Understand the numbers? Don't count on it.

I have written here before about what philosopher Douglas Hoffstader called "innumeracy", the numerical equivalent of illiteracy. That is, the inability to understand numbers. Three stories in the media in the week leading up to writing this got me thinking again about how the public can be confused by numbers, and sometimes even deliberately misled.

The first story was the biggest lottery prize in Australia's history – the $90 million NSW OzLotto draw. During the week leading up to the draw almost every commercial news broadcast I saw on television had some man-in-the-street interviews with people asking them how they would spend the money, following that with the bad news that the probability of winning was very low (about one in 45 million). It was never mentioned that the odds of winning are the same every week and have nothing to do with the size of the prize. The problem is that many more people buy tickets when a big prize is on offer, so the probability of winning stays the same but the likelihood of having to share the prize increases. When Lotto had one of its first multi-million dollar prizes people ran syndicates to buy large numbers of tickets. If I remember correctly the prize was $13 million but was shared by over thirty winners. Imagine going into the boss's office on Tuesday morning and telling him what you really thought of him and then getting the phone call to tell you that you had won not quite enough to buy a small home in Sydney's western suburbs.

By the way, the $90 million prize was shared two ways. You can see I was not a winner, otherwise I would not be sitting here typing but would be at the Aston Martin dealership selecting paint and trim options while waiting for the estate agent to get back to me with prices for islands in the Whitsundays. Sad, isn't it?

I am not a gambler, although I admit to buying Lotto tickets despite calculations showing no statistical significance between the chances of winning and zero. In laymen's terms, that means that you don't increase your chances of winning by buying a ticket so you might as well save your money. Isn't maths fun? Of course, warnings about gambling statistics mean nothing to true believers. I remember standing in the Rio casino in Las Vegas looking at a two-metre-high sign saying that the Rio was the best casino in town because it returned a massive 97% to players. As far as I could see in all directions people were throwing money at slot machines and roulette tables (both of which return less than 97%, as it happens).

Then there's the swine flu statistics. I have seen much ridiculing of warnings about this new form of the virus, with much of the ridicule focussed on the small number of deaths. One reason for the small number of deaths was the preparation undertaken following the recent avian flu scare. Also, the WHO didn't declare swine flu as a pandemic because it was killing a lot of people. It was because of the rate of spread across the world. Again it was a statistical argument – that any new disease appearing in five or ten new countries each week and for which no immediate cure is available is cause for concern. A statistic that I only saw once but which put a whole new perspective on things was that the death rate among infected people exceeded that of the 1918 flu which killed a significant proportion of the world's population. We were lucky this time.

Now we have looked at how people don't understand very small numbers like the chance of winning Lotto and small numbers like the probability of dying of influenza, let's look at a blatant case of abuse of a large number.

An anti-vaccination organisation cited the US FDA as saying that HPV vaccine caused a 73.3% increase in unrelated illnesses. This was obviously intended to scare potential users of the vaccine. Looking at the facts, the report actually said that 73.3% of subjects in clinical trials experienced an unrelated medical condition (which could have been toothache or pregnancy) during the entire course of the trial. I currently have influenza and a sprained ankle, both of which occurred within twelve months of moving house. Relating these conditions to the move makes as much sense as the scare campaign against the vaccine does. The news release forgot to mention that 76.8% of the placebo group suffered an unrelated condition during the trials, so perhaps doing nothing is worse than the vaccine.

Have a nice day. You have a .003% chance of having an extremely bad day at least once in your life but a whopping 14% chance of it happening on a Wednesday.

This article was published as the Naked Skeptic column in the August 2009 edition of Australasian Science

It was republished in Issues magazine in June 2011