95% of percentages are annoyingly useless

There's a notice on the intranet here at work, which reads as follows:

Lock it or lose it!
75% of theft from motor vehicles happens to unlocked cars

It's annoying me. It's been annoying me for a while.


Because it's emblematic of a common theme in the presentation and usage of statistics. In the absence of other essential data - in the absence, indeed, of context - the 75% figure is largely useless.

To really evaluate what it means, we have to know at what rate cars are left unlocked. If, for example, 85-90% of cars are left unlocked, then to have 75% of theft happen from locked cars would mean that it's less likely that an unlocked car will be stolen from. And we'd also like to know at what rate from-car thefts happen per car per year full stop, as well as "does the ratio vary with the value of goods stolen?". Without these kinds of figures, that magic 75% doesn't tell me anything useful.

Yes, I know that on the topic of thefts from cars common knowledge states that a large majority of cars are in fact left locked when unattended, and are relatively rarely broken into anyway. But what about in the case of less commonly understood statistics, where this absurd present-the-percentage-and-hang-the-context reporting takes place too?

Take, for example, anti-vaccine campaigner Meryl Dorey of the Australian Vaccination Network.

A veteran liar-with-statistics-she-doesn't-understand, Meryl Dorey has fold us that 80% of pertussis cases happen in the vaccinated population, as if to suggest that the vaccinated are somehow, illogically, more likely to contract whooping cough than the unvaccinated. This we know is not the case - the vaccine is shown to have a good - though not by any means perfect - efficacy rate in preventing infection. This still doesn't stop Meryl throwing the percentage out there in support of her topsy-turvy world view.

Still, so what if 80% of cases are in the vaccinated? The important question is whether you're more or less likely to contract an infection if vaccinated, and for that you need to know rates of vaccination versus rates of infection with a solid contextual basis. From Meryl's 80% claim alone, it is impossible to tell - and therefore the assertion is useless, as well as being flat-out wrong.

Dorey also, oddly enough, tries to state that our national pertussis vaccination rate is 95%, sometimes in conjunction with the 80% lie, sometimes not. This, again, is a bad statistic, cherry-picked as it is from a small subset of the overall population. 95% of young children in a given year were vaccinated. This does not hold true for an older cohort, or indeed for adults, where the rate is down around 11.3% (see link above). Again, percentages prove utterly useless in the absence of more basic questions - such as "is this figure from the population as a whole and does it hold true over time?" and "does the status 'vaccinated' line up with the status 'produced antibodies in response to vaccination'?", and "since population profiles vary widely, what use is a single blanket percentage anyway?"

What allows Dorey to lie this easily? People don't understand statistics. They don't even understand simple percentages and the limitations thereof.

Still, Dorey's innumeracy can result in some funny moments, when her own made-up figures are used to disprove her own made-up assertions:


So anyway, that's why the car theft banner annoys me, and why everyone should stop using ungrounded, unsubstantiated, context-free percentages right now, unless you actually understand how they work and how to present them correctly.

Thank you.

posted @ Friday, January 27, 2012 1:49 PM


Comments on this entry:

# re: 95% of percentages are annoyingly useless

Left by Andy at 1/28/2012 1:27 AM
In a similar, but only vaguely, distantly related vain, I'm always miffed by ads that say things like "Book early so you don't miss out".

Assuming the thing on offer if of finite quantity - and that supply is less than demand - someone will always miss out. Even if everyone booked days early - or weeks or months... or years... the same number of them still have to miss out.

But Meryl's grasp of maths is a constant source of mirth.
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