Friday, 8 January 2010

The Null Hypothesis

The null hypothesis is an incredibly potent tool for truth-seeking. It is the tool by which science functions. It really is an incredibly simple concept to understand and is so important a tool in helping us to make good objective decisions that it amazes me that I have to explain what it is to so many people that I meet, including scientists. I believe that everyone ought to know what it is and it should probably be taught in schools at an early age.

So what is it?

If you want to know whether something exists/works or not, you invoke the null hypothesis.

The hypothesis is that said thing does exist/work.

The null hypothesis is that said thing does not exist/work.

If you can’t provide significant evidence to support the hypothesis, then you reject it and accept the null hypothesis. This is always the default position. Innocent until proven guilty. You always assume that said thing doesn’t exist/work unless shown otherwise.

Why do you always accept the null hypothesis as the default position, and not the other way round? If the system were the other way round, you would have to believe in everything until shown otherwise, which is clearly a mad, mad concept. In fact an impossible concept, since in accepting every possible thing that could exist you invoke paradoxes faster than you can say "omnipotence."

What if a situation arises where you can't decide which isthe null hypothesis? Which possibility do assume is true before testing the other? Well there's an easy way to determine which one is the null hypothesis. It is the simplest, least complex option. Usually this is easy to spot.

Let's look at a story for an example. A car repairman is out on call in the middle of nowhere. He's finished his work and walking back to his truck. On the way he passes a phone booth. As he walks past, the phone rings. The man stops, puzzled. Who could be calling this booth in the middle of nowhere? Curious, he answers the phone to find that the caller knows his name and began talking to him about a business appointment he had the next day. He realised that he recognised the caller's voice as his secretary. He asked her how she had found the number to the booth but she implored that she had dialled his new mobile number. She checked her papers and realised that really she had accidentally dialled the number written just below: his paycheck number. It just so happened that his paycheck number matched the number of the phonebooth he walked past and she just so happened to call him just as he was walking past. Coincidence? Some people say that it's easier to invoke some sort of supernatural power than attribute it to coincidence, so supernatural powers should be the default belief, until proved otherwise.

But imagine two parallel worlds; one in which supernatural powers are the cause and one in which coincidence is the cause. Now reduce both worlds as far as possible. In other words, identify and consolidate everything about those worlds that is exactly the same. You end up with one model of the world, and a second model of the same world, plus supernatural powers. So it's actually the supernatural powers that are the hypothesis since they represent the highest complexity. And the null hypothesis is that supernatural powers do not exist and that coincidence is the only remaining explanation.

Or as Carl Sagan elegantly put, extraordinary claims require extraordinary evidence.

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