The computer analysis of factorial experiments is discussed in terms of a new generalized matrix notation which highlights the special properties of factorial designs. A method of calculating an analysis of a variance suitable for programming as a library subroutine is described. An orthogonal transformation is used to obtain components of variance based on single degrees of freedom. The transformation is done sequentially so that no additional storage for intermediate results is required. The analysis of variance table is obtained by summation of the components according to a simple indexing procedure. An algorithm for the calculation of sums and means over all combinations of factor levels is proposed.