Human Height is not Bimodal

No, you were the one confusing evidence and proof which is why I corrected you in the first place.

You must have misunderstood me, I was not confusing anything. I confirmed in my first reply to you that I wasn't claiming anything was absolute.

All of which is rather beside the point I was trying to make, which is we don't need to look at the combined distribution of M+F height to demonstrate that there are two different distributions involved, it's much better to look at the distributions of M and F separately.

Though it is true in the other direction that if something does have a bimodal shape, and you didn't already know there were two distinct populations involved, you would go looking for them.

No, you were the one confusing evidence and proof which is why I corrected you in the first place.

I am always bemused by mumsnet's obsession with height.

I've explained my point to you twice and genuinely don't know what you're struggling with. You seemed to think that a significance test actually tells you if there are two different populations. It doesn't: it is merely a rule that you specify beforehand to decide whether you will reject the hypothesis that the two groups are the same.

I think you may be confusing "evidence" and "proof". Something happening that would be highly improbable under the null hypothesis is a piece of evidence pointing to the null hypothesis being wrong. That's the whole point of doing significance tests. It's how medical science works. We can't 100% prove that treatment A works better than a placebo, but if we can repeatedly in multiple independent studies reject a null hypothesis that it is not better, that gives us a high degree of confidence that it /is/ better.

(To be completely pedantic, we already know there are two populations or we couldn't run the test at all. The question is whether the two populations have different height distributions. They do. It has been very long established. Nobody seriously doubts it. But if you wanted additional evidence you could find some data and do a hypothesis test.

If you're passing well, you're probably the basketball player!

OMG I’m either a man or a basketball player - why did no one tell me in the last 50 years? Maybe I’ve been passing so well as a woman?

This is exactly why ideas like “Men are from Mars, Women are from Venus” are nonsense when they get turned into stereotypes such as “boys are better at Physics”.

Just because there is an observable or measurable difference between male and female populations, it tells you nothing whatsoever about individual males and females within the population. I am not weird because I’m female, good at Maths and hate pink.

I've explained my point to you twice and genuinely don't know what you're struggling with. You seemed to think that a significance test actually tells you if there are two different populations. It doesn't: it is merely a rule that you specify beforehand to decide whether you will reject the hypothesis that the two groups are the same.

I'm not sure what point you are trying to make. If you want to convince medical people that two populations have a different measurement (say that a treatment has worked better than the placebo, or that two populations have different mean heights), what you do is carry out a significance test.

Technically what the test result will say is that if men and women were from the same height distribution, then the chance of your data showing a difference at least as big as it has in mean heights is less than say 0.1% (if that's the level I chose for my test). That is very convincing evidence that they are not from the same distribution. A 1-in-1000 unlikely thing would have had to have happened. And the more times the test is repeated with the different samples and the same result, the more unlikely it becomes that they'd all say men were taller if they weren't.

If you have a p value a tiny bit below your threshold you would reject the null hypothesis and if you have a p value a tiny bit above your threshold you would not reject it. There's nothing magic about the threshold, it's just the arbitrary level that you decided ahead of time to use as your cutoff.

Nothing is absolute, but significance levels is how people convince themselves of stuff in medical research. it could technically all be a huge coincidence that every time we measure the heights of a group of men and an equivalent group of women the men are taller on average, but it's incredibly vanishingly water might fall upwards-ly unlikely that would happen.

Well, yes, except that a significance test doesn't infallibly tell you whether they are different distributions: it merely provides a decision rule on whether to accept the null hypothesis that the distributions are the same or not.

Statistically speaking bimodal is when the combined frequency density graph has two local peaks. Two points for which that value is more likely than one just above or below it.

The thing about standard deviations is just a rule of thumb for when it's likely to happen. Probably based on if the individual distributions were normal.

If you combine two different but overlapping single-peaked distributions, like height, the result may be a combined distribution with two peaks or one with one broader peak.

It's obvious they're two different populations just by looking at the separate distributions before adding up. You don't need to be able to deduce it from the combined graph, you deduce that from the differences in the individual graphs. If there was any doubt you could do a significance test. Spoiler: if you do this with height, the difference is going to be significant as long as you have any decent sample size.

As there is very close to equal numbers of M and F to get the combined distribution shape you pretty much add up the densities of the two separate distributions (the heights of those bell curves people keep showing us) and divide by 2. So it's about whether one graph is falling away between the two individual peaks faster than the other one is growing, or not.

If the combined distribution only has one peak then it's unimodal.

I think according to PP there is a specific statistical definition for bimodal. Something something standard deviations and means

From a statistical perspective, I’m not sure that the fact the peaks overlap means it is not a bimodal distribution. The curve is still better fitted by two populations with different means, each with a normal bell curve distribution. Isn’t that still bimodal?

This absolutely bears repeating.

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.

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

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.

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!

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.

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👏

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.

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.