Some observations on estimation of plot size and shape, Bartlett's Rate Index and yield loss adjustments

Observations on three different topics have been made and suitable modifications have been suggested. First related to estimation of optimum plot-size and shape. Smith's variance law has been generalized to two-dimensions for estimating and testing the effect of plot-size, and to develop an objective method of quantifying and testing the effect of plot-shape. He obtained optimum plot-size by minimizing cost per unit of information and this plot-size has been found to minimize the variance of the mean for fixed cost. However, Smith obtained the optimum plot-size assuming that the border area is proportional to the net plot area which is seldom true. Expression of the optimum plot-size has been obtained by keeping the desired size and shape of border area. Differences between optimum plot-sizes as determined from co-efficient of variation and variance laws have been worked out. This difference has brought to light the mistakes of many agricultural statisticians who computed the optimum plot-sizes while estimating the Smith's equations from co-efficient of variation. This led to much smaller optimum plots. Second related to obtaining yield adjustment for missing/diseased plants in field experiments. Yield adjustments have been obtained for structures of seven continguous plants. Lastely, modifications have been obtained to improve upon the scope and accuracy of Bartlett's Rate Index in agricultural experiementation.