Re: Small probabilities

Iain,
    You and I are in so much agreement that we can't get a good argument going. By all means, probabilities and statistics are vital in scientific methodology, particularly in the areas you cite. I would suggest that this is quite different from determining whether a unique event was 'intelligently designed." In this particular case, we know that many surprising coincidences can occur and, in my opinion, we are not justified in jumping to a conclusion of a deliberate supernatural message being conveyed. I am tempted to say that "God wouldn't communicate to his people in that way" but I have stated elsewhere that arguments such as "God wouldn't do it that way" aren't compelling or appropriate. So I won't say it. And you'll all be glad to know that this will be my last post on this topic.

    Randy
  ----- Original Message -----
  From: Iain Strachan
  To: Randy Isaac
  Cc: asa@calvin.edu
  Sent: Tuesday, January 10, 2006 11:03 PM
  Subject: Re: Small probabilities

  On 1/11/06, Randy Isaac <randyisaac@adelphia.net> wrote:
    Vernon,

        With all due respect to Iain, this is a point with which I disagree.
    Per our previous discussion, the only argument offered against coincidence
    is very low probability, which I argued is, in general, insufficient to
    prove that something is other than random or a coincidence. It can be a
    good "search warrant" or cause to search for other explanations but, lacking
    such evidence, coincidence is by no means ruled out.

  As someone who works in probabilistic modelling, I'll have to take issue with Randy on this one. It seems to me that many scientific deductions are based on probability and statistics. You conduct a double-blind placebo controlled trial of a new drug and collect the statistics on it. You want to know if the drug has any effect. Sometimes it does and sometimes it doesn't for individual cases. So you collect the stats for a large number of patients, and determine the probability that the measured benefits could have occurred by coincidence.

  You said, Randy that coincidence is by no means ruled out. Of course, I agree you can NEVER rule out coincidence, but if the probability of the perceived beneficial effect of a trialled drug occurring by coincidence is less than 0.01, then statistically it is deemed "highly significant". Probably enough to justify the claim that the drug is useful. There is nothing magical about the 0.01; probability is always a grey area and there has to be some point where you draw the line in the sand, and say "we believe this is a real effect".

  Another example might be the link between smoking and heart disease/lung cancer. I'll bet the tobacco industries are promoting the idea that it isn't proven. Yes, of course it isn't proven, but the evidence is overwhelming. But "evidence" is a probabilistic thing here (statistical studies etc). Indeed, the term "evidence" has a specific mathematical definition in Bayesian statistics.

  Now Vernon's "evidence" might overwhelm or underwhelm different people, but that just means they draw the line in the sand at different points. But I'm afraid it won't do just to say "coincidence is not ruled out". I don't disagree there, but then it's not ruled out in the examples I gave above. Would you smoke 60 cigarettes a day because the evidence that it's bad for you could be just a coincidence? Depends how badly you want to smoke, I guess.

  Best wishes,
  Iain
Received on Wed Jan 11 21:23:00 2006