personal and too incomprehensible in their scope to allow a comparative measure. Irrespective of the specific nature of the hate crimes the FBI list, there is something distinctly unpleasant about Goldberg arguing that since over nine years 1377 is still less than 3000, Muslims have gotten off easy.
So please, don’t under any circumstances interpret what follows as an attempt to prove that the truth proves anti-Muslim sentiment is actually worse than 9/11. That is not something I – or anyone else - can do. What I can do is point out that even once you get past Goldberg’s initial unsettling, distasteful framing, he still needs to rely on misrepresenting the statistics to try and persuade people of his case.
Actually, I’m not even sure the numbers he wields count as statistics at all. Giving this shower of deliberate buffoonery that name is like describing the Spanish Inquisition as lacking a sense of humour, or labelling the Hindenburg disaster an interruption to the flight schedule. Or calling Jonah Goldberg a thoughtful writer. It takes a unique form of chutzpah to lie with mathematics in an attempt to show that mathematics is lying. It’s the sort of thing Harry Mudd would use to short-circuit an android’s logic circuits.
Regardless, in the quote above, Goldberg is taking a valid point and twisting it into a ludicrous new shape. It is certainly true, for example, that if something happened once last year, and twice this year, running around screaming about a 100% increase is pretty ridiculous. In other words, it’s bad form to misrepresent small absolute changes by reporting them as large relative ones.
Hate crimes against Muslims did not double after 9/11, though. They increased sixteen-fold. They’ve now settled back down to four times what they were before (assuming 2000 wasn’t a particularly good year for Muslim relations in the US). And that’s not some random variation that it would be unfair to compare to what preceded it. That’s the new status quo.
There are ways to measure whether this is a statistically significant change or not. In an earlier article I explained how one can measure probabilities for situations in which you have a known number of identical trials, each one either succeeding or failing. So, for example, you could take the trials as being a year in the life of each of the 1.8 million Muslims living in the US today, and call it a success when they go through a full year without reporting a hate crime directed against them. Would an increase from 28 failures to 112 constitute anything but a random fluctuation? Put another way; is there any reason to believe the increase in hate crimes is genuinely due to 9/11? Or are the vagaries of chance to blame, like how seeing no squirrels one day and seeing four the next doesn’t mean the furry little bastards have been cloning themselves in treetop labs as they prepare to overthrow humanity.*
Well, let’s test it. According to Goldberg’s figures (which I have some reason to doubt, but we’ll come to that), the chance of a Muslim reporting a hate crime in 2000 was 0.0016% (that’s assuming one victim per hate crime, which is admittedly a shaky proposition). We can ask ourselves: if we assume that chance didn’t change after 9/11, i.e. there was no more hatred of Muslims after that event than before it, and there is a “math mirage” at work here, how likely is it that there would be as many as 112 reported hate crimes two years later?
We can use the binomial distribution to discover this (or rather, an approximation to that distribution). We simply assume the chance has stayed at 0.0016%, and check how likely, given that chance of failure, we would see 112 failures or more (I suspect I will discuss this technique, known as hypothesis testing, in more detail in a later article, so you can check I’m not pulling a trick of my own).
Trying to do the calculation broke the program I was using. It just wasn’t able to deal with such a small chance. It could tell me that an increase from 28 to 60 could happen without the underlying chance of reporting a hate crime changing. What are the odds of that actually happening? One in a billion.
In other words: no fucking chance, mate.
Of course, I’m not blind to the fact that 112 crimes a year in a country the size of the United States is far less than one might expect – though once again I’d be uncomfortable giving a value to the number of such crimes I’d deem “acceptable”. Regardless, in the second part of this article I shall talk more about about how to interpret that number. I’ll also dissect Goldberg’s claim that anti-Jewish hate crimes are six times more common than those targeted at Muslims. Then in conclusion I’ll move beyond the structure of mathematics (because analysis without statistics is no more dangerous than analysis with statistics alone) and make some more general points about the fraudulent message Goldberg and his allies are pushing.
*Humour, to lighten the mood.