A Graphical Approach as Multiple Comparison Method for the Balanced and Partially Balanced Lattice Designs

This study proposes a reliable and easy understandable statistical solution for the selection of varieties in the balanced and partially balanced lattice experiments, which are widely used in plant breeding studies. For this purpose, the Analysis of Means (ANOM) was adapted to the balanced, simple and triple lattice designs and an R function is developed for it. The adapted ANOM approach was compared with the Tukey, Duncan and Fisher’s LSD tests with respect to the actual type I error rate in all of the balanced, simple and triple lattice designs. In addition to this, the ANOM approach and Tukey test were examined comparatively using a hypothetical example. According to the simulation results, LSD and Duncan could not maintain the actual type I error rate at 5.00% under any conditions. This situation became more dramatic with the increase in the number of groups. While the actual type I error rate for LSD and Duncan tests varied between 54.36%-100.00% and 37.49%-99.96%, respectively, for ANOM and Tukey tests it varied between 4.64%-6.08% and 4.62%-6.45%, respectively. ANOM and Tukey tests were quite successful in terms of maintaining the actual type I error rate. However, since the number of groups in lattice designs was quite high, the given hypothetical example showed that it would be more understandable to use the ANOM method.