BTIB Designs and their Efficiencies for Comparing Test versus Control Treatments with Correlated Observations

Abstract

The experimental design for comparing test treatments with one or more controls is an important part of scientific experimentation. All possible paired comparisons among treatments may not be of equal interest. The main interest is to compare test treatments with control treatments and variancebalanced designs may not be useful. Balanced Treatment Incomplete Block (BTIB) designs and some reinforced BIB designs are usually considered for comparing test with one or more control treatments. Experiments to compare certain test with control treatment were first considered by Hoblyn, et al. (1954). Most of the authors developed block designs with no correlation among the plots in a block. But, in agricultural experiments, correlation among the plots or neighbour plot effect is quite common. Thus, an attempt has been made to develop BTIB designs having one control treatment with correlated observations. The designs are developed from 1st order neighbour balanced (NN1) block designs in linear blocks. List of developed BTIB designs having one & two control treatments are presented with their corresponding efficiencies for rho values (0 ≤ρ ≤1), where rho (ρ) is correlation coefficient among plots within a block.