A very common problem which arises in animal or plant breeding research is that of assessinig the gain which has resulted from a selection program carr'ied oIn ovei a number of years. To be specific, let us suppose that we have a closed dairy herd which has been maintained over a number of years with selection being practiced. The records available for assessing any genetic improvemient consist of production records of cows in the various years and can be represented by a twoway classification, cow by year. At first it might be thought that such a two-way classification could be analyzed by the method of fitting constants Yates, 1934. Applications of this technique have, however, led to the apparent conclusion that the environment gradually deteriorated over the period of years, as indicated by the fact that the constants fitted for years tend to decrease year by year. Heinderson 1949 pointed out that a least squares procedure in which the cow effects are regarded as fixed leads to biased estimates. Lush and Shrode [19501 gave a simple explanation of the biases arising in the estimation of age correction factors; similar considerations apply to the estimation of year effects. The present paper is the combined
Henderson et al. (1959) studied this question.