On Wed, 12 Apr 2000, Robert Dawson wrote:
>
> I'm afraid that I don't follow your definition of a "plausible null".
> On the one hand, you say that my value (in the simulation I included) of
> 102 for the mean IQ of a population is "a priori false"; you then say that
>
> "I like interval estimates because they give me a good
> range for my plausibly true values for the null."
>
> But if I had computed a 95% confidence interval from almost any of those
> simulated data sets, 102 would have been in it.
>
> Had I said that the mean IQ was actually 102 and that I was testing
> the null hypothesis that it was 100, would you have called _that_ a
> plausible null? My point - that repeated failures to reject the null
> should *not* automatically increase one's belief in its truth - would
> be equally valid.
One of the reasons I have been enjoying this discussion is I am learning
about the unshared assumptions that I have been making.
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.
So, the values identified by a confidence interval would fit my usage of
plausible. They are consistent with current knowledge, but some, most of
them, will eventually be eliminated. While a value pulled from thin air
is arguably plausible given no prior information, I would include a
requirement for parsimony. Absent information a no effect hypothesis is
the most parsimonious.
I have been using "a priori false" to refer to a hypothesis that is known
to be inconsistent with current knowledge. It is not even a reasonable
guess at the correct value.
If I choose to follow up on research in which a non-zero effect is well
established but the parameter estimate has, to me, an unacceptably wide
range I can use the previous estimate as my null and either find that my
results are explainable as a chance deviation from the existing estimate
or my results indicate that the existing estimate is too large/small.
That is my results would either tend to support the status quo or refute
it.
In a discussion about the estimation of the speed of light the authors
(sorry, I can't remember who or where. If anyone recognizes this example
please point me to the reference) describe how the initial estimates of
the speed of light were too high and had a very wide CI. Over the course
of years with improved technology the best guess estimate of light speed
changed and the CI narrowed. While the mechanics that we know as
hypothesis testing were absent the researchers were clearly using the
established best estimate as the equivilent of a null and modifying it as
better data became available, and leaving it stand otherwise.
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.
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).
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? How about if n = 1000? 10,000? How much
power has to be present before failure to reject the null is support of
the null?
Michael
>
> -Robert Dawson
>
>
>
>
>
*******************************************************************
Michael M. Granaas
Associate Professor [EMAIL PROTECTED]
Department of Psychology
University of South Dakota Phone: (605) 677-5295
Vermillion, SD 57069 FAX: (605) 677-6604
*******************************************************************
All views expressed are those of the author and do not necessarily
reflect those of the University of South Dakota, or the South
Dakota Board of Regents.
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