To my knowledge a z score is basically a mean divided by the standard error but it can also be z = (x-μ)/σ.
There are equations to convert z-scores into snp effects such as b=z/ 2p(1−p)(n+z^2) and SE=1/ 2p(1− p)(n+z^2) (https://images.nature.com/full/nature-assets/ng/journal/v48/n5/extref/ng.3538-S1.pdf). However, the desired units in this paper are the effect of the SNP on the raw trait units?
I want my outcome (the trait with the GWAS summary statistics in question) to be in SD units. Is the Z score the same as a standardised unit? In the readme file of the summary statistics, they say that the z-score in the summary statistics I want to use is "Combined z-statistic for the magnitude and direction of the association between the reference/coded allele and the volume of xxx, weighted on sample size.". Should I use the measure reported (i.e. z score) if I want interpretation to be "per standard deviation higher measure"? From what I understand, a standardised SNP effect on trait estimate and zscore for effect of SNP on trait is the same but not sure here as they use sample size.