Bell curves, power laws and conceptual abstractions

From Cancel Culture is Girl Culture by Louise Perry.  The subheading is Part 1: How feminine aggression works.  

She starts with a couple of important observations which are often the basis for public misunderstandings and fruitless conversations - 1) people often do not understand bell curves and their implications and 2) people wrestle with overlapping bell curves, especially when they are non-sensory in nature.  

You can’t understand the social world (or indeed the natural world) if you don’t understand graphs like this: 

The size of snowflakes, the weight of newborns, milk production in cows – all of these phenomena are normally distributed. That is, most of the data points are to be found around the middle point, while just a few are to be found at the extremes (‘the tails’). The resulting graph looks like a bell, hence the term ‘bell curve.’ 

Overlapping bell curves are also common, and are a useful way to visualise a lot of human phenomena. Some are easy enough to understand. Male height is normally distributed, as is female height, but the male mean is about four inches greater than the female. This is the result: 

There are plenty of men and women to be found in the 5’6” to 5’8” range, but very few men are shorter than 5 foot, and very few women are taller than 6 foot. This is the nature of overlapping bell curves: the differences between groups are most obvious at the tails. 

For a very visible trait like height, this is intuitive enough. Everyone understands that the existence of one tall woman does not disprove the assertion that men are the taller sex. We can hold both ideas in our heads simultaneously without any difficulty. 

But it is less intuitive for psychological phenomena, particularly those with any kind of political charge. Differences between male and female desire for sexual variety, for example (also known as sociosexuality), could be represented as overlapping bell curves. Women with an unrestricted sociosexual orientation exist, but they are rare. To run with the comparison with male and female height, someone very sexually adventurous like Aella should be thought of as the equivalent of a 6 foot woman. 

She then makes a different point.

When it comes to most of the major psychological sex differences, I am typical of my sex. I am more agreeable, risk averse, and neurotic than the average man, and I also have a restricted sociosexual orientation (or, colloquially, I like being monogamous and vanilla). I’m generally more interested in people than in things. I regard spending time with my children as more important than my career, and have turned down a lot of professional opportunities as a result (one of the causes of the gender pay gap). I cry easily, particularly in response to the suffering of vulnerable people and animals. I enjoy sewing, interior design magazines, and cooking. I have no interest in watching sports. 

But on one crucial point, I am abnormal. When behavioural scientist Cory Clark appeared on my podcast earlier this year, she spoke of the tendency for women to prioritise being kind over being truthful – a tendency that I don’t share. A tendency that I regard, in fact, as very bad and very stupid, which apparently makes me unusual for a woman.