  The determination of the longitudinal spin Seebeck effect (LSSE) coefficient
is currently plagued by a large uncertainty due to the poor reproducibility of
the experimental conditions used in its measurement. In this work we present a
detailed analysis of two different methods used for the determination of the
LSSE coefficient. We have performed LSSE experiments in different laboratories,
by using different setups and employing both the temperature difference method
and the heat flux method. We found that the lack of reproducibility can be
mainly attributed to the thermal contact resistance between the sample and the
thermal baths which generate the temperature gradient. Due to the variation of
the thermal resistance, we found that the scaling of the LSSE voltage to the
heat flux through the sample rather than to the temperature difference across
the sample greatly reduces the uncertainty. The characteristics of a single
YIG/Pt LSSE device obtained with two different setups was $(1.143\pm0.007)\cdot
10^{-7}$ Vm/W and $(1.101\pm0.015)\cdot 10^{-7}$ Vm/W with the heat flux method
and $(2.313\pm0.017)\cdot 10^{-7}$ V/K and $(4.956\pm0.005)\cdot 10^{-7}$ V/K
with the temperature difference method. This shows that systematic errors can
be considerably reduced with the heat flux method.
