Dear Anne,
let me just add a few things to the previous contributions on a subject that I
believe is relevant.
Tom Johnstone defined the framework correctly. Null hypothesis cannot be proved.
He also suggested the use of a power test to extract the information on the Null
you want.
A weak point of combining a statistical test with an ensuing power test is that
the power test is going to be based on estimated parameters (p-value, effect
size etc.). Since no added information or data is inserted in the analysis than
the information content of the power analysis can be no better than the original
test. In short, confidence intervals may be a simpler and wiser tool in the
context (Hoenig and Heisey, 2001).
May I suggest at this point another way of approaching the problem that is a
reformulation of Tom's approach. It is called Equivalence Testing (Schuirmann,
1987) and simply consists in resetting the Null Hypothesis.
The old Null hypothesis was:
Ho: "This region of the brain show a difference in fMRI signal"
The new is now.
Ho: "This region of the brain show a difference in fMRI signal greater than x"
You can easily test the above with two one sided tests, each one at the alfa/2
level (where alfa is either corrected for multiple comparisons or not depending
on your taste).
For all the regions that are significant out of the above tests (a conjunction
!) you can then reject the Null. For the regions that don't you cannot obviously
infer anything.
The above should be easily implemented in SPM.
References:
1) Hoenig JM, Heisey DM (2001)"The abuse of power: the pervasive fallacy of
power calculations for data analysis", The American Statistician 55(1):19-24
2) Schuirmann DJ (1987)"A comparison of the two one-sided tests procedure and
the power approach for assessing the equivalence of bioavailability," Journal of
Pharmacokinetics and Biopharmaceutics 15,657-680.
Regards
Federico E. Turkheimer
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