# Standard variation

It was during a competition for junior firefighters that somebody first noticed something unusual about the small Polish village of Miejsce Odrzanskie. Every single one of the uniformed children showing off their skills was a girl.

The reason is as simple as it is surprising. No boys have been born in Miejsce Odrzanskie for almost a decade, while the village’s women in the rural backwater of 300 souls have given birth to 12 girls.

The boy shortage is so acute that the mayor has offered a cash reward for the first family to produce a son. The world’s media have descended on the village in the fields of south-west Poland not far from the Czech border to investigate the phenomenom.

We can work it out can’t we? Chance of – not accurate but what the hell – girl is 0.5, assuming a birth takes place. Chance of 12 on the trot in one series of 12 is 0.5×0.5×0.5 a total of 12 times.

Or, across an entire country of many series of 12 births the chance approaches 1 again, doesn’t it?

Unless of course they’re all Israeli fighter pilots in which case….

## 24 thoughts on “Standard variation”

1. 1/4096?

How many such communities across Poland? 500? 1,000?

Haven’t there been families of 6, 7, 8 children all of one gender?

Bound to happen.

2. Standard deviation.

Variance (not variation) is the square of standard deviation (we never use it, it’s just a step on the way to calculating SD).

Standard deviation of course, since we are discussing matters of sex and gender expression, no doubt gives this house many punning opportunities. Take it away, Steve.

3. Of course, when you get odds like that of 14 boys, what are the odds that there is some chromosomal thing going on that’s auto-aborting females at conception?

4. The boy shortage is so acute that the mayor has offered a cash reward for the first family to produce a son.

Just get one of the girls to self-identify as a boy and claim the reward.

5. Surely for each birth, the chance is ~ 50/50 and ‘resets’ for every baby – so this would just be a cluster in a genuinely random pattern?

6. BiND: that would be pretty PC for Poland.

7. Other Jonathan: there has been some research that shows that in some cases, the sex of child n can influence the likelyhood of the sex of child n+1 being the same. Residual hormones in the womb and stuff.

8. Tom,

Yes, and this is rural Poland so even more so. But lets not under estimate the power of incentives, they have the Internet to guide them.

9. Andrew C,

That can happen (before conception) in some flies, but let’s stick with the null hypothesis until we find a greater number of families with 12 boys and no girls than the normal distribution would predict.

10. BiG

Statistically, surely you could do this on any population.

Calculate (for a given number of siblings) the expected distribution (eg, for 4 kids, “expected 50/50” chances of 4-0, 3-1, 2-2, 1-3, 0-4), and then compare with actual population data.

Is there any meaningful statistical bias towards the extremes or (on the contrary) towards 2-2?

Ditto 5, 6, 7 kids etc.

It’s technically easy enough to do, if you have the data, hence I’m guessing no meaningful variation has ever been found?

11. Small village, back of beyond in Poland, what are the chances a lot of the families are interrelated? In that case a genetic favouring of girls will shorten the odds considerably.

12. Doubtful. X and Y are determined before that. However, there is considerable ability for the womb to decide to accept or reject a zygote. That could well be influenced. One argument about Downs is that frequency of conception doesn’t change over life. Rather, acceptance of implantation does. Hell, if this is going to be the last one why not allow a potentially slightly flawed one?

13. PF, of course you can and Mr C has done so. Provided the chance of any child being female is 50% (near enough) and there is nothing except randomness influencing that, then the chances of any 12 randomly selected childreen being girls is 1 in 4096. We double our chances as either will do for the “remarkable coincidence. So 1 in 2048 such random selections of children will be all of the same sex.

If we saw this happen significantly more frequently (and the fact that every time is newsworthy suggests not) then we might conclude that some cause is skewing the births away from being truly random.

Poland must have rather more than 2048 villages. As Terry Pratchett very accurately observed, one in a million chances crop up nine times out of ten. One of the two reasons* for that is that we notice them because they stand out, and they stand out because they are relatively unlikely so attract attention, but likely enough to happen quite a lot. There are lots of these things – look up double lottery winners for example.

*: The other is that actually any particular scenario is itself extremely unlikely given all the potential alternatives, but reality has to happen sonehow.

14. BiG

Of course. I meant actual statistical studies using real (large scale) population data rather than casual observation. And on smaller sibling groups, and hence substantially more data.

I am not disagreeing with you. I’m assuming that bods have attempted this and no meaningful variations have ever been found.

15. At the population level I don’t think you even need to look into it, 50/50 is obvious. It’s the covariates that count, the obvious ones being parent (gametes skewed, which does sometimes happen in fliies, or womb selectively rejecting) and village you were born.

The problem is if you pick enough covariates, you will find some (around 5%) for which there is a significant departure from the expectation of randomness without there really being one. In other words, it’s the same basis as most modern junk epidemiology. If you have to test dozens of covariates to find any that support a departure from random expectations, it becomes very difficult to separate signal from noise.

16. “If you have to test dozens of covariates to find any that support a departure from random expectations, it becomes very difficult to separate signal from noise.”

Aye, but it makes it easier to make a living, eh?

17. Umm, this isn’t about standard variation or deviation, it’s longest run. Tim pretty much gets to it by comparing the rate of girls in the village to the rate across Poland; it’s going to happen somewhere, sometime.

The only other thing is that Miejsce Odrzanskie is clearly dying on it’s arse, and has been for sometime now. Given the population of 272, “normally” I reckon you’d have a population of women of childbearing age of about 40~50 may be, so the average birth rate pa over ten years should be about 4-ish. Since it’s only about 1-ish per year, the population is already badly skewed older, and news items about birth defects probably figure in the future, sadly.

18. I had a friend in school who was one of five boys, and here in Thailand I know a guy with seven daughters. One additional factor is that people who have had say three of the same sex keep trying to get one of the other leading to a larger family than would otherwise be the case.

19. Hi All:
Let me just say what everyone is thinking: The first boy born will be attending a school with all girls. This means the parents are duty-bound to give him the most fitting name possible: “Lucky”!
Thoughts?

20. @Vern

Randy – after Randy Mamola

or Henry Arthur Vernon Edward Richard Zxyiloski : H A V E Dick Zxyiloski

21. BiG

Thanks for that, I understand.

22. 12 girls in a row is a highly statistically significant departure from randomness, but you get a lot of throws of the dice (villages in the world) and are looking for the result post hoc.

If Baba the witch had placed a “travelling communty” curse on the village, and this village only, saying the next 12 children would be girls, you would by now be wondering if there wasn’t something in this black magic.

23. This is interesting:

https://www.biorxiv.org/content/biorxiv/early/2015/11/24/031344.full.pdf

I haven’t time other than to broadly skim, but page 9 is perhaps closest to my question above. And which does suggest some very slight skewing towards unisex (rather than mixed sex), but only at larger family sizes, the opposite being true at smaller family sizes.

Though I can see how one of the family planning reasons given – families stopping once they’ve had one of the other – might also impact the results with smaller families.

I take your point, BiG, re complexities.