Efficient estimation of the relationship between plot size and the variability of crop yields
Efficient estimation of the relationship between plot size and the variability of crop yields
复制标题
有效估计地块大小与作物产量变异性之间的关系
DOI：
10.2307/2527785
复制
发表时间：
1958
期刊：
影响因子：
1.9
通讯作者：
E. J. Williams
中科院分区：
文献类型：
--
作者：
W. Hatheway;E. J. Williams
田间试验的最佳小区大小取决于固定成本和成本随单元数量变化的关系以及土壤的变异性。也许最有用的衡量土壤异质性的方法是史密斯[1938]，他的经验表明，给定大小的地块之间的方差的对数与地块大小的对数是线性相关的。在本文中，我们只考虑大小和可变性之间的关系。本文的目的首先是说明如何确定这种关系中的常量的有效估计，其次是说明当数据是相关的且变异性不相等时，确定有效的线性估计的一般方法。Koch和Rigney[1951]证明，方差的对数对小区大小的对数的回归系数可以从存在处理效应的实验数据以及均匀试验的数据中估计出来。他们指出，史密斯曾建议，在估计回归系数fi时，不同大小的地块的方差应按其各自的自由度进行加权。事实上，由于均匀试验和实验数据中不同大小小区的方差估计都是由公共分量建立的，它们往往高度相关，因此简单地按自由度加权是不准确的。科赫和里格尼指出了实验数据的这一困难，但似乎没有意识到他们的论点同样适用于均匀试验数据。本文提出一种加权观测方差的方法。
The optimum size of plot in field experimentation depends on the relationship between fixed costs and costs varying with number of units, and on soil variability. Perhaps the most useful measure of soil heterogeneity yet devised is that of Smith [1938], who showed empirically that the logarithm of the variance between plots of a given size was linearly related to the logarithm of the size of the plot. In the present paper we consider only the relationship between size and variability. The objects of the paper are, firstly, to show how efficient estimates of the constants in this relationship may be determined, and secondly, to illustrate a general method of determining efficient linear estimates when the data are, as in the present instance, correlated and of unequal variability. Koch and Rigney [1951] demonstrated that the regression coefficient of the logarithm of variance on the logarithm of plot size could be estimated from experimental data in which treatment effects are present, as well as from the data of uniformity trials. They noted that Smith had recommended that, in estimating the regression coefficient fi, the variances of the different sized plots should be weighted by their respective degrees of freedom. In fact, since the variance estimates for different size of plot, both in uniformity trials and experimental data, are built up from common components, they are frequently highly correlated, so that a simple weighting by degrees of freedom is not accurate. Koch and Rigney point out this difficulty for experimental data, but do not seem to have realized that their arguments apply with equal force to uniformity trial data. The present paper presents a method of weighting observed variances