Thread by @Frances_Coppola

Considering writing a post about percentages and small numbers. Since, you know, some people seem to think percentages are meaningful when numbers are very small....

So if only one person committed a certain type of offence last year, and two people committed that type of offence this year, that's an increase of 100% in the offending rate. SHOCK HORROR! WE NEED MORE POLICE! JUDGES MUST IMPOSE LONGER SENTENCES!

It's particularly depressing when academics and researchers who should know better use percentages about very small populations. Especially when they also resort to the fallacy of division, as this lot do here: fairplayforwomen.com/transgender-pr…

What's the inconsistency in this? Well, the proportion of sex offenders among the 125 known trans prisoners is far higher than in the male prison population. Either the figures are wrong, or trans prisoners are very different from male prisoners.

Either way, you can't assume that the proportion serving sentences of less than 6 months is the same as in the male prison population.

The fallacy of division assumes that the characteristics of a small proportion of a population are the same as those of the whole population. In this case, we already know they aren't the same. So the researchers' assumption that they are is not merely baseless, it is wrong.

Here's another one: thecritic.co.uk/neither-margin…

What's wrong with this? Yes, you guessed it, the numbers are far too small for the percentage to be remotely meaningful. The link cited by the author actually says this:

This author was not the only one to fail to mention the serious problems with these statistics. Kathleen Stock - who should know better - similarly said without caveat that trans people are less likely to be murdered than the general population.

To add insult to injury, this statement is in a section of her book where she castigates trans activists for misusing statistics.

I've used trans issues as my examples here because the numbers involved are so very small. But there are numerous other occasions when percentages need to be taken with a very large pinch of salt.

Someone's just pointed out that interest rate changes are a good example. Indeed they are. If bank rate is 5%, and the Bank of England raises it by 1%, that's an increase of 20%. But if bank rate is 0.5%, and the Bank of England raises it by 1%, that's an increase of 200%.

In December, the Bank of England increased bank rate from 0.1% to 0.25%. That's a tiny increase - only 15 basis points. But if you express it as a percentage, it is a whopping 150%. Percentages are meaningless when numbers are this small.

Then there are the ups and the downs. Particularly important when discussing GDP, I've discovered. If GDP falls 5% then rises 5%, it has NOT returned to its previous level. It is lower than it was before.

We have Kathleen Stock to thank for another piece of statistical idiocy too. I refer to her argument that gender-nonconforming women must put up with being harassed out of women's spaces, because the potential harm to women from trans women using those spaces is so much higher.

Again, the problem is very small numbers. But on this occasion, percentages are helpful. Stonewall estimates that about 1% of the population are trans/non-binary. The UK population is about 68m, so that's about 680,000 people.

There have historically been more trans women than trans men, though the proportion is dropping. So there are perhaps 400,000 trans women in the UK.

How many gender nonconforming women are there in the UK? We literally have no idea, because statistics like this are (rightly imho) not collected. We can't assume that lesbians are necessarily gender nonconforming, nor that heterosexual women are gender conforming.

Can we be sure that the proportion of gender nonconforming women in the population is smaller than the proportion of trans women? I don't see how we can.

Indeed, as the feminist movement over the last half-century has given women the right to present themselves in ways conventionally thought of as "male", we might expect gender nonconformity to be quite common among women today.

Given this, there would seem to be greater potential harm from excluding gender nonconforming women from women's facilities, if this means they are forced to use men's facilities, than from allowing trans women to use women's facilities.

It is not clear to me why gender conforming women's need for protection from trans women is greater than gender nonconforming women's need for protection from men.

And while we are on the subject of statistical idiocy.... dear crypto folk, if you have issued 10,000 tokens at a unit price of $10,000 but only sold 1 of them, it is ridiculous to say you have a "market cap" of $100m.

At the opposite end of the scale are the covid sceptics, who appear unable to comprehend that in a population of 68m, a 1.5% fatality rate is over a million people.

Though perhaps they just don't care, since the vast majority of that million are old or sick...

Here's another example of percentages deliberately deployed to get a "Shock! Horror!" reaction from readers which is not warranted by the actual numbers. In the case of boys, they didn't even report the numbers, because they knew they were trivial. quillette.com/2020/01/02/the…