Let's say you want to prove something horrid, but you can't. Like genetic differences in intelligence between groups. Of course no one knows what intelligence is, really, or race, for that matter. But you've got the benefit of already knowing that you want to prove that your race is superior. Now you've just got to be prepared to ask the 'tough questions' and prove yourself right. But the problem is there's no evidence. So you prove something else, and pretend it's the same thing.
So the authors of the Bell Curve set out to prove genetic differences in intelligence, and went out and measured differences in average IQ. What's IQ? A test that sample's an individual's ability to answer IQ test questions (whatever anyone says about it being representative, really representative, or really really representative, that's what it measures and what the hell else could it measure?) Are differences in IQ statistically significant? What's the standard deviation? Then they take the results and group them by 'race', a social construction that measures your place in the Euramerican racial caste system (and nothing else, again-- they didn't look at the genes of the people they were testing, because if they did they would have found no differences between the groups that were bigger than the differences between individuals within the groups). Then they took averages (which kind?) and compared them (deviation? Significance levels?). And they seriously think they're saying something about genetic intelligence?
The aim of their book is not to use statistics to handle uncertainty, but to peform enough calculations to convince you that they're smart enough to be doing something meaningful. They aren't.
To get back to logic for a second though, you might ask people interested in this question why they're pursuing it at all? Why not group people by height, and look for IQ differences? Why not group people by eye color or hair color?
Clearly because the social system does not have any consequences for people of different heights or eye colors, there are no political or policy implications, and there is no hierarchy of power to try and rationalize. But that's not a statistical issue, is it?