People in posts and comments still seem to be confused about heritability (esp. compared to inheritability), and how these relate to the discussion about intelligence. I'm going to do my best not to wade into that discussion much, but hopefully this will provide a good reference point.

Some Basics - Normal Distributions (Bell curves)

A "normal" distribution is the fancy statistical term for data where, if you plot it as a histogram, it makes a bell curve (if you don't know what a histogram is, this is going to be tough to follow - this video from kahn academy is a pretty good primer).

There are basically two properties that describe a normal distribution - the mean and the standard deviation. Since we're talking IQ tests, we know they're normalized to a mean of 100 and standard deviation of 15, so IQ scores look like this:

histogram1

The variance is directly related to the stdev - it's not really important for this, but basically, high variance means high stdev and vice versa. In terms of our histogram, a normal distribution with low variance is skinny, and one with high variance is wider. So if our standard deviation for an IQ test were 5 instead of 15, it would look like this:

histogram2

Got it? Great! Let's talk heritability.

Heritability

Heritability is a measure of variance in a population that's explained by ancestry. I think the easiest way to think about this is to consider how the histograms would look if we plotted a genetically diverse sample versus a genetically homogenous (similar) sample (this is sort of how twin studies work).

Let's consider two traits - trait A is highly heritable, trait B is barely heritable. For trait A, since a lot of the variance we see is attributable to genetics, if the population we measure is genetically homogenous, the measured variance is substantially lower than if the population is diverse.

histogram3

For trait B, there's not much influence of genes, so whether we look at genetically diverse or homogenous populations, we see roughly the same variance.

histogram4

The crucial point here is that "heritability" does not tell us anything about the extent to which the trait is "genetic" in the sense that I think most of us think about. In another thread, someone used an example I liked - the number of fingers on people's right hand has very low heritability*. There's almost no variance, but where people have 4 or 3 fingers, that's almost never because of their genes. In other words, almost none of the variance is explained by inheritance.

Another example - if we measured the number of letters in a person's last name, there's a wide variance. Almost all of that variance is explained by who the person's parents are**, so it's highly heritable, but certainly not genetic.

Spurious Conclusions

So here we get to the meat of the problem, in my view. First, the things we know and that (it seems) basically everyone agrees on:

1. IQ scores in a random sample of humans is normally distributed.
2. IQ scores are heritable to a large extent.
3. The mean IQ score for people who self identify as black is lower than for people that self identify as white.

But, given these facts, we are left unable to make any claims about the extent to which any difference measured between populations is due to genetics. We also can't say that the variance within a given subpopulation is the same as within a population as a whole. In fact, particularly if intelligence is highly heritable, we would expect it to be different.

An example of a possible outcome that I think is a bit unintuitive: even given the facts above, it could be that there are a substantial number of black people that have much higher IQs than the smartest white people, and that there are very few white people of exceptional intelligence.

At one point, I read that people with recent (within the last 500 years) African ancestry are more genetically diverse than people of European ancestry. I didn't look for the citation, but this also makes sense intuitively.

If true, you'd expect that the variance in intelligence for black people to be higher and the variance for white people to be lower. Here's one possibility:

histogram6

I want to emphasize here that I'm not saying the plot above is correct, I'm saying that its entirely consistent with the facts stated above.

It's also completely possible that, while IQ scores are normally distributed in a random sample of humans, it's not randomly distributed for sub-populations. For example, the IQ plot could be bimodal, such that there's a subgroup of black people have a mean IQ similar to that of whites, while all others have substantially lower IQs. Again, I'm not saying this is true, just that it could be. And it need not be the case that the same pattern will hold for all racial groups (eg, it may be that the IQs of white people are not bimodal in the above scenario).

Finally, the part that's been most muddled in the conversation since Murray's podcast: even if we assume that sub populations all have normally distributed intelligence, and there's similar variance within subpopulations, along with the three facts I listed above, it need not be the case that any of the difference between black and white people has a genetic cause. In other words:

histogram7

Sure, as Sam said in the last podcast:

It would be a miracle if the mean value for any heritable trait were precisely the same across two genetically distinct populations generation after generation.

But the following would be entirely consistent with the data that I've heard and seen posted here (again, not saying this is correct, but...): black people are genetically predisposed to have ~5 point higher IQ than white people, but growing up experiencing racism on average decreases IQ by 20 points.

This is obviously extreme, and I doubt it's true, but it highlights the point. What would we observe if racism accounted for a large proportion of the IQ difference? It would look entirely genetic! We'd find genetic signatures in genes for melanin, and in hundreds of other alleles that are associated with recent African ancestry.

Conclusions

Again, my intention is not to make any claims about the links between genetics and race, but merely to clarify what the facts actually mean. Hope this helps.

* It's worth noting that the number of fingers is not normally distributed, but the point holds.
** Assume here we're talking about the last name on your birth certificate to avoid complications about name changes in marriage. Also, if you did a twin study you wouldn't see differences between fraternal and identical twins. The type of measurement matters!