||Direct numerical simulations (DNS) provide useful information for the understanding and the modeling of turbulence phenomena. In particular, new methodologies recently allowed the achievement of high Reynolds number in DNS of the benchmark plane channel flow. In this scenario, estimating the statistical errors associated with DNS is a difficult but necessary task. Here, we present a methodology to evaluate the statistical errors of the second-moment DNS data. In this methodology, the momentum balance equation is used to calculate the mean velocity profile by considering the Reynolds stress tensor provided by DNS. This error evaluation was applied to different plane channel flow databases available in the literature. We show that using the Reynolds stress statistics obtained from standard DNS can lead to significant discrepancies for turbulence modeling. One interesting consequence of this approach is that we are able to compute the Reynolds shear stress from the converged first order statistic. This information can be used, for instance, to extract a more accurate turbulent viscosity for turbulence modeling purposes. Moreover, the new methodology seems to be a promising path to formulate a convergence criterion for future plane channel DNS.