EXPERIMENTAL RESULTS ON THE FREQUENCY-DISTRIBUTION OF HARVEST INDEXES OF WINTER OILSEED RAPE

The harvest index Z is defined, for example for cereals, as the ratio of grain yield X and the total biological yield Y : Z = X/Y. For individual measurements x(i) of X and y(i) of Y the individual harvest indices are calculated by z(i) = x(i)/y(i). These individual measurements i may be based on quite different experimental units (single plants, random samples from plots, total plots). For many applications (development of tests of significance, determination of necessary sample sizes) the distribution of harvest indices is of particular relevance and interest. In this paper the frequency distribution of the z(i) has been investigated for an extensive data set of 10 European winter rapeseed cultivars and lines, which are quite different in morphological and physiological traits. For the fit the following three theoretical distributions have been applied: 1) normal distribution, 2) beta distribution for the complete interval from 0 up to 1 and 3) beta distribution for a restricted interval from 0.10 to 0.50. For almost all cultivars/lines the normal distribution as well as the two beta distributions exhibit a good fit of the theoretically expected to the empirically observed frequencies. The three theoretical distributions don't differ among each other in their goodness of fit. Finally, the necessary sample sizes for the calculation of mean harvest indices have been estimated for each cultivar/line: If - for an error probability alpha of alpha = 5 % - the difference between the sample mean and the 'true' mean shall be less than D = 0.01, one obtains necessary numbers between 25 and 93. For D = 0.02 these numbers are between 7 and 24.