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