Dear Stuart,
Thanks for this - my failure to respond is not through pique but, rather, I
was away on holiday..
I agree with much of what you say. One must of course be wary of assuming
that something like fMRI will identify differences in task-related activity
with the same degree of certitude that we can identify blackness in ravens.
A lack of difference in 12 fMRI subjects, or even, if it is a huge fMRI
study consisting of 16 or 20 subjects, would not be as weighty as finding
1000 black ravens. in the latter case, sheer numbers, plus a clear
understanding of what constitute raven-ness and blackness must instil
confidence. Therefore, I concede to you in principle but suggest caution in
practice when the independent variables are under-specified and the outcome
variables are noisy (and the n is relatively small). As you say, though,
replication or, at least, accumulation of consistent data cannot be ignored.
This is currently rare rare in functional imaging I think.
(Isn't there also a logical problem to be considered - i.e. all ravens are
black is the equivalent of all non-black things are non-ravens. Thus, every
time you find something white that isn't a raven, you've added evidence in
favour of your hypothesis. So every seagull that I saw on my holiday was in
fact a piece of evidence in favour of your view that all ravens are black.
Tee hee).
Thanks for the mail
Very best
Paul
----- Original Message -----
From: "Dr. Stuart WG Derbyshire" <[log in to unmask]>
To: <[log in to unmask]>; <[log in to unmask]>
Cc: <[log in to unmask]>
Sent: Thursday, June 10, 2004 10:45 PM
Subject: Re: accepting the null hypothsesis
Dear Paul et al:
At the risk of generating a thoroughly annoying debate let me state
that I believe finding 1000 black ravens is tremendously informative
if trying to prove that all ravens are black.
If it is my hypothesis that all ravens are black, discovering black
ravens is obviously supportive of that theory but it is also the
only evidence in favour of the hypothesis that I can possibly
uncover. Does it ever get more important and informative than this?
So I find my 1000 black ravens and report the finding to a reputable
journal. It is published and then you go out and find another 1000
black ravens and publish your findings. Two continents, 2000 black
ravens. Then our good friends and colleagues in Asia, not to be
outdone, hunt down a further 2000 black ravens. Their work, too, is
published in a fine journal and things are looking pretty good for
the "all ravens are black" hypothesis.
Then someone finds a white raven and it appears on the front cover
of Science. Darn it. So all ravens are not black then? Well, maybe.
Perhaps that raven fell into a bucket of white paint and was really
black all along. Or perhaps that raven is a dove looking a bit
ravenish?
Whatever Popper might have said, science does advance through an
accumulation of evidence that facilitates a growing consensus about
the natural world. Once we have developed an idea that fits the
evidence, and is predictive, we become highly skeptical of white
ravens popping up to spoil the story. This is not necessarily
because we are being dogmatic, though that can be the case, but it
is because we believe we are saying something important about the
character of ravens rather than about this peculiar white raven.
You can pelt me with raven poop in Budapest.
Stuart.
---- Begin Original Message ----
From: Paul Fletcher <[log in to unmask]>
Sent: Fri, 28 May 2004 08:45:09 +0100
To: [log in to unmask]
Subject: Re: accepting the null hypothsesis
Hello,
I would be a bit careful about making this the basis for an
experiment:
accepting the null hypothesis is avoided for very good reasons.
First, it is
an unsatisfying way to go about things - if you want to prove that
all
ravens are black (if this is your null hypothesis), finding one
white one is
far more informative than finding 1000 black ones. Second, the idea
of a
less stringent p value doesn't really help much. Imagine that you
set a p
value of 0.1 and found no difference - this would enable you to say
that,
even if you accepted a 1 in 10 chance of falsely rejecting the Null
hypothesis, you were unable to reject it. This isn't a very
convincing way
of saying that the null hypothesis is acceptable. If you increase the
threshold to p=0.5, you're giving yourself a 50% chance of falsely
rejecting
it. Still not a very compelling foundation for accepting it.
If I were you, I would try somehow to incorporate the
putative "sameness" of
the conditions into your design. I'm assuming that you believe them
to share
a process and that this sharing should be reflected in coincident
activation
in a given region (the region that does the process, if we want to
get
phrenological). One way of providing evidence that this is the case
would be
to compare the two conditions directly and to find no difference.
This would
be subject to the problems that you clearly recognise and that are
rehearsed
above. However, if each of them were compared separately to their own
control tasks (note: not to a common control task) and shown to
activate the
same region, then this would at least allow you to point to two
separate
null hypothesis rejections and to suggest on this basis, a shared
process
(assuming that there is a one-to-one mapping of process to region).
This is
akin to the position that Price and Friston put forward in advocating
conjunction analyses.
I don't think that this is watertight approach (for example, if you
want to
say that the two regions show the same magnitude of activation, it
becomes
more difficult) but it will perhaps allow you to formulate an
experiment
that is not dependent upon the dreaded acceptance of the null
hypothesis.
best wishes and good luck
Paul Fletcher
----- Original Message -----
From: "Johannes Gerber" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Thursday, May 27, 2004 4:20 PM
Subject: [SPM] accepting the null hypothsesis
Hi,
a question: how would you design and analyse a functional imaging
experiment where you are interested in not rejecting the null
hypothesis.
that is, where you don't want to see a difference between two
conditions.
is there a great example in literature?
asking some knowledgeable people, there was the suggestion to lower
the
thresholds. but you always see something in SPM when lowering the
thresholds.... is there a more elegant way of doing it? I would be
happy
with any comment.
thanks in advance!
Johannes
Dr. med. Johannes Chr. Gerber
FA Diagnostische Radiologie
Abteilung Neuroradiologie
Institut und Poliklinik für Radiologische Diagnostik
Universitätsklinikum Dresden
D-01304 Dresden
Tel.: 0351-458 5227 / -2660
Fax.: 0351-458 4370
---- End Original Message ----
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