... deviation¹

Note that in the simplest cases the variance of the mean is the variance of the residuals divided by the number of data points.

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... pooling²

The first factor of $1/n$ in FV comes from taking the mean of the first-level variances, i.e., pooling them, and the second factor comes from converting this higher level variance from a variance of residuals into the variance of the (higher-level) mean. For more detail see [16].

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... mixed-effects³

Note that the terms ``mixed effects'' and ``random effects'' are often (incorrectly) used interchangeably.

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... FE⁴

We are attempting to identify voxels of potential interest in ME-Z images; given that ME-Z can be thought of as being related to FE-Z but scaled down by a factor related to session variance, this seems like a good way of choosing voxels which have the potential to be activated in the ME-Z image, depending on the session variance. In order to investigate the dependency of this approach on the FE-Z threshold chosen, we re-ran the tests leading to the ME-Z plots presented in Figure 8, having determined the regions of interest using a lower FE-Z threshold (Z$>$1.64, i.e., a factor of 5 more liberal in the significance level). The mean ME-Z results were all scaled down, as expected, but the qualitative (i.e., relative) results were exactly identical to those presented in Figure 8.

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... above).⁵

Whilst we are primarily investigating analysis efficiency and session variance by looking at regions of potential activation, note that it is also necessary to ensure that the non-activation (null) part of the ME distribution is valid, i.e., not producing ``incorrect'' numbers of false-positives; this investigation/correction of the ME null distribution is addressed below and uses the whole ME-Z image, not just the regions of potential activation.

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... variability.⁶

Noting the much greater variability (across methods) in these ratios than in the plots in figure 8, and by looking in detail at separate ME and FE variances, it is clear that the variation in these figures across methods is primarily due to variation in FE variance. This is possibly caused by differences in the methods of correcting for temporal autocorrelation at first level.

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