01284naa a2200121 a 450000100080000000500110000800800410001910000200006024500650008026000090014552009710015477300370112516494382000-08-28 1952 bl --- 0-- u #d1 aWILLIAMS, E. J. aThe interpretation of interactions in factorial experiments. c1952 aWhere the joint effects of two or more factors are not additive, a simple model is proposed for representing the effecting the effects. The effects of one factor are assumed to be proportional, rather than equal, at different levels of the other factors. The main effects of the fist factor are given asweighted averages of the simple effects at the different levels of the other factors, the other factors, the weights being the estimated factors of proportionality. The weights are as the latent vector of a matrix of sums of squares and products correspondding to the largest latent root of the matrix the sum of equares for the weighted main effect is mulltiplle of this latent root, and the other latents roots correspond to a partition of the interaction sum of squares. The analysis is closely related to the canonical analysis of a set of variates. Tests of significance of the residual interactions and the adequacy of proposed set of weights are discussed. tBiometrikagv.39, p.56-81, 1952.