Effects of the logarithmic and site mean transformations on the relative yields from a variety trial

Summary

Two transformations commonly used in the analysis of multilocation variety trials are the logarithmic transformation and the site mean transformation, in which each observation at a site is divided by the site mean yield prior to analysis. Expressions are derived for differences between the yields of varieties after each of these transformations, in terms of the original yields. Similar expressions are also determined for the regression mean method of estimation, which is based on linear regressions of variety means on site means. It is shown that the two transformations produce almost identical analyses of variance, and that relative yields are very similar on the three scales of measurement provided that the harmonic mean of site means is used as the predictor value in the regression method.