The Null Hypothesis

[Ryft]

I have been trying to think of how to describe the statistical heuristic of "null hypothesis" in a way that people would find easily digestible and understandable. All of the references I find tend to describe it in ways that the average person might find obfuscatingly technical. Many of them are confusing even to me, and I am highly literate.

So I had this idea occur to me today, as I wrestled with this issue at work, and I want to run it past you guys here. It seems to work analogously. Now, analogies by definition are not identicals, so there exists the inherent problem of imprecision; i.e., analogies fall apart if pushed too far. But does this analogy capture the essence of "null hypothesis" accurately enough that the average person could get a good sense of what it is about?

The legal principle of 'innocent until proven guilty' is a helpful illustration of the null hypothesis. The legal system does not operate under the notion that Smith is guilty (the operating hypothesis that puts the system into motion), waiting to see the evidence that proves it. The legal system operates under the notion that Smith is innocent, and then decides whether or not the evidence proves this false. In other words, the criminal investigators and prosecuting attorneys look for evidence that contradicts the idea that he is innocent. If the evidence contradicts this null hypothesis of Smith's innocence, it is considered "rejected" and the alternative hypothesis of Smith's guilt is favoured. On the other hand, if the evidence fails to disprove it, then it is considered "not rejected"—which means the alternative cannot be favoured either.

Under a proper research principle, the null hypothesis is never accepted; i.e., it is either 'rejected' or it is 'not rejected'. If it gets rejected, that does not prove the truth of the operating alternative hypothesis but simply adds to its probability. Similarly, under this illustration the null hypothesis "Smith is innocent" would be rejected or not rejected, but never accepted; sort of like saying, "Smith was not proven innocent. He was found not guilty"—in other words, (i) the evidence did not allow us to reject the idea that Smith is innocent, (ii) but nothing proved the idea that he is innocent either.