ABSTRACT

In 2n factorial experiments, the number of treatments increases with in­ creases in numbers of factors. For example, in 23, 24, 25, 26, and 27 experi­ ments, there will be 8, 16, 32, 64, and 128 treatment combinations, respec­ tively. A large number of combinations of treatments leads to large-sized blocks. As blocks become larger and larger, they are likely to encounter greater and greater soil heterogeneity within blocks. Consequently, the er­ ror would be increased. Such a difficulty may be overcome by a device called confounding. Confounding enables the experimenter to carry out the study with blocks containing lesser numbers of treatments than a full repli­ cation of the treatment combinations, thus increasing the accuracy of the experiment. Each block is an incomplete block in the sense that a block does not contain all the treatments of the experiment. When treatments are assigned to incomplete blocks, we require several incomplete blocks de­ pending upon the number of treatment combinations. For example, if there are eight treatment combinations, four can be allotted to one block and an­ other four to the second block, i.e., a replication is subdivided into two blocks each containing four plots so that the plots within each block be­ come less heterogeneous. The treatments are then allotted to the incomplete blocks. By doing so, some treatment differences are merged (confounded) with blocks and they are not separable from the blocks.