Paglia's smile

From Attempts To Put Statistics In Context, Put Into Context by Scott Alexander.  C.P. Snow's Two Cultures is often characterized as STEM distinct from Arts.  A further refinement might be distinguishing between those who understand statistics and those who struggle with its nuances.  Even people within STEM often are challenged by stats.  It is an immensely powerful and useful tool but it is not simple either in concept or application.  

Alexander notes:

Sometimes people do a study and find that a particular correlation is r = 0.2, or a particular effect size is d = 1.1. Then an article tries to “put this in context”. “The study found r = 0.2, which for context is about the same as the degree to which the number of spots on a dog affects its friskiness.”

But there are many statistics that are much higher than you would intuitively think, and many other statistics that are much lower than you would intuitively think. A dishonest person can use one of these for “context”, and then you will incorrectly think the effect is very high or very low.

He is trying to find some means by which clarity can be increased and dishonesty revealed.

He offers a list of effect sizes and of correlations in order to better situate comparisons.  

Some effect sizes and correlations are naturally misleading, or depend a lot on context. I’ve tried as hard as I can to avoid these and make all my examples clear, but they will necessarily require some charity.

Effect Size:

DARE keeps kids off drugs: 0.02

Single-sex schools improve grades: 0.08

Smaller class sizes improve grades: 0.21

SSRIs help depression: 0.4

Ibuprofen helps arthritis pain: 0.42

Women are more empathetic than men: 0.9

Oxycodone helps pain: 1.0

Smokers get more lung cancer than non-smokers: 1.1

Men commit more violent crime than women: 1.1

Men are more into engineering than women: 1.1

Adderall helps ADHD: 1.3

Men are taller than women: 1.7

Children tutored individually learn more than in a classroom: 2.0

Independent of Alexanders objective in the essay, there is the serendipitous juxtaposition of two data points which takes me in a different direction.  

Men commit more violent crime than women: 1.1

Men are more into engineering than women: 1.1

The fact that these are equally robustly true in terms of effect size and of generally broad recognition is not what grabbed my attention.  It was their juxtaposition.

There is a well known observation, the male variability hypothesis:

The variability hypothesis, also known as the greater male variability hypothesis, is the hypothesis that males generally display greater variability in traits than females do.

It has often been discussed in relation to human cognitive ability, where some studies appear to show that males are more likely than females to have either very high or very low IQ test scores. In this context, there is controversy over whether such sex-based differences in the variability of intelligence exist, and if so, whether they are caused by genetic differences, environmental conditioning, or a mixture of both.

Sex-differences in variability have been observed in many abilities and traits –– including physical, psychological and genetic ones –– across a wide range of sexually dimorphic species.

The male variability hypothesis is controversial not so much because of its associated data (which is reasonably clear and consistent) but because it is extremely inconvenient for several ideological and policy positions and because people often are extremely imprecise when either speaking about or hearing about male variability (especially in defining and measuring which traits, to what degree and for what reasons.)

In terms of IQ, the substance of male variability hypothesis is that it appears that men and women have the same average IQ but that men have greater variability; there are more male geniuses and more male dullards than we would see with a normal distribution and in comparison to women.  

The feminist academic, Camille Paglia has her own version of the hypothesis.  At minute 4 in this video.  

There is no female Mozart because there is no female Jack the Ripper.

Not male IQ variance perhaps, so much as male extreme behavior variance.  

So when I see:

Men commit more violent crime than women: 1.1

Men are more into engineering than women: 1.1

I immediately think, Professor Paglia would smile.