Nonadditivity in a Two-Way Classification: Is It Interaction or Nonhomogeneous Variance?
讨论了在每格只有一个观测值的双向表中，非可加性可能源于行或列相关的方差不齐或交互作用，提出一个通用模型来检测这两种非可加性，并结合科学背景帮助数据分析者解释观察到的非可加性。
Abstract Nonadditivity in a two-way table with one observation per cell may be due either to row- or to column-related nonhomogeneous variance or to interaction between the row and column factors. A general model that can detect both of these types of nonadditivity is discussed. The data alone are not sufficient to distinguish between interaction and row- or column-related nonhomogeneous variance when there is one observation per cell. A study of the fitted coefficients in the proposed model together with the scientific background of the problem can, however, provide the data analyst with the information necessary to develop a useful interpretation for the observed nonadditivity. Examples are included to illustrate the proposed methodology. In one example, involving the effects of four varieties of wheat in 13 locations, it is shown that the variety-related nonhomogeneous variance detected by several authors is more usefully interpreted as a level-dependent interaction due to the differences among the yields of the different varieties of wheat being larger in those locations that have higher yields.