Biases encountered in large-scale yield tests

Abstract

Abstract does not appear. First page follows. Introduction Certain difficulties in interpreting the results of the ordinary analysis of variance when applied to yield tests of genetically similar wheat strains, derived through backcrossing, prompted a critical examination of the data. These data indicated a bias inherent in any large-scale experiment that imposes an inflexible design upon a soil whose fertility may fluctuate markedly within short distances. Because of this bias, the usual analysis of variance tends to overestimate significance grossly when the number of varieties is large and the productivity levels of the soil change rapidly and erratically (as at Davis). One may briefly describe the bias by saying that the inflexible design of the experiment tends to subtract too little from the naturally high-yielding plots and too much from the naturally low-yielding plots in attempting to correct for differences in soil productivity. This has a spreading effect on the part of the variation that is labeled “varietal differences” and thus causes a serious overestimation of significance. In a conventional analysis of variance, the natural variation of an experiment is arbitrarily partitioned into categories according to a preconceived mathematical model. These categories are labeled “variation due to varieties,” “variation due to soil productivity,” and so on. If the experiment is in exact accord with the model, the labels are accurate. If the experiment is not as called for by the model, the labels are misleading: for instance, the category labeled “variation due to varieties” may contain some of the variation due to soil-productivity. A mathematical model may be pleasing and beautiful to its creator or users. If, then, nature does not conform to the model, workers having limited firsthand experience with the vagaries of biological material may even feel that nature has erred and should be corrected.