The trueness of an analytical method can be assessed by calculating the proportional bias of the method in terms of apparent recovery. If the apparent recovery does not differ significantly from one, the analytical method has not a significant bias. If this is the case, the bias is neglected and the uncertainty associated with this bias is included in the uncertainty budget of results. However, when assessing trueness there is always a probability of incorrectly concluding that the proportional bias is not significant. Therefore, the uncertainty of results may be underestimated. In this paper, we study how non-significant bias affects the uncertainty of analytical results. Moreover, we study how to avoid the underestimation of uncertainty by including the non-significant bias calculated in the uncertainty budget. To answer these questions, we have used the Monte-Carlo method to simulate the process of estimating the apparent recovery of a biased analytical method and, subsequently, the future results this method provides. The results of the simulation show that non-significant bias may underestimate the uncertainty of analytical results when bias contributes in more than 20% to the overall uncertainty. Uncertainty is specially underestimated when bias contributes in more than 50% to the overall uncertainty.