The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce

In a number of cereal experiments, three on wheat, three on barley and one on oats, the yields of grain and straw per plot were estimated by weighing the total produce on each plot and taking samples, usually from the sheaves, to estimate the ratio of grain to total produce. This paper discusses the sampling errors of this method. The method proved considerably less accurate than was anticipated from previous calculations made by Yates & Zacopanay. Amongst the reasons which are suggested to account for this are the larger sizes of plot and sampling unit used in these experiments and the additional variability introduced by the presence of weeds, undergrowth and moisture.Nevertheless, the method appears to be substantially superior to the older method of cutting small areas from the standing crop, without weighing total produce, only about one-quarter of the number of samples being required to obtain results of equal precision.The samples were taken both by an approximately random process and by grabbing a few shoots haphazardly from each of several sheaves. The grab samples gave on the whole a slightly higher yield of grain, the greatest positive bias being 6%, but were otherwise just as accurate as the random samples. Since the grab samples can be selected and bagged in about one-third of the time required for random samples, their use is recommended for the majority of the samples required in any experiment.The validity of an approximate formula for calculating the variance of a ratio (in the present instance the ratio of grain to total produce) is discussed briefly in an appendix.