Dear Sue,

Many thanks for your thoughtful question. I would not worry too much about the statistical imperatives for sample size: the key thing is to report clearly what you have done and qualify your statistical inference appropriately.

In your case, I recommend that you do a small number of subjects and use a random effects analysis of the between subject level under a pooled variance assumption. This sort of modelling was implicit in the use of PET and is ideally suited to small and longitudinal studies. Practically, you would analyse each session from each subject separately and summarise the effects of interest with an appropriate contrast image. These contrast images would then be passed to the second (between subject) level but, crucially, treating each session as an independent observation. This means that your degrees of freedom will be the number of subjects times the number of times each subject was scanned. This should provide more than enough power to detect consistent effects over subjects and is implicitly assuming that the error variance between sessions (within subject) is the same as between subject variability. As long as you make this explicit, everything should be fine.

I hope that this helps.

With very best wishes,

Karl

________________________________________
From: Sue Pockett [[log in to unmask]]
Sent: 23 September 2011 23:41
To: Friston, Karl
Cc: Suzanne Purdy
Subject: Re: How many subjects constitute a study?

Dear Professor Friston

As a newcomer to fMRI, I wonder if I could ask your advice.

My question relates to an fMRI experiment we are proposing on the
question of how brain activity changes as an adult subject learns a
new language.  Existing literature on bilingualism suggests the
prediction that learning a new language will initially involve
relatively widespread brain activity – specifically, bilateral
activity in Broca’s area and its right hemisphere analogue – and that
as the language is learned this will contract to activity only in the
classical language areas.  We propose to investigate this prediction
by doing a longitudinal study in which individual subjects are
repeatedly scanned at 6 monthly intervals while listening to stories
(a) in their native language (English) and (b) in the language they
are learning (with degree of learning tested by scores on standard
language tests). The expectation is that brain activity during the
English story will involve the standard language areas and will remain
relatively constant over the course of the study, while activity
during the L2 story will evolve as predicted.

Your excellent paper “How many subjects constitute a study?” promises
to make a longitudinal study of this sort possible, by pointing out
that if all we are trying to do is “establish the observed effect as a
typical characteristic of the population, while allowing for the fact
that some subjects may not show this effect”, relatively few subjects
are necessary.  Unfortunately the same paper then says “Learning
experiments, over protracted periods of time (as opposed to
withinsession adaptation), require random-effect inference because the
treatment only exists on a subject- or session-specific level” –
which statement is presently being used to prevent our embarking on
the proposed study on the grounds that a financially impossible number
of subjects is necessary.

I frankly don’t understand the statistical arguments in your 1999
paper, but it seems to me that the paper as a whole is motivated by a
desire to provide statistical support for the common-sense view that
“knowing a particular characteristic is typical is more useful than
not knowing this fact.”  It also seems to me that knowing that our
prediction is either not borne out at all, or, for example, borne out
in 5 of 6 individual subjects who are comparable in age and experience
of learning languages, would be interesting.

Could you possibly give us the benefit of your statistical expertise
on this question?

Many thanks

Sue Pockett
Dept of Psychology
University of Auckland
New Zealand