On the Variability of Harvest Indices

The harvest index Z is defined, for example for cereals, as the ratio between grain yield X and biological yield Y: Z = X/Y. For many purposes the variance of Z is of major interest. In this paper several approximations for this variance are derived and their accuracy was investigated. These explicit formulae depend on some characteristics (means, variances or coefficients of variation, covariances or correlations) of the component variables grain yield X and biological yield Y. It is shown that for most practical applications the approximation v²z = v²x + v²y - 2rv_xv_y provides a sufficient accuracy for numerical calculations (v_x v_y and v_z are the coefficients of variation for grain yield X, biological yield Y and harvest index Z and r denotes the correlation coefficient between X and Y). Some conclusions on the relations between v_x, v_y and v_z are derived.
Finally, all the theoretical investigations and results are demonstrated and applied to a numerical example of winter-rapeseed data.