PREDICTION INTERVALS FOR SUMMED TOTALS

Methods are discussed for calculating prediction intervals for total estimates that are sums of individually derived estimates. Special attention is given to the problems encountered when the variances of each of the individually derived estimates cannot be assumed to be equal. This problem is essentially identical to the well-known Behren-Fisher problem except that here the context is one of deriving a 't-ratio' for summed means. For the case of unequal variances, the prediction interval is based on a statistic with an approximate t-distribution and the interval itself must be viewed as an approximation. Examples are given for each of the cases considered.