Classification by likelihood ratio of a one-dimensional random variate drawn randomly and with equal probability from one of two independent Gaussian populations is known to be optimal if misclassification costs are equal and statistics (true means and variances) are available; the expected classification error is then a known function of the statistics. In practice, likelihood functions are computed with sample statistics estimated from training sets of n samples. The effect of sample statistics in lieu of true statistics on the expected classification error is calculated to order n−1. The error is found to increase by a term proportional to n−1 over a wide range of statistics, unless the random variate is from the training set; in the latter case, the error decreases by that term. Monte Carlo experiments were performed with results supporting the theory.