The naive estimation of errors in averages obtained from molecular simulation calculations may lead to serious underestimates due to the strong correlations that usually exist within the series. A commonly employed procedure to overcome this difficulty is to estimate the error from the deviation in the averages over subseries that are considered uncorrelated. However, without knowledge of the correlation the choice of the number of subseries cannot be soundly based. A method to estimate the statistical error using the correlation explicitly without serious additional computational effort and without the need for a tedious examination of the correlation behaviour itself is presented. Results of a test of this method for a molecular dynamics study on the polarization energy of xenon in liquid water are given and a comparison is made with the procedure based on subaverages and with a recently suggested method by Smith and Wells [1].