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Re: patient vs group of normal subjects

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Fri, 29 Feb 2008 15:40:35 +0100

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 ```Hallo Jerome, > Is "2-sample t-test" valid as the variance for the single patient is > not estimable? yes. If y is your patient piece of data, and x the data from the control sample, then under the null hypothesis and standard modelling assumptions, y ~ N(m, sigma_square), x ~ N(m, sigma_square), and average_x ~ N(m, sigma_square/n), where m is the mean under the null, n the size of the control sample (16 in your case), and N is the normal distribution. Under the null hypothesis, the variate y - average_x ~ N(m - m,sigma_square + sigma_square/n) = N(0, sigma_square * (n + 1) / n), and if you replace sigma_square with the variance estimate from x you have Student's t instead of N with n - 1 df (one df goes into estimating the mean of the x). If you put your data (x,y,n etc.) into the formula for the 2-sample t-test you see that you get a formula algebraically equivalent to the one above, t(0, sigma_square * (t + 1) / n), after some simple manipulation. Beware that this test is extremely unbalanced because one of the two groups has size 1. You'll have heard that unbalancedness leads to skewness being retained in the estimate etc. This is because you can't rely much on the central theorem to get closer to normality assumptions, since the distribution of y - average_x is dominated by the distribution of y (I mean, in terms of skewness and kurtosis). y is, so to speak, an outlier with high leverage. Hence, your test is rather vulnerable to departures from normality assumptions. All the best, Roberto Viviani Dept. of Psychiatry III University of Ulm Quoting Jérôme Redouté <[log in to unmask]>: > Dear SPMers, > We would like to compare FDG-PET scan from 1 patient to a group of > normal subjects (N=16) > Which model should we use (with SPM5) to do such a comparison? > Is "2-sample t-test" valid as the variance for the single patient is > not estimable? > Thanks for your help > Jerome > > -- > =============================================================== > Jérôme Redouté > CERMEP - Imagerie du vivant > Centre d'étude et de recherche multimodal et pluridisciplinaire > 59 Bd Pinel > 69667 Bron - FRANCE > tel : 33 (0)4 72 68 86 13 (bureau) > tel : 33 (0)4 72 68 86 00 (standard) > fax : 33 (0)4 72 68 86 10 > =============================================================== ```