Different River

”You can never step in the same river twice.” –Heraclitus

June 15, 2006

How Hated Are You?

Filed under: — Different River @ 2:32 am

Clayton Cramer, and one of his readers, together have what makes a fascinating analysis of the FBI Hate Crimes data.

The report says, for example:

Law enforcement agencies reported 4,863 offenses within single-bias incidents that were motivated by the offender’s racial bias. Among those offenses, 67.5 percent resulted from an anti-black bias, and 20.5 percent were due to an anti-white bias.

Clayton analyzes:

At first glance, the high number of crimes that “resulted from an anti-black bias” suggests that racism against blacks is a bigger problem than racism against whites. But spend a little time thinking about these numbers. In 2004, blacks were 12.8% of the population; whites were 80.4% of the population. Unless some of these hate crimes against blacks were being done by blacks (which seems rather unlikely), this means that the hate criminals came from the 87.2% of the population that are non-black, and these hate criminals committed the 67.5% of the racially based bias crimes that were designated as anti-black.

Similarly, the white haters must have come from the 19.6% of the population that are non-white Americans, and these criminals committed the 20.5% of the anti-white racial bias crimes.

Non-whites are thus more likely to commit anti-white crimes than non-blacks are to likely to commit anti-black crimes. This suggests that anti-white hate crimes are disproportionately present. Not quite what you were expecting, is it?

Let’s define a ratio of “potential sources of hate crimes” to “percentages of hate crimes” and you get what I call the “How Hated Are You?” Ratio. Divide 67.5% by 87.2%, and you discover that blacks are the victims of racial bias crimes only 77.4% of the amount that you would expect if racial hate crimes was evenly distributed. On the other hand, 20.5% divided by 19.6% gives 105%–whites are slightly more likely to be victims of a racially based hate crime than you would expect for their numbers.

In short, the HHAY percentage, if it is below 100, indicates that you are victims of a hate crime less than you might expect, relative to the percentage of the population that isn’t a member of your group. If your group’s HHAY percentage is above 100, then your group is receiving more hate crimes than you would expect.

Clayton reports that a(n unnamed) reader looked at the problem from the other direction — the percentage of each group that becomes a victim of hate crime, rather than the percentage that commits a hate crime:

It seems to me your “How hated are you” statistic does a poor job of measuring the actual problems caused by hate crimes for different groups. For example, using the figures you give, 67.5% of 4863, or 2164 crimes were motivated by anti black prejudice and only 20.5%, or 997 were motivated by anti-white prejudice. But 12.8% of the population (let’s call the US population 250 million, though that’s a bit out of date) is black, or 32 million people, while 80.4 %, or 200 million, is white. So a black person has a probability of 2164/32000000=0.000068 of being a hate crime victim in a given year — 17 times the odds of 0.000004 that a white person does. It seems to me reasonable to say that hate crimes are 17 times as significant a problem for black people as for white people.

What your HHAY statistic measures is the probability that a randomly chosen person of a different race will have committed a hate crime against someone of your nationality. It seems to me that, if I were given a chance to choose my race, this would matter much less to me than the odds that I would be a hate crime victim. (Or, for that matter, a crime victim of any sort.)

It is strange that black people are both more likely to commit and to be the victims of hate crimes than white people are, but I guess that’s just a nice example of how statistics don’t always do what you’d expect.

Actually, I’m not sure that we shouldn’t expect precisely that results. Blacks make up about one-eight o the U.S. population, which means there are about 7 non-Blacks for every Black. That means that even if a much lower percentage of non-Blacks commit hate crimes, there can still be a lot of anti-Black hate crimes simply because there is a much larger pool of non-Blacks. In fact, non-Blacks will commit more hate crimes (in absolute numbers, not percentages) as long as their rate is greater than one-seventh of the Black hate crime rate. Furthermore, since there are far fewer Blacks “available” to become targets of each hate crime, then for any given number of hate crimes, the probability of any one individual Black becoming a victim is much higher.

To take an extreme example, imagine for a moment that Blacks and non-Blacks each committed, as a group, precisely the same number (not percentage) of hate crimes. In that case, each Black individual would be both seven time more likely to be victim of hate crime — and seven times more likely to commit one. Even if the rates are closer together, as long as the percentages of non-Blacks commiting hate crimes is lower than that of Blacks, we will see something like this outcome.

So the figures that Clayton and his reader found are in fact precisely how you should expect the statistics to come out.

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