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.

Indeed. It often seems to be the really big bastards who are so desperate to be a woman. Like that huge footballer knocking the women players over like ninepins or the giant cyclist.

I'll concede there is some variation in gamete size - but it's infinitesimal compared with the difference between the 2. So effectively irrelevant.

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.

Extremes of height are very often related to medical conditions, many of which are life shortening. And if you're a long way from average height the world isn't built for you, making accidental death more likely.

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

So what? There's enough difference between the heights of men and women for it to be obvious that most men are taller than most women.

For goodness sake, even limiting the data to people with dwarfism - most male people with dwarfism are taller than most female people with dwarfism, even though all people with dwarfism are shorter than the rest of the population.

The statement "men are taller than women" is not a false statement.

That seems plausible. Another thought I had was that maybe the older cohorts are more ethnically homogenous, which would reduce variance.

The difference in means is also greater in the older cohorts - maybe some of that is owing to nutritional differences in childhood?

Being taller than average does seem to shorten your lifespan even without a specific medical condition.

Sorry, haven’t read the whole thread, but I did look at the article. Two points stand out

1. the data its based on ‘young people’, I think 20-29. Didn’t look hard enough to find sample sizes etc, but immediately that says to me that a decent proportion of the men in this study haven’t finished growing whereas most of the women have
2. the authors don’t’ at any point, suggest that the two populations have the same distrubution. Statistically, this is critical. women are still statistically shorter than men

i get the impression OP is trying to suggest that the heights of people form a ‘normal-ish’ distribution, so they can be considered one group. But the paper doesn’t show that at all.

I get the impression that you believe all men are taller than the tallest woman. That's not true at all.

Ok, not sure if you’re shouting at me for not reading the thread, or actually think I’ve said that?

Edited to clarify - I haven’t. Coming from 2 separate distributions doesn’t imply there’s no overlap (see cats & microwaves above)

I'm not shouting at anyone. I'm merely mimicking the lack of understanding shown in your post of the interesting point being made.

Emma Hilton has adequately dealt with this but some points to remember:

• height is not sex.

It may be used in some contexts as a proxy for sex (ie a taller human of unknown sex is a bit more likely to be male than female, but it’s not certain that they are)

• a bimodal distribution of a characteristic suggests 2 populations that are likely differ in other identifiable respects

Big rabbits may be heavier than tiny dogs (so the weight distribution will overlap in the middle) but you can’t argue that there’s a spectrum between dog & rabbit with doggit in the middle.

Seeing the recent discussion on X where Femi had produced a graph with no units marked (Sexons? Genderbits?) to - he claimed - prove sex is bimodal, & the guy who made the graph to prove the claim is nonsense popping up, inspired me to write lyrics to the tune of Goldfinger.

Bi Modal -

Bi modal! what is sex? A male with a female touch?
A girl who’s butch?
Let’s say it’s … bi-modal!
Here’s a graph, a graph with no units marked
But don’t get narked!

From GI Joe to Barbie the path is clear
But these lies don’t disguise what liars fear
If a girl is tall that means she’s half a mister
A shorter man must be her sister

Because it’s - bimodal!
Pretty graph, beware of the blank axes
It’s just a tease
Designed to please!

Lots of words we will pour into your ear
Graphs and charts to disguise what should be clear
A clownfish, a lioness’ mane
To lie it’s all the same
and …

Bimodal!
Don’t ask what the units are!
Don’t look that far!
A kind of plan
To blur a woman with a man
That is the plan
…

i get the impression OP is trying to suggest that the heights of people form a ‘normal-ish’ distribution, so they can be considered one group. But the paper doesn’t show that at all.

Happy to clarify that I don't think either of those things. The whole-population distribution is not particularly close to Gaussian (see the pdf attached to the OP), and the sex-conditional distributions are significantly different from each other.

My only suggestions are that human height is not bimodal, whereas other sex-affected characteristics such as grip strength are. As a result of this thread, I now know that this fact is somewhat surprising to some people, and obvious or well-known to others.

I also now know that in some sub-populations, e.g. elderly Germans or Olympic basketball players, height is in fact bimodal, for possibly several reasons. But in broad populations - it is not.

i don't understand the point of the thread, at all.

I think it's saying something like:

"yes, men are taller than women, obviously, but the size of the gap [measured in number of standard deviations or suchlike], real as it plainly is, is not quite big enough to meet a particular threshold [one of many possible thresholds] taken from very obscure statistician-speak."

i have to say that my reaction is "so what?".

e.g. in sport, i very, very much doubt that the performance difference between u-11 boys and u-10 boys, or between middleweight and super-middleweight boxers, is big enough to qualify as 'bimodal' according to this particular statistical threshold... but does this make any of those categories somehow invalid? obviously not.

The term "bimodal" isn't all that obscure, and nor is the concept it refers to. A mode is a peak of the distribution - a value which is more likely than the values on either side of it. A bi-modal distribution is one which has two modes. So when drawn as a graph there are two peaks.

The word bimodal is often used in discussions about sex-affected characteristics such as height or strength. It's often claimed in such discussions that human height is bimodal. I thought it was interesting to note that this is incorrect.

Apologies if you were hoping for something more exciting.

I have found the thread quite educational!

How long’s a piece of string OP?

I've found it interesting and it's taught me something new. I don't understand the people upset at the OP, is there a controversial posting history or something?

Ha yes I think that would have been a good idea!

Although technically bimodal it's so far removed from how people usefully use the term (ie only when there's at least some overlap) that using it in the OP obscured much more than it clarified! The last thing we want is some eejit TRA going round telling them Mumsnet said gametes are on a spectrum.

Don't worry OP, I think we're just a bit too used to posters plopping in with [irrelevant but interesting bit of science] therefore AHA! Men are women! Gotcha!

So we were all looking for a gotcha in your post when it really was just an interesting bit of science.

You are quite right, people do put up the separate distributions and say height is bimodal. And it is interesting to know that actually it isn't.

And of course there's no aha to it, men are still not women, it's still two populations with different but overlapping height distributions combined.

That's brilliant, Sazzasez - I mean the Goldfinger parody, I've no idea whether what you said about bimodal distribution of characteristics is brilliant or not.

I am experiencing deep feelings of bitter resentment towards you, as I just popped on here to post that I've cleverly worked out that you can sing the thread title
'Human Height is Not Bimodal'
to the tune of
'Deck The Halls With Boughs of Holly'

only to find I've been thoroughly and brilliantly gazumped by a whole song!
Tra la la la la la la la la to you, party-pooper!😡

Only kidding - it's very clever and funny👏

nah - it's really incredibly, wilfully obscure, truly.

a far more straightforward topic title would be:

A 2002 US study found an average female height of 5'4", an average male height of 5'9"

the fact that this 5 inch difference isn't big enough to qualify the two distributions as 'bimodal' in obscure stats terminology is really, well, who cares, honestly.

Exactly this! And I disagree with some other posters that it's irrelevant- it's good to be accurate if only because maths is the best form of defence in some arguments!

i don't understand the point of the thread, at all.

I'm an (ex-) mathematician myself, so i appreciate OP's pedantry.

I hadn't thought to push back on people saying height was bimodal, but thinking about it, I should have stopped to think that it wasn't quite plausible. The spread is too wide and the gap too narrow.

But still, what I would take away from the thread is: a population difference can become clear and obvious - like the difference in male and female height - well before the it's significant enough to create a double-humped distribution.

So when you do see double-humped graphs about things you maybe don't have an intuitive grasp of, like testosterone, speed, or grip strength, or whatever - stop and appreciate how wide those differences must be to get that graph.

They're far bigger differences than the height difference you're familiar with and see every day. Human sexual dimorphism in other areas is far more significant.

Just because you don't understand the point sufficiently to appreciate it doesn't mean that other people don't.

I think “human height is not bimodal, fa la la la la lala la la” is a great song, & I will now be humming that for the rest of the day.

We need to do a musical.

I’m in Lancashire at the moment & it’s very sunny.

This absolutely bears repeating.