Improving the Accuracy of Growth Indices by the Use of Ratings

Abstract

A statistical procedure is developed whereby the precision of estimation of growth increments and various growth indices is greatly increased, especially where the variability of the plant material is great. The procedure takes account of the fact that the difference between the mean wts. of 2 succesive harvests includes the difference between the sample means at the time of the 1st harvest. The importance of this factor is reduced by the use of ratings of both samples taken at the time of the 1st harvest. Wt. comparisons are made by reference to the mean rating at this time or, where a succession of harvests in involved, to a suitable estimate of this mean rating. The procedure is applied to a study on growth of tomatoes on a range of soil treatments and using simple chains of leaf area ratings. It is exemplified in detail from the control series of that expt. The data are examined critically to see whether they satisfy the assumption inherent in the development of the theory. It is found that the variables of the bivariate distrs. are highly correlated, with no evidence of a departure from a linear trend. Under these conditions, bias introduced from small departures from normality in the marginal distrs. will be negligible. Estimates of total wt., leaf wt., and leaf area based on max. likelihood estimates of mean rating are more precise than are those based on-mean rating at 1st harvest. Gains in precision in estimates of relative growth rate and net assimilation rates are quite substantial, but there is little advantage in the use of max. likelihood estimates in place of mean rating at 1st harvest for this purpose. For estimates of wt. leaf area, and growth indices, the gain in information using ratings is as great for the absolute as it is for the logarithmic data. General considerations relevant to the appln. of the procedure are discussed, and its merits and limitations are indicated.