Yes, and it's the same arguments nearly every time. I do not know if that is because of particular strains of misinformation being out there or because people's intuition about the issue leads them down instinctive paths of reasoning. Your post is great and covers pretty much the whole gamut of issues typically brought up with IQ, so I will try to keep what could perhaps be added short.
(This post turned out long after all. Sorry.)
These seem to be the most common questions that come up:
1.) How can you express something as complex as intelligence in a single number?
2.) Why do measures over such large populations matter when we only directly deal with individuals?
3.) Why does intelligence matter if there are so many individuals that are more successful than many with higher IQ?
4.) How can we measure something so fundamental about the brain when we still understand so little about it?
5.) IQ is just an arbitrarily defined metric - how can it tell us anything meaningful or be used to compare people?
This post already turned out long, on an older thread, so I’ll only try to answer 1.) primarily. Answers to the others can probably be inferred from parts.
How can you express something as complex as intelligence in a single number?
I do not think we should find this surprising. There are far more complex things that we summarize into a single or a few numbers. And that number does not fall from the sky, either, or is an oversimplification because it is a single number. It is a summary of a variety of complex tasks. You mention WAIS and WISC already, so everybody is free to look up the kind of tests being used:
(I do not have a better link to a free download as the full manual, from official sources, is about $250. There are several scribd downloaders that can grab the whole file.)
An intuitive way one can think of IQ scores is to liken it to a benchmark for a computer, perhaps (I am aware, though, that this analogy will probably break down if over-stretched and humans cannot be assembled from modular components like PCs). How would you go about comparing the speed of different PC configurations, as there are a huge number of possible combinations and hardware around? What tests would you use for comparison, as you cannot possibly test all available software in existence?
What you would likely do is run a few programs that are particularly representative of a particular performance aspect, such as floating point arithmetic, memory throughput, storage and so forth. Those scores you then summarize into a number for comparison. The underlying system is still very complex and there might be many aspects you do not understand about modern architectures, such as pipelining, hyper-threading, branch prediction, etc. but your goal is to abstract from all these details.
Your friends might now ask: “How can you possibly measure something as complex as computer with a single performance score?” What would you do to convince them of the usefulness of your score is how well it predicts what you are interested in, i.e. how fast their games run, in terms of FPS, perhaps. You can see how good your score is by how well it correlates with what you wish to predict. It does not matter, for the most part, that you are not an engineer at Intel who can design a modern RISC CPU from ground up. If you were to test a car, it sure helps to know a little about cars, but you do not need to be able to build an engine to perform meaningful tests on cars.
You still express a whole bunch of complexity in a single number. I see a lot of references to statistics in this thread, so I am surprised there is so much pushback against a concept that is practically just a factor analysis. It does not matter that you get a single number or a few factors in the end. What matters is how well that set of factors correlates to the metric you are interested in, how much of the variation the set of factors predict. What we are interested in, cognitive performance on g-loaded tasks, is very well correlated, based on available studies. This has been alluded to already and it is what is often referred to as the observation that performance on particular tasks is on a so-called “positive manifold", and, according to Spearman's hypothesis, can be expressed as the g-factor, i.e. if you are better than someone else on one g-loaded task you are likely to also be better on all g-loaded tasks.
Spearman, Charles. “‘ General Intelligence,’ Objectively Determined and Measured.”
The American Journal of Psychology 15, no. 2 (1904): 201–292.
What the g-factor might represent is something like a metric how well your brain works. That would be consistent with IQ even strongly correlating with factors that seem to have nothing to do with intelligence at all, such as the already mentioned reaction speed, but also color acuity. The higher your IQ, the higher your color acuity typically is (r=-0.68, between total error score and verbal IQ):
Cranwell, Matthew B., Bradley Pearce, Camilla Loveridge, and Anya C. Hurlbert. “Performance on the Farnsworth-Munsell 100-Hue Test Is Significantly Related to Nonverbal IQ.” Investigative Ophthalmology & Visual Science 56, no. 5 (2015): 3171–3178.
Woodley of Menie, Michael A., and Heitor B. F. Fernandes. “Showing Their True Colours: Possible Secular Declines and a Jensen Effect on Colour Acuity — More Evidence for the Weaker Variant of Spearman’s Other Hypothesis.” Personality and Individual Differences 88 (January 1, 2016): 280–84. https://doi.org/10.1016/j.paid.2015.09.009.
Take an example test here:
https://www.colormunki.com/game/huetest_kiosk
(It’s probably not perfect because a bad screen can give you an unfair disadvantage. Obviously, if there is something wrong with your vision, this would not be a good metric, either.)
But here is where the confusion sets in: this applies to g-loaded tasks. There are many tasks that might require huge amounts of memorization (some memorization abilities do correlate with IQ) or some that are not g-loaded, but which we commonly associate with "being smart", where aspects of endurance, motivation, and character are more decisive than your IQ. But that is not a shortcoming of IQ, that is a misunderstanding of what constitutes intelligence, or what we mean by the word in different contexts. Chess, for example, is apparently less g-loaded than often portrayed in popular culture, so, even though it's an advantage to be more intelligent in chess, other factors, possibly related to personality, might outweigh pure IQ differences.
There is also misunderstanding how much IQ must have some direct biological correlate in order to be useful or valid, which is sort of expressed when asking how we can measure when so much of the brain’s structure remains unexplored. In order for a construct to be valid (referred to as “construct validity”), however, it does not mean that IQ cannot simply be a purely psychometric artifact. In principal component analysis, for example, a mix of features that correspond to the original aspects being measured can be subsumed in a single eigenvector and that eigenvector has a corresponding eigenvalue, which roughly speaking corresponds to the contribution the component makes to the overall variance of the underlying data. But the principal component itself might be largely meaningless (from the perspective of being interpretable as a directly observable aspect of the object measured) and have no intuitive unit associated if taken as a metric, like mile, pressure, or weight. But depending on how much variance of the data it predicts, it can tell you how good of a measure it would be if it stood in for the original data. The eigenvalue can be a completely arbitrary number (technically it need not even be normalized I think), yet, it is dismissive to just say that it is an oversimplification of a complex system because we chose to express a highly predictive and representative aspect as a single number.
Examples to play with yourself:
https://wilkelab.org/classes/SDS348/2016_spring/worksheets/class9.html
https://stats.idre.ucla.edu/r/dae/canonical-correlation-analysis/
I am only using PCA as an example, not making a statement about how appropriate it would or would not be for FSIQ in WAIS, WISC, etc. Similar illustrations could probably be made with canonical correlation analysis (CCA) and other methods of factor analysis or construct validation. But it also illustrates that there is room for other factors, where Big Five Personality (NEO, MMPI, etc.) might come in. You can test that by looking at how much variance is explained by your model, how much these additional factors add to the predictive accuracy of your model.
Last but not least, why should we expect there to be a single factor of general intelligence in the first place? That is actually a question that people who defend the use of IQ do not explain well. In fact, there is no good reason to simply assume that and studies on animal intelligence have actually shown that some species might show a much stronger clustering of abilities. Spearman’s hypothesis might not apply universally. Chimpanzees, for example, might have such a clustering. Mice, on the other hand, appear to have general factor of intelligence similar to humans and it seems to explain a similar size of variance in cognitive performance.
I did not go into the basics of distributions. There are many people, even policy makers, who either pretend to or do not understand that a statement about a group or statistic does not allow one to make direct determinations about individuals. But here is a calculation example:
Assume that a population has a mean IQ of 85 with a standard deviation of 15. That would mean that (1-pnorm(120,85,15))*100 ≈ 0.98% of such a population would have an IQ above 120 (use the cumulative distribution function of the Gaussian distribution and subtract it from 1.0 to obtain the portion above the upper limit of the integral). If you had a population of a million, there would still be about ten thousand such individuals. Some R code for that here: https://ideone.com/EtxYKl.
Another frequent question is to ask why any of that is useful for dealing with individuals. It is not. But we do not exclusively deal with individuals. That is like asking why statistics or sociology are of relevance. When you deal with groups of people, you use a level of analysis that is appropriate for groups. When you deal with an individual, you use a level of analysis that is appropriate for individuals. For example, if you were to design a seat for a car, complete with seatbelt, it would be useful to know how potential drivers are distributed according to weight and height. You would be interested in such statistics as mean weight/height, standard deviation/variance, and p-values of a given confidence interval to be reasonably sure your car is safe. When you have someone come in for an interview, it would be silly to pull out population statistics of the town they were born in. You would use metrics that are more applicable to an individual, such as academic achievement, university attended, years of experience and so forth. But that does not mean statistics are unimportant. Far too often are they misused and any difference in (statistical) outcome is used as evidence for discrimination. For that reason alone it would be good for us to accept population differences in IQ, if there are such differences, and stop chalking up every disparity to evil racists.
And because it is a distribution there are naturally also outliers like Kim Peek, who was able to perform incredible feats of memorization but does not measure very high on IQ tests, consistent with his general difficulty to navigate common life situations autonomously:
https://www.youtube.com/watch?v=36K1HQvUdWg
But outliers are not evidence that statistics is wrong, nor is it evidence that it's not useful. It can also certainly be unfair to an invidividual. Work some time at an insurance company. Some teenagers might be perfectly safe drivers, but if you have a large population of people, it is in your financial interest as an insurance company to do a good job on estimating the probability that a given driver, absent of a long driving record, is going to get into a car accident you might have to pay out for.
Matzel, Louis D., and Stefan Kolata. "Selective attention, working memory, and animal intelligence." Neuroscience & Biobehavioral Reviews 34, no. 1 (2010): 23-30.
Deary, Ian J., Steve Strand, Pauline Smith, and C. P. D. Fernandes. “Intelligence and Educational Achievement,” 2007. https://doi.org/10.1016/j.intell.2006.02.001.
Reynolds, Matthew R. “Interpreting the g Loadings of Intelligence Test Composite Scores in Light of Spearman’s Law of Diminishing Returns.” School Psychology Quarterly 28, no. 1 (2013): 63–76. https://doi.org/10.1037/spq0000013.
Rushton, J. Philippe. “The ‘Jensen Effect’ and the ‘Spearman-Jensen Hypothesis’ of Black-White IQ Differences.” Intelligence 26, no. 3 (1998 ): 217–225.
