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
under book chapters, random effects analysis.
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
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,