Nested Designs

1. Nested Block Designs Heterogeneity in the experimental material is the most important problem to be reckoned within the statistical design of scientific experiments. If it is not suitably taken care of, in designing of an experiment, is likely to over shadow the real treatment differences making them remain undetected, unless they are large enough. Occasionally, one can find a certain factor (called nuisance factor) which, though not of interest to the experimenter, does contribute significantly to the variability in the experimental material. Various levels of this factor are used for blocking. Blocking is the technique used to bring about homogeneity of experimental units within a block, so that the treatment contrasts are estimated, making use of the intra-block information, with higher efficiency. For the experimental situations where there is only one nuisance factor, the block designs are used. When two such cross-classified factors are present row-column designs such as latin square, lattice square, Youden square, generalized Youden, pseudo Youden designs etc. are being used. In many a field and laboratory experiments the experimental units or conditions differ due to several factors which influence the response under study. It might not always be possible to remove such heterogeneity in response due to the factors other than treatments by blocking alone. There are the experimental situations in which there are one or more factors nested within the blocking factor. When there is one such factor, then nested block designs have been developed. To make the idea more clear, let us have a look at the following experimental situations.