Is variation in human brain size related to mental functioning? It seems that the head size of human beings has evolved to be relatively similar, yet there is still some amount of variation. While I'm sure the correlation is not absolute, I read that larger heads do imply larger brains. 

Thus, my questions:


What is the correlation between head size and brain size?
What is the relationship between brain size and mental processing ability (e.g., intelligence, emotional responses to certain stimuli, reaction time, etc)? 
Why might these correlations exist or not exist?
One relatively recent review on this topic is Rushton &amp; Ankney (2009). They report that there have been a large number of studies with varying results:


28 studies, covering a total of 1,389 subjects, used brain imaging techniques to estimate the size of the brain. Correlations with general mental ability (GMA) ranged from 0.04 to 0.69, with an unweighted mean of 0.40. Weighting the correlations with the sample size produces a mean of 0.38.
59 studies, covering a total of 63,403 subjects, used external head measurements to estimate the size of the brain. Correlations with general mental ability ranged from 0.02 to 0.55, with an unweighted mean of 0.21. Weighting the correlations with the sample sizes produces a mean of 0.20.
6 studies used Jensen's method of uncorrelated vectors to distill g, getting a mean correlation of 0.63.


The last point probably needs some explaining. The g-factor, or g for short, is the quantity that IQ tests are designed to measure. The name "g factor" comes from the fact that it is a common, general factor which all kinds of intelligence draw upon. For instance, Deary (2001) analyzed an American standardization sample of the WAIS-III intelligence test, and built a model where performance on the 13 subtests was primarily influenced by four group factors, or components of intelligence: verbal comprehension, perceptual organization, working memory, and processing speed. In addition, there was a common g factor that strongly influenced all four. The model indicated that the variance in g was responsible for 74% of the variance in verbal comprehension, 88% of the variance in perceptual organization, 83% of the variance in working memory, and 61% of the variance in processing speed. In other words, if a person has a lot of g, then (s)he is likely to also get a high score on tests measuring all subtypes of intelligence. This is possibly because g is something in the brain that all the subtypes of intelligence benefit from. But note the word likely - the correlation is not perfect, so it's still possible to have a high g but be worse than average in some subtype of intelligence. It's just less likely than the converse.

Now experts might be cringing at that previous paragraph, because I talked about an individual having a lot of g. Technically, g is something that is computed from the correlations between various test scores in a given sample, and there's no such thing as the g of any specific individual. The technique doesn't even guarantee that g actually corresponds with any physical quantity, as opposed to something that the method just happened to produce by accident. So when you want to measure someone's intelligence, you make a lot of people take tests that are known to be strongly g-loaded. That means that the performance on the tests is strongly correlated with g. Then you take their raw scores and standardize them to produce an IQ score, so that if e.g. only 10% of the test-takers got a raw score of X, then anyone getting the raw score of X is assigned an IQ indicating that they're in the top 10% of the population. And although this still doesn't tell us what an individual's g score is, it gives us a score that's closely correlated with g. IQ also seems to predict a large number of things like life outcomes and performance in a variety of tasks and so forth. See e.g. Jensen (1998) for (much) more on this.

So now that I've explained all that, what does the "6 studies used Jensen's method of uncorrelated vectors to distill g" bit mean? Well, if I'm understanding the paper right, then the 28 + 59 other studies calculated the correlation between brain size and IQ. In other words, between brain size and performance on some particular intelligence test, that ultimately measures performance on one or more subtypes of intelligence. Subtypes which are closely, but not perfectly, correlated with g. The 6 studies were different in that they attempted to calculate the actual correlation between g and brain size, which is different from the correlation between IQ and brain size. Which one is better? Here I must admit that my expertise isn't sufficient to answer the question confidently, but I'd suppose that it depends on what you're trying to measure. If you want to know the extent to which the common factor influencing all the subtypes of intelligence varies between brains, then you want to use the estimate where g has been extracted. If you want to know how much brain size seems to correlate with mental ability in practice, you might want to use the correlation with IQ. Neither is more correct than the other.

Other findings from the paper:


The brain volume–GMA correlation is equally strong in males and females.
It is also found in people of East Asian, East Indian, European, Turkish, African, South American, and Amerindian descent.
Studies using a narrow age range of younger or older samples show the same magnitude of correlation.
Many studies appear to show that the size effects are manifest throughout the brain and not specific to any particular region; however, other studies show GMA centered in the frontal brain regions. Two studies found support for both positions - the more g-loaded subtests were distributed throughout the brain but concentrated most in the frontal lobes.
The correlation between head size and GMA is found both within families and between families. From the paper: "the within-family finding is of special interest because it controls for most of the sources of variance that distinguish families, such as social class, styles of child rearing, and general nutrition, that differ between families."
Body size and brain size are correlated. The average correlation is 0.2 for MRI studies, or 0.3-0.4 for studies that use skull measurements. But body size and GMA are also correlated, at around 0.20-0.25. There is disagreement about whether the size of the body should be controlled for when estimating brain size/GMA correlations, but a correlation is found regardless of whether or not body size is controlled for. In other words, both relative and absolute brain size are correlated with IQ.
The brain size/intelligence correlation is also found in non-human animals, both within a species (e.g. rats) and between different species (e.g. species of birds, species of primates).
Brain size is also environmentally sensitive: for instance, rats raised in complex environments have thicker cortices and larger brains than rats reared in impoverished environments.
The paper also reviews results showing that brain size and GMA are correlated with age, socioeconomic position, sex, and population group differences, but those aren't relevant for the question so I won't go into them here.


References:

Deary, I.J. (2001) Human intelligence differences: a recent history. Trends in Cognitive Sciences, 5, 127–130.

Jensen, A.J. (1998) The g Factor – The Science of Mental Ability. Praeger.

Rushton, J.P. &amp; Ankney, C.D. (2009) Whole Brain Size and General Mental Ability: A Review. International Journal of Neuroscience, 119(5), 692-732.