Indeed, proving the null hypothesis is not only difficult, it is almost
sure to be impossible, since the null hypothesis is practically never
correct. That is, the brain activation for two different conditions will
almost never be *exactly* the same.
A more meaningful question to ask would be "does this region of the brain
show a difference in fMR signal between two conditions that is greater than
x%?". x% in this case is an estimate of what constitutes a theoretically
meaningful change in fMR signal. One can then combine the statistical test
of difference with a calculation of the statistical power for that given
experiment (i.e., the probability that you would be able to detect a
difference of x% at a given statistical p-value given your experimental
design and the variance of the data you collect). Then, if you do not
detect a significant difference, and your statistical power is high enough,
you can start to make inferences about the lack of effect of the given size.
<rant> Unfortunately, one still sees far too many articles that make the
blunder of logically equating "lack of statistically significant
difference" with "no difference". The frequency that such blunders get
through the review process is disturbing. </rant>
Tom Johnstone
At 03:07 PM 12/7/2001 -0500, Dr. Stuart WG Derbyshire wrote:
>Hi Anna:
>
>Proving a negative is never easy but in your case it is quite clear
>you have failed to succeed!
>
>The question is not "Are these activations there by chance?" but
>rather "Do I have sufficient evidence to reject the hypothesis of
>activation?".
>
>Normally the intrepid researcher must protect against false positive,
>hence the statement that result X has less than a 1-in-20 (p<0.05)
>chance of being a false poitive.
>
>Your aim, however, is the reverse and you must protect against false
>negative and be able to state that the absence of result X has less
>than a 1-in-20 chance of being a false negative.
>
>Exactly how this might be achieved I am not sure (others may want to
>pitch in here) but with activation at a Pun<0.001 I do not see how
>you can possibly fulfill the criteria above.
>
>Hope that helps...
>
>Stuart.
>
>
>---- Begin Original Message ----
>
>From: Anna Barnes <[log in to unmask]>
>Sent: Thu, 6 Dec 2001 16:10:28 -0500
>To: [log in to unmask]
>Subject: thresholds and a priori hypotheses
>
>
>If you have a hypothesis that there are no differences between one
>brain
>scan and another in a group and you set your thresold at the a priori
>hypothesis level of Pu<0.001 expecting there to be a blank SPM(t) map
>and
>this map shows blobs at this significance level what does that mean
>as far
>as your a priori hyopthesis of no difference goes. Are the blobs
>real or
>are they there just by chance ?
>
>Best regards
>Anna
>
>Anna Barnes (PhD)
>North Shore- LIJ Research Institute
>Functional Imaging Laboratory - Centre for Neuroscience
>New York University School of Medicine
>
>350 Community Drive
>Manhasset, NY 11030
>Phone: (516) 562-2498
>Fax: (516) 562-1008
>
>
>---- End Original Message ----
>
>
>
>Sent by Medscape Mail: FREE Portable E-mail for Professionals on the Move
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