Analyzing large quantities of physical data during transient or other changing state conditions requires special treatment if results are to be useful. In this paper, results are derived for the accuracy to be associated with average response computations on a wide class of nonstationary data as a function of underlying signal and noise variations and the available sample size. Input and output signal-to-noise ratios are defined in terms of these quantities. Confidence bands are determined for both arbitrary probability distributions and for Gaussian probability distributions. A special result shows the increase in sample sizes required to analyze unknown distributions as opposed to Gaussian distributions in order to achieve a desired confidence band.