The use of a reference variety for comparisons in incomplete series of crop variety trials

In a series of crop variety trials, 'test varieties' are compared with one another and with a 'reference' variety that is included in all trials. The series is typically analyzed with a linear mixed model and the method of generalized least squares. Usually, the estimates of the expected differences between the test varieties and the reference variety are presented. When the series is incomplete, i.e. when all test varieties were not included in all trials, the method of generalized least squares may give estimates of expected differences to the reference variety that do not appear to accord with observed differences. The present paper draws attention to this phenomenon and explores the recurrent idea of comparing test varieties indirectly through the use of the reference. A new 'reference treatment method' was specified and compared with the method of generalized least squares when applied to a five-year series of 85 spring wheat trials. The reference treatment method provided estimates of differences to the reference variety that agreed with observed differences, but was considerably less efficient than the method of generalized least squares.