Statistical analysis of field trials with changing treatment variance
This is a discussion paper that presents no new material but challenges the way that field trials with changing treatment variances have been traditionally analyzed. We argue that one should always expect the variance of yield to change when the yields are obtained from plots with different plant densities. To illustrate, a turnip (Brassica rapa L.) sowing density by sowing date experiment is analyzed using analysis of variance and residual maximum likelihood methods. Deviance is used to compare the statistical models and demonstrate that residual maximum likelihood provides a better analysis when a linear mixed model is fitted to account for a changing variance due to sowing density. The analysis is further improved when sowing date, which also has a changing variance, is incorporated into the model. Plant density trials should always be assumed to have changing variance. Linear mixed models (with a residual maximum likelihood algorithm for estimating variance parameters) can be used to obtain superior analyses and make better research decisions.