The analysis of complex factorial experiments is performed most efficiently and reliably by means of a tabular procedure suggested by Yates and described originally for the case ofnfactors each at two levels. In the present paper the method is generalized to factors at any number of levels, not necessarily the same for each factor. The calculations involved lend themselves to standard punch card equipment, and a fully programmed example of an experiment with factors at 2, 3, and 4 levels is described.