Statistically Speaking – The Lottery Fallacy

Have you ever thought about someone, then the phone rings and THEY are on the other end? Ever had a dream that something would happen and then it did a few days later? Are you somehow the cause of any of these events? Many would say yes, though no evidence exists to say that could ever be the case. What’s at work here is probability. This intuitive lack of understanding of statistics that I will elaborate on here.

Statisticians tell us we are virtually more likely to be hit by lightning than win the lottery. An event such as lightning striking some poor sod happens everyday despite the odds of it being incredibly slim. The fact is, it does happen because given enough lightning strikes (there are thousands every day) some will just happen to be in line with a person.

Remember this analogy when someone uses the argument from personal incredulity (I can’t believe it therefore it can’t be). Human beings have a poor innate sense of statistics. This fact alone is responsible for a good number of weird beliefs people hold. Science is in one sense a way of overcoming the flaws inherent in our perception that lead us to draw false cause and effect inferences.

The superstitious mammal

The religious and superstitious impulses thrive in conditions where we encounter something we can’t fathom – something so improbable it seemingly defies reason. This is where statistical fallacies begin. There are two flavours: fallacies arising from improbable events taking place; and statistics of small numbers.

An example of the first one often trotted out by religious apologists is that conditions are too perfect to have been created by chance. Therefore there must have been an intelligent force that created these conditions for us.

There are several fallacies in reasoning at work here. The major flaw being made is that if you look at some property of the universe in isolation, it can appear more miraculous than it actually is. What are the odds that the perfect conditions for life would arise on Earth? The probability is, of course, very small.

This however, is ignoring the fact that Earth is but one place in a universe filled with trillions of stars, many with which would have planets revolving around them. When you ask the correct question – What are the odds of conditions being perfect for life arising somewhere in the universe? The answer is of course very probable (we know this is a 100% probability because we are here!)

This is called the lottery fallacy – what are the odds that you will win the lottery? The answer is the same as the scenario above – very small (too miniscule to rely on winning it to be successful in life as many do). What are the odds that someone will win it?

What do most people say when they win? It’s a miracle! I’m so lucky! The real answer is neither luck nor miracles. Someone was going to win the lottery. The person who does win does so at random.

Random acts of randomness

But random doesn’t sit well with the human mammal. We make all kinds of inferences about causes and effects. We are so good at it, we can often ascribe effects to causes where no scientifically plausible link exists. As Bruce Hood says in his book Supersense Why We Believe the Unbelievable, our abiltiy to infer cause and effect allowed us to thrive in the environment better than our rivals.

The science shows that we are so good at creating causal links that it is innate in us to go beyond the evidence to infer causes that we cannot detect. In fact, given the choice, people would rather have some meaning than none at all, regardless if the created meaning is real or not. People, understandably, favour feeling certainty over uncertainty. Belief before doubt.

Given these tendencies inside all of us, it is hardly surprising that a many superstitious-based belief systems thrive today. Attributing supernatural agency as a solution to “how’d that happen” is written in our genes.

In a city of a million people, events of a 1/1000,000 probability occur all the time.

Statistics of small numbers

The second fallacy – the fallacy of statistics of small numbers relies on developing conclusions after only a few or even one experience. This has its advantages. Cognitive shortcuts are obviously more favourable to a mammal because that means less exposure and hey, the initial impression would have been enough in primitive humans. And so we form beliefs about the world based on a small subset of available experiences.

People do this all the time. A woman goes on five dates and meets five loser guys. The questions flow: “What’s wrong with me?” “Why can’t I find a good guy?” The conclusions are drawn: “There are no good guys”; “all the good ones are taken”; “I will never find the right guy”. Are any of these correct? After five dates, it would be impossible to know for sure.

Of course, if the woman approached this situation as a scientist, she would realise that 5 is a small number given the number of available guys. She might think: “Maybe if I meet 20 guys and the current situation holds, then maybe my intuitions about guys has more validity”. But would 20 be a representative sample of the whole population? Statistically significant? No.

Shoddy research

Shoddy researchers, particularly those with prior ideological leanings, love small studies. Small numbers can be incredibly deceptive. Many claims to reality, particularly in the alternative medicine camp, are made on the basis of small studies. Science works on the basis of well designed, large studies with statistically significant samples sizes. Even then, one study cannot be the basis to confirm something as real. Over time, the good ideas survive multiple well designed studies and we can say, with a high degree of probability that something has scientific validity.


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