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.

I don't think you can explain anything that we could understand, perhaps a link. We know Smith is guilty because he was arrested. The cops don't arrest innocent people.

I'd have to look at Smith, 'cause I can tell if a person is guilty just by lookin' at them.

(July 10, 2009 at 7:09 am)LEDO Wrote: The cops don't arrest innocent people.

What kind of backwards world do you live in?

Anyway, I think your explanation of the null hypothesis is a good one. Certainly a nice way to introduce people to the concept.

(July 10, 2009 at 7:09 am)LEDO Wrote: We know Smith is guilty because he was arrested. The cops don't arrest innocent people.

That is not only irrelevant to the question I was asking, it is also completely delusional (i.e., invalidated by evidence to the contrary).

Good analogy and well explained.

Saves time whenever one's musing over the subject

EvF

What's that smell? Is that agenda I smell? I know it is agenda, but what are the ingredients?

Arcanus,

I sit on the edge of my chair waiting for the other shoe to drop. What now, lessons on Gaussian curves, confidence intervals, central tendency, and six sigma quality management methods?

What are the two populations you are going to compare? What is the sample size? How is babby formed? Are you going to use student's T or a z-test?

Rhizo

The agenda is to find a non-technical and easily understandable way for the average person to grasp the "null hypothesis" methodology, using an analogy from common experience that could also perhaps illustrate the value of it. But then again, I sort of alluded to this in my original post.

I would love to know what reason I have given you to attribute ulterior motives to me. I will not, however, hold my breath.

So by the null hypothesis, we would say god doesn't exist until proven to exist.

(July 11, 2009 at 6:58 am)LEDO Wrote: So by the null hypothesis, we would say god doesn't exist until proven to exist.

I would agree with that.