Page 2 | Human Height is not Bimodal

atoo · 2025-05-17T20:44:15+00:00

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 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.

Kuretake · 19/05/2025 12:59

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?

TeamKenwood · 19/05/2025 12:54

How long’s a piece of string OP?

BernardBlacksMolluscs · 19/05/2025 12:50

I have found the thread quite educational!

Original poster

atoo · 19/05/2025 12:44

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.

OP posts:

puffyisgood · 19/05/2025 09:39

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.

Original poster

atoo · 18/05/2025 20:13

DragonRunor · 18/05/2025 18:11

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

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
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 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.

OP posts:

Sazzasez · 18/05/2025 19:55

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
…

Etaerio · 18/05/2025 19:01

DragonRunor · 18/05/2025 18:26

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)

Edited

Show quote history

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

DragonRunor · 18/05/2025 18:26

Etaerio · 18/05/2025 18:19

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

Show quote history

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)

Etaerio · 18/05/2025 18:19

DragonRunor · 18/05/2025 18:11

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

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
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.

DragonRunor · 18/05/2025 18:11

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

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
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.

Almostwelsh · 18/05/2025 17:40

atoo · 18/05/2025 17:27

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?

Show quote history

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

Original poster

atoo · 18/05/2025 17:27

NoBinturongsHereMate · 18/05/2025 17:11

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.

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?

OP posts:

Circumferences · 18/05/2025 17:25

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.

NoBinturongsHereMate · 18/05/2025 17:11

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.

Berryslacks · 18/05/2025 15:16

MyPresumablyScrotum · 18/05/2025 10:49

Tall women are not men.
Short men are not women.
HTH.

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.

JeannieDark · 18/05/2025 15:15

JellySaurus · 17/05/2025 23:30

So the pink lines and blue lines are more close to each other than more separate?

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

Original poster

atoo · 18/05/2025 15:12

JillAndJenTheFlowerpotMen · 18/05/2025 15:01

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.

OP posts:

JillAndJenTheFlowerpotMen · 18/05/2025 15:01

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).

thirdfiddle · 18/05/2025 14:54

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.

Original poster

atoo · 18/05/2025 14:52

LadyQuackBeth · 18/05/2025 13:22

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.

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.

Anthropometrische Messungen in der NAKO Gesundheitsstudie – mehr als nur Größe und Gewicht - Bundesgesundheitsblatt - Gesundheitsforschung - Gesundheitsschutz

High levels of adiposity in the population have a major impact on various diseases, but previous epidemiologic studies have largely been restricted to simple anthropometric measures such as the body mass index (BMI), an imperfect predictor of disease r...

https://link.springer.com/article/10.1007/s00103-020-03096-w?error=cookies_not_supported&code=ffc706e4-bafe-4f57-a2a1-80f25780e1fd

OP posts:

PriOn1 · 18/05/2025 14:32

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.

LoudlyMeowingCat · 18/05/2025 14:15

I'm lost 🤔

Original poster

atoo · 18/05/2025 14:01

Kuretake · 18/05/2025 13:22

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!

OP posts:

Kuretake · 18/05/2025 13:22

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?