Spatial Correlation Analysis of Uniformity Data

SUMMARY A spatial correlation analysis of uniformity data is presented as an alternative to the conventional method of analysis based on the model proposed by Smith (1938, Journal of Agricultural Science 28, 1-23). The spatial correlation model permits arbitrary patterns of behavior of the correlations, in contrast to the strict monotonic decrease required in Smith's model; it also provides more information about the nature of the variation in the uniformity trial. Results, presented in terms of spatial correlation matrices, standardized variances among plots of all possible sizes, and In-In graphs of variances among plots against plot size, provide a complete summary of the uniformity trial and reveal any inadequacies of Smith's model. Analyses of several sets of uniformity data demonstrate that in most cases Smith's model does not describe the behavior of the spatial correlations although in some of the cases it adequately describes the behavior of the variances. Although Smith's model was not put forward as a model for spatial correlations, it does have implications for their behavior. Departures from Smith's model are detected more readily by inspection of the correlation matrices than by Smith's analysis. These departures include sizeable negative spatial correlations and cycling of correlations with increasing lag.