Michael Granaas wrote:
> I have in my own mind been using "plausible" to refer to a hypothesis that
> has not been refuted by data. We may certainly find at some point that
> the hypothesis is in fact false, but at the time we propose it it could be
> true. We may even wish it to be false at the time we propose it. But as
> of the time we propose it we cannot say with conviction that it is false.
...
> The only context for your example was that the data were generated with a
> specification that they come from a population that was N(100, 15). We
> therefore have prior knowledge that 102 is not the correct answer.
In a simulation, the specified sampling distribution is "playing the
part" of a sampling distribution; its parameters are thus "unknown for the
purpose of the exercise". Within the
context of the simulation we do *not* know that 102 is not the correct
answer.
> But, if I were in fact trying to guess at the IQ of a population, the data
> from a sample of n = 10 provides precious little information, as you
> clearly demonstrated. But, if I had to try, my likely null for an unknown
> population would be 100 since that is the normed mean IQ for some
> population and therefor is consistent with prior knowledge. That is a null
> of IQ=100 is a credible true value until I can get better data (it might
> even be the correct value).
And you still claim not to be a Bayesian? <grin>
> If n = 10 and I cannot reject a null of 100 I certainly agree that the
> corroboration value is low. But, if n = 100 and I can't reject a null of
> 100 I am starting to see support for 100 as a correct value. If n = 500
> and I cannot reject a null of 100 would you still demand that I had no
> evidence supporting the null?
Yes, given that mu=100.5 is part of the alternative
How about if n = 1000?
Yes, given that mu=100.1 is part of the alternative
10,000?
Yes, given that mu=100.05 is part of the alternative.
And note that repeating any of these will give the same result with high
probability: you cannot, then, assume that a long sequence of tests with
n=10,000, most failing to reject mu=100, provide any evidence whatsoever
that mu is not equal, say, to 100.1 .
-Robert Dawson
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