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Subject:

Re: Seond level con vs spmT images

From:

Penny, William

Date:

Wed, 31 Aug 2011 16:30:32 +0000

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 ```Dear Vladimir, Another perspective is that if one bases the second level analysis on con images then this 'summary statistic approach' is equivalent (on average) to a 'gold standard' (but computationally more expensive) random effects analysis. This equivalence does not hold if the summary statistics are t-values. You can read more about this equivalence in chapter 12 of the SPM book - also available from my web page http://www.fil.ion.ucl.ac.uk/~wpenny/ under book chapters, random effects analysis. Best, Will. -----Original Message----- From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Roberto Viviani Sent: 31 August 2011 16:58 To: [log in to unmask] Subject: Re: [SPM] Seond level con vs spmT images This is an interesting question which has come up at least once on the list previously. This is my argument: The t statistic is not a consistent estimator of an effect size. That is, for df -> Inf (for increasing sample size), var(t) -> 1. This is because t gradually approximates z, the normal variate, at infinite degrees of freedom. Instead, let b_hat a parameter estimate in a linear model (the values in con images), and then we have for df -> Inf, var(b_hat) -> 0. That means b_hat is a consistent estimate of b, as it implies Prob([b_hat - b] > epsilon) -> 0. (Actually, it's well known that parameter estimates in a linear model are consistent, so my argument only concerns t.) > > Why in the second level of analysis in SPM the con images are used > but not spmT images? I am a biologist and not an expert in > statistics, thus I need a simplified explanation, if possible. > > Thank you in advance for your responses! > > Sincerely yours, > Vladimir > ```