The estimation of the uncertainties affecting the determination of var
ious parameters characterizing spectral line profiles recorded in Stok
es I and V that are used in the diagnosis of stellar magnetic fields t
hrough the moment technique is described. Simple statistical considera
tions are presented, to demonstrate that the errors are properly asses
sed and to illustrate how their evaluation can be exploited to derive
information about the physical properties of the studied stars. It is
shown that taking these uncertainties properly into account allows one
to achieve better determination of the mean longitudinal magnetic fie
ld. Improved Values of the latter are derived for observations already
analysed in earlier work. The approach sketched in this paper is inte
nded as a basis for future studies of magnetic fields of Ap stars.