An empirical law describing heterogeneity in the yields of agricultural crops

Using data from a blank experiment with wheat it was found that the regression of the logarithms of the variances for plots of different areas on the logarithms of their areas was approximately linear. A graphical review of variances, etc., reported in the literature for thirty-nine other blank experiments indicates that the results of most such experiments conform to the same law. It is shown that the above law can be generalized (so as to be applicable to any size of field) by applying a certain adjustment to the regression coefficient b ', so as to give a modified coefficient b applicable to an “infinite” field. From this generalized relationship there has been deduced an expression ((4), p. 16) to indicate average relative efficiencies to be expected for randomized block experiments with varying numbers of plots per block in a field for which the coefficient b is known. A formulae (5), which may be used to estimate the most efficient size of plot for any given experiment, has also been deduced. The cost of using plots of other than the most efficient size is indicated graphically in Fig. 7.