WE consider a set of pq observations xij in a two-way classification, which we may suppose represented by the model where αi and βj are constants and the eij are independent normal random errors with zero means and variances σj2; αi, βj and σj2 are unknown, and it is desired to estimate σj2. The problem arises, for example, in investigating the accuracy of a food-tasting panel; αi depends on the food-specimen tasted, βj is the bias and σj2 the residual error variance of the jth panel member.