Is being gay smarter?

An unserious statistics problem post

The following is an unserious Friday post, to pad a slow week. Also, apologies for being behind on reading and responding to yesterday’s comments.

I do still take a naive pleasure in basic thought problems — seeing through logical puzzles and statistical fallacies. Last week, Richard Hanania committed the former with the following twitter post, which itself was likely only an unserious troll designed to spur "engagement" anyway:

@RichardHanania (twitter.com)

Hanania's graphs are taken from a study which pursues the "Savanna IQ Interaction Hypothesis," a theory that anything evolutionarily novel requires intelligence to be preferred over whatever was the pre-civilizational default: Dumber people can only follow instinct, while smarter people can adapt to new options created by post-tribal social life. This study is Kanazawa, Satoshi. (2012).¹

The study, however, approaches this theory in a rather unsatisfactory way, which in fact leads to the fallacy Hanania commits in his tweet.

The inputs for this portion of the study are generated by asking a sample of young Americans whether they have heterosexual, mixed, or homosexual preferences, while also giving them verbal intelligence tests. But if the idea is that "being gay requires brains," then the analysis of these surveys which is useful would be "who said they were gay?," not "was more smartness associated with gay?" But, slave to notions that only statistically processed results are valid, Kanazawa only presents the answer to the latter question, resulting in the graphs Hanania shared:

The first big "problem" with this graph is that almost everyone has reported being heterosexual. "1.28" corresponds to a scoring system in which 1 is fully heterosexual, and 5 is fully homosexual: Thus, even among the "very bright," almost everybody is a 1. Of the whole group, only 472 individuals out of 14,955 individuals report being bisexual (a 3) or above. How many of those 472 are actually coming from the "very bright"?

More helpful is a second graph, which shows the portion of individuals who reported having ever felt attraction to someone of the same sex. This will be 1416 members of our same survey respondents:

So, in brighter groups, more people report feeling same-sex attraction. Does this support Hanania’s conclusion that gayness requires intelligence (“if you’re not gay, it might be because you’re too stupid”)?

By now, the reader perhaps sees the fallacy which has taken place in Hanania's tweet. It is given below the divide, for those who wish to first answer for themselves.

Answer

Since most people are not bright or very bright, it is actually not likely that a gay person will be a member of that group.

Hanania (and the original study's design choices) are laboring under the Base Rate Fallacy.

If all you know about someone is that they share a trait which is associated with a rare type of other trait (if "shy" is known, how likely is "librarian" compared to "salesperson"), this does not make it more likely that they also possess that second trait (librarian is unlikely, because it is a rare job). Just as e.g. 60% of 2% is less than 5% of 98%, knowing that someone has a trait common within a small group doesn't make it likely they are of that group.

In this study, given that individuals are sorted according to the same standard deviation-based score system used for IQ tests, it is rather easy to quantify our same-sex-attraction-feelers. Note that Kanazawa has chosen asymmetrical cutoffs for each category, with “normal” corresponding to 50% of all test scores:

This can be converted into a simple graph, visualizing the result that if a survey respondent is gay, there is a 70% chance they are not bright:

Corrected from original, which was missing “very dull”

Of course, if not gay, then there will be closer to a 75% chance that an individual is not "bright," given that "bright" is defined as being in the top 25% of test results. Yes, this is “higher” than 70; but doesn’t mean that intelligent people are not mostly heterosexual, almost just as much as unintelligent people.

This result, naturally, answers the question which should have been asked by this study to begin with. Never mind whether more intelligence is "associated" with reporting gay-ness: Who is actually gay?

If you derived value from this post, please drop a few coins in your fact-barista’s tip jar.

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1. Kanazawa, S. (2012). "Intelligence and Homosexuality." Journal of Biosocial Science, Volume 44 , Issue 5 , September 2012 , pp. 595 - 623