Wiskundige beschouwingen bij eenige hoofdstukken uit de philosophie der landbouwwetenschap

Because of the many factors involved in agricultural problems experimental methods could not be based on ceteris paribus, as in other natural sciences, but required factorial trials with simultaneous variation of many factors. A complete factorial experiment was unworkable in practice because of the large area required but trial size could be reduced by ignoring interactions of higher order.

Interactions of higher order sometimes cancelled out main effects and interactions of lower order. To avoid this undesirable effect, analogous functions called 'main action' and 'interplay' were introduced. The trial could be reduced to a smaller size by splitting the complete factorial experiment into partexperiments of factorial form for a small number of factors. Various possibilities were studied, including the replication of some treatments in different experiments to adjust results. Replicates were needed also to estimate variances and to compare these with interactions. Thus the estimation of variance from interaction terms could be avoided.