Wednesday, November 28, 2012
Correlation coefficients as angles
Harry Altman has an interesting piece over at Less Wrong suggesting that it makes more sense to think of correlation coefficients as angles. To many people a correlation coefficient is nothing more than a number between -1 and 1 which shows in some easy to quantify but hard to intuit way of how related two variables are. Harry's suggestion gives a useful way of thinking about them and is worth a read.
Saturday, June 2, 2012
Conservatism, racism, and stupidity
A recent study argues that there is a correlation between racism, political conservativism, and stupidity. More intriguingly, the study claims that this is not just a correlation but an actual causal link, with the third causing the other two. The study is not at all persuasive.
Not surprisingly, this sort of thing produces a fair bit of discord. From the abstract:
While the claimed result is fairly moderate, bloggers on the left end of the political spectrum quickly jumped on the study, with one stating:
Many simiar comments ignored the fact that the main part of the study took place in the United Kingdom while the traits mentioned above tend to be more highly associated with American conservatives. This isn't too surprising since few people actually linked to the actual study but apparently got their information from secondary news sources.
Commentators elsewhere on the political spectrum have not been much better, dismissing the study as more liberal propaganda rather than actually addresssing the questions that the study raises.
One of the most substantive responses came from William Briggs. Judging from Briggs's remarks he has over advantage over many of the commentators: he has apparently read the study in question. While most of Briggs's criticism is superficial, minor or unfair, he does have some valid points.
Briggs's first criticism is that only parts of the intelligence test data was used. He is correct to note this. The apparent implication is that the omitted data would if included undermine the claim in question. While it might be interesting to look at that omitted data, there is a prosaic explanation for the exclusion of this data: The removed tests are for aspects of reading and math ability which are more function of education and background, and are not as useful indicators of actual cognitive ability.
Briggs also criticizes as badly phrased the questions used to measure social conservativism:
There's such as a thing as the framing effect, where the phrasing a question can influence how people will answer the question. However, in this particular case, neither question seems obviously more biased to me. Moreover, even if there is some form of framing effect here, that should alter the overall percentage who answer one way or another, there's no reason it should impact whether conservatism and intelligence will be correlated. If any readers can construct a hypothesis about how framing would have a disparate impact, I'd be very interested in hearing it.
Briggs also complains that the intelligence measure used a latent variable, g, for which he felt a need to put in scare quotes. While Briggs might be unhappy with such a variable, the existence of a general fluid intelligence is well documented, going back to Charles Spearman's work around a hundred years ago. Psychometricians have a good understanding of how g and similar variables behave. While the g here is not precisely identical to Spearman's g, the existence of such an underlying factor is essentially uncontroversial.
By far the best criticism that Briggs makes is to question whether the results are genuinely statistically significant. There are some subtleties with whether their p values are correct, and Briggs is correct to note potential issues there. However, the real problem is as Briggs observes, that the actual impact of intelligence on the issues in question is tiny.
What Briggs does not discuss in detail is that the second part of the study, which analyzes attitudes towards gays and intelligence levels in the US sample, showed a much stronger and more clear correlation between intelligence and attitude. The data for the attitudes towards gays isn't original to this paper but comes from a previous paper by a different author which showed a correlated between intelligence and greater acceptance of gays. While this paper does try to construct a causal model, the model is complicated and not convincing. However, the weak nature of their model doesn't reduce the fact that the prior paper's data is quite strong.
Despite all this, I think that the conclusion that, within the US self-identified liberals are on average smarter than self-identified conservatives is correct. That conclusion has nothing to do with these two papers but is based on other sources. The General Social Survey shows a strong correlation between larger vocabulary (which is highly correlated wit a variety of intelligence metrics) and liberalism. The actual pattern in the GSS data is actually a bit more subtle: smarter people are in general more likely to have extreme political views than dumber people, and smarter people more likely to have liberal views. Essentially, as intelligence increases, the distribution of political opininon becomes more bimodal and moves to the left. This is part of a general pattern in the US that I've discussed before - moderates are stupid and ignorant. The GSS isn't the only place one sees these twin patterns.
However, neither of these two trends is strong. Both these trends occur in large samples. They are true only on average. At an individual level, the differences are simply not that large. Moreover, the marginal popularity of a set of viewpoints among more intelligent individuals is not by itself a strong argument for their correctness. Some memes may be more appealing to intelligent people regardless of their validity, and memetic founder effects could easily cause ideas to be associated with certain populations.
Not surprisingly, this sort of thing produces a fair bit of discord. From the abstract:
We proposed and tested mediation models in which lower cognitive ability predicts greater prejudice, an effect mediated through the endorsement of right-wing ideologies (social conservatism, right-wing authoritarianism) and low levels of contact with out-groups. In an analysis of two large-scale, nationally representative United Kingdom data sets (N = 15,874), we found that lower general intelligence (g) in childhood predicts greater racism in adulthood, and this effect was largely mediated via conservative ideology. A secondary analysis of a U.S. data set confirmed a predictive effect of poor abstract-reasoning skills on antihomosexual prejudice, a relation partially mediated by both authoritarianism and low levels of intergroup contact. All analyses controlled for education and socioeconomic status. Our results suggest that cognitive abilities play a critical, albeit underappreciated, role in prejudice. Consequently, we recommend a heightened focus on cognitive ability in research on prejudice and a better integration of cognitive ability into prejudice models.
While the claimed result is fairly moderate, bloggers on the left end of the political spectrum quickly jumped on the study, with one stating:
Wait a minute. You’re saying the people who almost all believe a Canaanite Jew rose from the dead 2,000 years ago, who deny global warming, who deny evolution, the people who think losing in court is a better use of money than education, who think letting people love who they wish is destroying America, who think not educating children about sex prevents pregnancy or disease…the study concludes that those people tend to be dumb?
Many simiar comments ignored the fact that the main part of the study took place in the United Kingdom while the traits mentioned above tend to be more highly associated with American conservatives. This isn't too surprising since few people actually linked to the actual study but apparently got their information from secondary news sources.
Commentators elsewhere on the political spectrum have not been much better, dismissing the study as more liberal propaganda rather than actually addresssing the questions that the study raises.
One of the most substantive responses came from William Briggs. Judging from Briggs's remarks he has over advantage over many of the commentators: he has apparently read the study in question. While most of Briggs's criticism is superficial, minor or unfair, he does have some valid points.
Briggs's first criticism is that only parts of the intelligence test data was used. He is correct to note this. The apparent implication is that the omitted data would if included undermine the claim in question. While it might be interesting to look at that omitted data, there is a prosaic explanation for the exclusion of this data: The removed tests are for aspects of reading and math ability which are more function of education and background, and are not as useful indicators of actual cognitive ability.
Briggs also criticizes as badly phrased the questions used to measure social conservativism:
When the kids became 33 and 30 year olds, they were asked whether they agreed with 13 or 16 questions like, “Schools should teach children to obey authority”, “Family life suffers if mum is working full-time.”
Another was, “People who break the law should be rehabilitated.” Just kidding! It’s actually, “People who break the law should be given stiffer sentences.” The bias in the question wording is ignored.
There's such as a thing as the framing effect, where the phrasing a question can influence how people will answer the question. However, in this particular case, neither question seems obviously more biased to me. Moreover, even if there is some form of framing effect here, that should alter the overall percentage who answer one way or another, there's no reason it should impact whether conservatism and intelligence will be correlated. If any readers can construct a hypothesis about how framing would have a disparate impact, I'd be very interested in hearing it.
Briggs also complains that the intelligence measure used a latent variable, g, for which he felt a need to put in scare quotes. While Briggs might be unhappy with such a variable, the existence of a general fluid intelligence is well documented, going back to Charles Spearman's work around a hundred years ago. Psychometricians have a good understanding of how g and similar variables behave. While the g here is not precisely identical to Spearman's g, the existence of such an underlying factor is essentially uncontroversial.
By far the best criticism that Briggs makes is to question whether the results are genuinely statistically significant. There are some subtleties with whether their p values are correct, and Briggs is correct to note potential issues there. However, the real problem is as Briggs observes, that the actual impact of intelligence on the issues in question is tiny.
What Briggs does not discuss in detail is that the second part of the study, which analyzes attitudes towards gays and intelligence levels in the US sample, showed a much stronger and more clear correlation between intelligence and attitude. The data for the attitudes towards gays isn't original to this paper but comes from a previous paper by a different author which showed a correlated between intelligence and greater acceptance of gays. While this paper does try to construct a causal model, the model is complicated and not convincing. However, the weak nature of their model doesn't reduce the fact that the prior paper's data is quite strong.
Despite all this, I think that the conclusion that, within the US self-identified liberals are on average smarter than self-identified conservatives is correct. That conclusion has nothing to do with these two papers but is based on other sources. The General Social Survey shows a strong correlation between larger vocabulary (which is highly correlated wit a variety of intelligence metrics) and liberalism. The actual pattern in the GSS data is actually a bit more subtle: smarter people are in general more likely to have extreme political views than dumber people, and smarter people more likely to have liberal views. Essentially, as intelligence increases, the distribution of political opininon becomes more bimodal and moves to the left. This is part of a general pattern in the US that I've discussed before - moderates are stupid and ignorant. The GSS isn't the only place one sees these twin patterns.
However, neither of these two trends is strong. Both these trends occur in large samples. They are true only on average. At an individual level, the differences are simply not that large. Moreover, the marginal popularity of a set of viewpoints among more intelligent individuals is not by itself a strong argument for their correctness. Some memes may be more appealing to intelligent people regardless of their validity, and memetic founder effects could easily cause ideas to be associated with certain populations.
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