Human Height is not Bimodal

[atoo]

This is a bit of a niche topic I know, but I thought it might be interesting to at least some people.

If there's a scalar characteristic which has a different mean in men and in women, then the distribution for the whole adult population will be Bimodal if the difference in the means is large compared to the variation within each sex.

This is the case for example in gamete size or testosterone levels. But it is not the case for height - the difference between the average man and average woman is less that the difference within each sex. So human height is not in fact a bimodal distribution. It's just a bit flatter than a bell curve (image attached).

Much more detail in this paper: https://faculty.washington.edu/tamre/IsHumanHeightBimodal.pdf,.including why people often find bimodality in practice - e.g. small sample sizes, and men lying about their height.

yep. a gallon of paint, average sized domestic cat, and a smallish microwave oven all weigh roughly the same amount. but are quite different to each other when you look closely.

Gamete type is binary (egg or sperm) but gamete size absolutely is bimodal. Some eggs are bigger than other eggs, some sperm are bigger than other sperm. If you took 1000 fertile people and measured the size of one of their gametes, you'd get a distribution with two peaks. (And an enormous empty gulf inbetween)

Apologies for not giving more context. This was indeed what I was intending to refer to.

I do think we need to read about doggit. It is always useful.

https://sex-matters.org/posts/updates/doggit/

This is a weird OP. I am a woman who is 6ft 1 and I am taller than most men. I am an absolute outlier though- seeing a woman taller than me is so rare I am startled when it happens but I pass dozens of men every day who are taller than me.

Men as a sex class are taller than women as a sex class. I’m not sure what needs to be analysed further.

As above, this was prompted by another thread, and I was solely saying that bimodal has a technical meaning, and that although men are typically taller than women, the difference isn't big enough to make height bimodal.

There are plenty of human characteristics which are bimodal in a sex-associated way. For example, in grip strength the difference between the average man and average woman is big enough to make adult human grip strength a bimodal distribution (data below is for 35 year olds).

I think power differentials eg grip strength is so important and not widely recognised in an easy to understand way.

I was looking the other day (but couldn’t find clear graphics) on if you lined up 100 men and 100 women by grip strength, on average where would they stand in the line?

Looking at the graph above I guess about 85% of all men are stronger than all women. Does that sound about right?

Your thought experiment would look something like this:
🔴🔴🔴🔴🔴🔴🔴🔴🔴🔵🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔵🔴🔴🔴🔴🔴🔴🔴🔴🔵🔴🔴🔴🔴🔴🔵🔴🔴🔴🔵🔴🔴🔵🔴🔵🔴🔵🔴🔵🔴🔵🔵🔵🔵🔴🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵🔵

"All women" includes some very exceptional women not captured on a graph of course. But it you say "99% of women", then I think that's roughly right.

In the data I'm using, almost all꙳ men would be stronger than almost any꙳꙳ woman of the same age as them.

꙳ >90% of men
꙳꙳ >90% of women of the same age

A better picture, with acually 100 of each.

I have always referred to my Chihuahua as a ratdog I am certain that rat-chihuahua is spectrum, with him falling more towards the rat end in many ways.

I may have to rethink some stuff.

Are any sperm bigger than any eggs?

The large and small descriptions of gametes are a comparison between the size of one type of gamete and the other

No, all human eggs are bigger than all human sperm. Gamete type is binary. Large gamete Vs small gamete is a binary dimorphism.

Actual (scalar) gamete size, e.g. diameter measured in mm or mass measured in ng, or volume in nl, has a distribution which is bimodal.

But when people talk about large vs small gamete size they aren't talking about the size distribution of a particular gamete type

I'm not talking about the size distribution of a particular gamete type either - I'm talking about the size distribution across all human gametes of both types - which is bimodal.

I'm now wishing I'd stuck with testosterone levels and grip strength as my examples of things that are bimodal. 😅

I don't find that article convincing, the mean difference is very, very close to the combined standard deviations. Some men haven't reached their full height by 20, I'd expect that to be enough to tip it into officially bimodal. I also don't understand why they didn't present the SD from the data, it looks like they had to compute it to make it "more normal" which they wouldn't have had to do it they'd recognised it was two normal sub groups.

Any estimates and projections would be more accurate if separated by sex, so why group them? We are moving towards recognising women in medical research, this would be a step back.

That has absolutely nothing to do with sex not being binary though, as we don't use height to "assign" sex to someone. The sex comes first. There is also no reason to say sex is bimodal, that just shows that someone doesn't realise there needs to be a measure/units along the x axis.

How interesting I would have said (wrongly I now see) that height of men and women was bimodal. Is there a cut off? Like how big does the overlap have to be before it's not bimodal distribution?

This isn't exact, but as a rule of thumb compare the difference in the means to the sum of the standard deviations. Using the numbers from the NBA graph that was posted upthread:

Female height: 159cm, with standard deviation 6cm
Male height: 171cm, with standard deviation 7cm

So the difference between the means is 12cm, and the sum of the standard deviations is 13cm, so its not bimodal. But it is quite close!

I'm lost 🤔

I’ve been told that before on Twix, OP and it is an interesting point.

I think there is similar relevance in brain size and of the structures within the brain. The differences supposedly noted that were used to imply that parts of the brains of transsexual males were like those of females were similarly small and within the normal ranges for the male sex.

I drew a related conclusion that just because you had a tall woman with a masculine face (and brain perhaps, who knows) she remained just that: a woman who was an outlier. The only true physical sex markers relate to the sex organs. Everything else is just a distraction.

Very good points! I think the article recomputed standard deviations because their data source only published centiles. I have some sympathy - data which reports a standard deviation and which also only covers fully-grown adults is surprisingly hard to find. This is the best I could do: https://link.springer.com/article/10.1007/s00103-020-03096-w (German).

From the data there:
20-29, diff in means 13.4cm, sum of standard deviations 13.8cm
30-39, diff in means 13.6cm, sum of standard deviations 13.7cm

So it's definitely very much closer to being bimodal once you exclude the not-yet-fully-grown men.

It does eventually become bimodal in the 60+ age group, mostly because the standard deviations decrease for both men and women - I'm not sure why that would be.

That's vaguely interesting. Not relevant to any of the arguments in the case that I can see, but interesting to know! It just depends on whether in that gap between the modes of the individual distributions, one distribution's density drops away faster than the other one increases, or not. I imagine some other sex influenced measures would be, it's close.

But it is bimodal.

If you draw the height distribution chart for women then the peak is not the same as that of the height distribution chart for men. (And this remains true whether you define ‘woman’ ln line with UK law or in line with self-identified gender).

That's not what bimodal means. A distribution is bimodal if when you draw the distribution for the whole population, there are two distinct peaks. In the case of height, the female and male distributions are close enough to each other that when looking at the whole population ignoring sex, the two peaks smear into one fairly flat & broad peak. In the case of grip strength, the female and male distributions are far enough apart that there is a main peak and a clearly distinct secondary peak.

Yes, and we all know which sex is represented by which line (even if they weren’t the stereotyped colours) even without a key.