Hi Gina,
In case this helps, my guess is that this may simply reflect a confusion on what the term "z-transform" is referring to here, as a very common practice in functional connectivity analyses is to use a "Fisher z-transformation" to convert Pearson correlation coefficient values (r) to Fisher-transformed correlation values (z), where the transformation is simply z = arctanh(r). Since, under certain assumptions, the resulting z values can be expected to follow a Gaussian distribution (with zero mean and variance that can be estimated from the data, see for example Afyouni approach in https://pubmed.ncbi.nlm.nih.gov/31158478/) these Fisher-transformed z- values are often perfectly appropriate measures of connectivity strength to enter into your second-level analyses (e.g. GLM analyses; this is exactly what the CONN toolbox does by default when computing seed-to-voxel functional connectivity maps or ROI-to-ROI functional connectivity matrices). Also because of the same Gaussian limit properties, it is not uncommon to somewhat loosely refer to these Fisher transformed correlation coefficient values as z-values or z- scores, or even refer to the entire Fisher z-transformation (with or without re-scaling to unit variance, e.g. z=arctanh(r) vs. z=arctanh(r)/sqrt(N-3)) as a "standardization" or "normalization" procedure. So my guess here is simply that perhaps the z-transform that the authors are describing corresponds to the transformation between correlation coefficients and Fisher-transformed z-values (i.e. z = atanh(r), or equivalently between T-stats and Fisher-transformed z-values, e.g. z = atanh(T / sqrt(df+T^2)), and not the transformation that I believe you are interpreting/describing between T-stats and "equivalent" z-scores (e.g. z = spm_invNcdf(spm_Tcdf(T,df)) ) which, as you describe, would be harder to justify and interpret in the context of GLM (although probably fine in the context of linear mixed effect models)? Please feel free to correct me if I am misinterpreting
Hope this helps
Alfonso
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