Measures of validity in cultivar performance trials

The coefficient of variation (CV) has been used for many years by researchers to determine the validity of performance trials. The premise behind the CV, that the standard deviation is proportional to the mean, compromises one of the assumptions of a normal distribution (i.e., that the sample mean and sample variance are independent), If there is a nonnormal distribution, then the data may need to be transformed, which in turn may invalidate the use of the CV. A constant CV across trials implies a relationship between the error variance and the mean such that the slope = 2.0 in the regression of In error variance on In mean. The purpose of this paper is to stress the relationship between the error variance and mean in the CV, review this relationship in actual yield data, and examine the effects of various transformations on CVs and coefficient of determination (R-2), The In error variance regressed on In mean for several agronomic crops ranged from -0.11 for full-season corn (Zea mays L.) to 1.31 for oat (A vena sativa L.). Although some crops had a nonzero regression coefficient for this relationship, none approached 2.0, the level that supports the hypothesis that the CV is a viable tool for comparing the relative variation of different trials. Data transformations (e.g., square root, logarithmic, angular, inverse, reverse, and addition of a constant) tend to lower CV values in most cases, but can cause dramatic increases, depending on the nature of the variance and the specific transformation. On the other hand, R-2, which is a measure of the amount of variability accounted for in the model, remains relatively unaffected by most transformations. Reasonable R-2 values for determining validity of performance trials may vary by location and crop species, Examination of North Carolina data revealed that discarded trials generally had R-2 values less than 50%. The R-2 may be affected by the size of the dataset, and so adjusted R-2 maybe more useful for comparing trials of varying sizes; however, adjusted R-2 will tend to be larger where there are larger differences among entries. There is no one perfect measure of the validity of trial data, but the R-2 and the adjusted R-2 are reasonable alternatives to the CV and should be examined along with other statistical measures when evaluating crop performance data.