Dear Stuart,
with your procedure of gathering evidence for black ravens you essentually
desribe statistics in a Bayesian framework (and in fact the way most people
would go about forming their beliefs about the world). In a Bayesian
framework
we start out with one or more beliefs/assumptions/hypotheses (the priors)
which are modified by the data we observe. In your example, we would
have the belief that ravens are black, but since we have never seen any
ravens,
we are not particularly sure about it. This would be captured in a weak
or even non-informativ prior. However, as more and more black ravens are
observed, we also become more and more certain about this assumption.
We are then in a position to say something like "Given all the data I
have seen
so far, I am 90 percent certain that ravens are black."
However, adopting the frequentist framework and conducting a null hypothesis
test you are asking yourself a different question, namely "If my
hypotheses were
correct, how likely is it that I see that data?" Now in this situation,
even if it is
extremely likely to find the data exactly as you have observed it, you still
cannot conclude that your hypothesis is correct. Even if I see thousands of
black ravens, I cannot say "Yes, all ravens are black" until I have seen
them all.
All I can say is "I am pretty certain that all ravens are black" (see
above).
I should add that the Bayesian way of thinking is not only very
intuitive, it also
becomes increasingly popular in the fMRI communitiy and should be viewed
as an alternative to Null Hypothesis Tests that enables us to draw
conclusions
from our data in an interesting and different way. Eventually, there is
no right
and wrong in choosing one of the frameworks to work in. However, when
using a certain method, we should be very clear about what it can and what
it cannot do!
Jane
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