## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考| Statistical Analyses for Sole Crop Respons

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Statistical Analyses for Sole Crop Respons

For crop $h$ in a mixture of $c$ crops in Design 1 and for the $v$ entries arranged in a randomized complete block experiment design of $r$ complete blocks, let the response equation, for crop $h=1$ say, be of the usual form:
$$Y_{g d_{\mathrm{H}}\left(d_{2 i} d_{\left.3_{j} \cdots\right)}\right.}=\mu+\rho_{g}+\tau_{d_{4 i}\left(d_{2 i} d_{j \cdots} \cdots\right)}+\epsilon_{g d_{1 i}\left(d_{2 i} d_{3 i}\right)},$$
where $\mu$ is a general mean effect, $\rho_{g}$ is the $g$ th complete block effect, $\tau_{d_{1 i}\left(d_{2} d_{3 j} \cdots\right)}$ is the effect of the $d_{1 i}\left(d_{2 i} d_{3 i} \cdots\right)$ th combination from the $n_{1} \times n_{2} \times n_{3} \times \cdots \mathrm{com}-$ binations of the density levels $d_{1 i}, d_{2 i}, d_{3 i}, \ldots, i=1,2, \ldots, n_{h}, h=1,2, \ldots, c$, the number of crops in a mixture, and the $\epsilon_{g d_{1 i}\left(d_{2} d_{3} \ldots\right)}$ are random error terms distributed with zero mean and variance $\sigma_{e h}^{2}$. An analysis of variance (ANOVA) for this situation is given in Table $14.1$ for the case when the lowest density level is not zero. The sums of squares are computed in the usual manner for a factorial treatment design in a randomized complete block experiment design.

If desired, each of the treatment sums of squares could be partitioned into single degree of freedom contrasts such as linear, quadratic, etc., or some other set of

contrasts dependent on the particular response function used for the relationship between a response such as yield and density level.

A response function of the following nature might be suitable for the $n_{2} n_{3}$ responses obtained on a single experimental unit $g d_{1 h}$ from Design 2 :
\begin{aligned} Y_{i j}=& \alpha+\beta_{1} d_{2 i}+\beta_{2} d_{2 i}^{2}+\beta_{3} d_{3 j}+\beta_{4} d_{3 j}^{2}+\beta_{5} d_{2 i} d_{3 j} \ &+\beta_{6} d_{2 i} d_{3 j}^{2}+\beta_{7} d_{2 i}^{2} d_{3 j}+\epsilon_{i j}, \end{aligned}
where $i=1, \ldots, n_{2}, j=1, \ldots, n_{3}, h=1, \ldots, n_{1}$, the $\beta$ ‘s are polynomial regression coefficients, and the $d_{2 i}$ and $d_{3 j}$ are the various density levels for crops two and three. Of course, other response functions may be more appropriate than the above one. However, this particular model does allow for linear and curvilinear responses for each crop as well as for some rather well-behaved interaction terms. The responses used would be the predicted values from the above regression equation. This response model equation may also be used for each of the $n_{1} n_{2}$ experimental units from Design 3. The main object of this analysis is to show the effect of changing levels of the densities of crops two and three at each level of crop one. An alternate analysis would be a MANOVA (multivariate analysis of variance) or discriminant function analysis, using the seven regression coefficients as the seven variates and determining their effects over all levels of crop one. Still another analysis would be to obtain the estimated maximum responses from the regression function in equation (14.2) in each of the $r n_{1}$ experimental units and perform an analysis on these values.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Statistical Analyses

Using these created variables, ANOVAs like those given above can be obtained. Such analyses as these are more useful than those in the previous section, as they deal with the system of intercropping rather than concentrating on the components, individual crops, of the system.

Other analyses such as AMMI (additive main effects and multiplicative interaction; see Gauch, 1988, Gauch and Zobel, 1988, Ezumah et al., 1991, and related references) and MANOVA (multivariate analysis of variance, see Chapter 4 of Volume I, e.g.) may be useful in certain cases. For these analyses, the responses for the individual crops form the variates for the multivariate analyses, and functionals combining response from all crops would be obtained. The interpretation of the resulting principle components and canonical variates may be a problem. These statistics may differ if a logarithmic or some other transformation of the responses had been made before using AMMI or MANOVA. Hence, selective and careful use of these procedures are necessary in order for them to be of practical and interpretive usefulness for a researcher. In some cases, little, if anything new, is added by these more complex procedures (see, e.g., Ezumah et al., 1991). For many situations using analyses involving the created variables in (i), (ii), (iii), and (iv) above will suffice. In some cases, other functionals such as AMMI and MANOVA may be useful.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Modeling Responses in Sole Crop Yields

Many yield-density or response-density relationships can be formulated [see Section 3 of Morales (1993) and references therein]. In order not to make the modeling process too complicated, we shall consider simple relationships. A simple model is a linear relation between yield and density. For a randomized complete block design with three sole crops, say cassava $=c$, maize $=m$, and beans $=b$, the

response models are
\begin{aligned} &Y_{g c h}=\mu_{c c}+\rho_{g c}+\beta_{1 c}\left(d_{c h}-\bar{d}{c}\right)+\epsilon{g c h}=\beta_{0 g c}+\beta_{1 c} d_{c h}+\epsilon_{g c h}, \ &Y_{g m i}=\beta_{0 g m}+\beta_{1 m} d_{m i}+\epsilon_{g m i} \text {, } \ &Y_{g b j}=\beta_{0 g b}+\beta_{1 b} d_{b j}+\epsilon_{g b j} . \end{aligned}

$$\hat{\beta}{1 m}=\sum{i=1}^{n_{m}}\left(d_{m i}-\bar{d}{m}\right)\left(\bar{y}{m i}-\bar{y}{m m}\right) / \sum{i=1}^{n_{m}}\left(d_{m i}-\bar{d}{m \cdot}\right)^{2}$$ 14.6 Modeling Responses for Mixtures Based on Sole Crop Model 89 $$\hat{\beta}{1 b}=\sum_{j=1}^{n_{b}}\left(d_{b j}-\bar{d}{b .}\right)\left(\bar{y}{b j}-\bar{y}{b .}\right) / \sum{j=1}^{n_{b}}\left(d_{b j}-\bar{d}{b .}\right)^{2},$$ where the $\bar{y}$ and $\bar{d}$ are mean values for the corresponding values of responses and densities, respectively, and $\beta{0 c}, \beta_{0 \mathrm{~m}}$, and $\beta_{0 b}$ are the intercepts averaged over replicates. Extension of the above to $c$ more than 3 crops is straightforward. The above assumes that density levels are the same from replicate to replicate. If this is not the true situation, e.g., missing plots occur, the above formulas will need to be adjusted to account for the change in density levels.

In the event that monocrop responses are not available, it is possible to model yield-density relationships using the lowest density levels for all other crops but the one under consideration. For example, this relationship for crop one, say, is obtained from the responses at levels $d_{21} d_{31} \cdots$ for crops two, three, etc. Using the above cassava-maize-bean example, the yield-density models would be
\begin{aligned} &Y_{g d_{c t h}\left(d_{m 1} d_{b 1}\right)}=\beta_{g} 0 c+\beta_{1 c} d_{c h}+\epsilon_{g d_{c h}\left(d_{m 1} d_{b 1}\right)}, \ &Y_{g d_{m i}\left(d_{c 1} d_{b 1}\right)}=\beta_{g 0 m}+\beta_{1 m} d_{m i}+\epsilon_{g d_{m i} i}\left(d_{c 1} d_{b 1}\right), \ &\left.Y_{g d_{b j}\left(d_{c 1} d_{m 1}\right.}\right)=\beta_{g 0 b}+\beta_{1 b} d_{b j}+\epsilon_{g d_{b j}\left(d_{c t} d_{m 1}\right)}, \end{aligned}
where $g d_{c h 1}\left(d_{m 1} d_{b 1}\right)$ is for level $d_{c h}$ at levels $d_{m 1}$ and $d_{b 1}$ in replicate $g$ and where the regression coefficients are defined in a manner similar to that for equations (14.3)(14.5). The least squares solutions for the parameters of (14.18)-(14.20) are much the same as given in equations (14.6)-(14.17). Because of the direct application of the above solution with the necessary changes to account for computing the regressions on the lowest-density levels of all crops but the one in question, the least squares solutions are not given, as they are straightforward.

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考| Varying Densities for Some

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|All Crops in a Mixture

The simplest form of intercropping with three or more crops in the mixture and with one major crop and two or more minor crops was considered in Chapter 12. The complexity of the statistical analyses over that in Chapter 2 (two crops) of Volume I is increased. The methods of Chapters 3 and 4 of Volume I were extended to mixtures of three or more crops in Chapter 13. Analyses for individual crop responses for each crop as well as analyses for combined responses for all crops in the mixture are presented. The density for a given crop in the mixture was held constant from mixture to mixture. In the present chapter, cropping systems which allow varying densities for some or all crops are considered. The methods presented herein are a generalization of those presented in Chapter 5 of Volume I.
Many patterns for varying and/or constant densities in a mixture are possible. The particular densities selected for study will depend on the makeup of the crop mixture as well as the goals of the experiment. With one major crop and two or more minor crops:
(i) The density of the major crop could be varied and the densities of the minor crops kept constant.
(ii) The density of the major crop could be held constant and some or all of the densities of the minor crops varied.
(iii) The densities of all crops in the mixture could be varied.
With three or more major crops and with some or no minor crops in a mixture, the following situations are possible:
78

1. Varying Densities for Some or All Crops in a Mixture
(i) The densities of all major crops in the mixture could be varied.
(ii) The densities of two or more major crops could be constant and the densities of the remaining crops could be varied.
(iii) The densities of any minor crops included in (i) or (ii) could be varied or held constant.
2. As discussed in Chapter 5 of Volume I, serious attention needs to be given to selecting the various density levels for each crop. The experimenter needs to decide whether to make the levels selected for one crop dependent or independent of the levels selected for the remaining crops in a mixture. It may make sense to approach a maximum density for all crops in the mixture as the total number of plants, regardless of crop, is the total population level beyond which there will be no increased yields. The amount of moisture, plant nutrients, sunlight, etc. may dictate the maximum population level that can be supported on a plot of ground. It is well known that overpopulation can result in reduced or even zero yields. In order to pinpoint density levels producing maximum or nearmaximum responses, it is advisable to select levels somewhat beyond the level giving maximum response. For example, the maximum yield of maize may be attained with 60,000 plants per hectare. A level of 70,000 , or even 80,000 , plants per hectare should result in decreased yields and should be included for study in an experiment. In determining response curves, experimenters often make the mistake of including only levels which “would be used in practice.” The inclusion of levels beyond those normally used in practice results in a more accurate response curve showing the relationship between response and density level. If a response curve does not show a decrease at the highest density, it is not clear that the maximum has been attained and that higher density levels should have been included.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Treatment Design

Several treatment designs may be used for studying responses over varying density levels of the crops in the mixture. We shall list some of the possible designs for studying yield-density relationships.

Consider a mixture of three crops at densities $0<d_{i 1}<d_{i 2}<\cdots<d_{i n_{i}}$ for crop $i$ at $n_{i}$ density levels. Then, for $n_{1}=3, n_{2}=2$, and $n_{3}=4$, the following combinations (marked X) are obtained where, for example, crop one is cassava, crop two is beans, and crop three is maize:In addition to the above 24 combinations, the 3 crops as sole crops could be included to obtain $(3 \times 2 \times 4)+(3+2+4)=33$ entries. Here the lowest densities $d_{i 1}, i=1,2$, and 3 , are greater than zero. As the number of density levels for a crop and the number of crops increase, the total number of entries for an experiment increases rapidly. For example, including a fourth crop at three density levels, say, to the above set would result in $(3 \times 2 \times 4 \times 3)+(3+2+4+3)=84$ entries. Therefore, the experimenter needs to exercise considerable care in selecting the precise levels and their number in order that the number of entries does not go beyond what can be done experimentally. This treatment design contains all possible combinations of density levels plus the levels for each of the sole crops.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|A procedure for reducing

A procedure for reducing the number of entries and the space requirements would be to utilize the ideas of Federer and Scully (1993) in the manner shown in Figure $14.1$, using the previous example for three crops. There are $n_{1}$ experimental units in each replicate; the density for crop two varies from the lowest to the highest density horizontally either continuously increasing or increasing by increments; and the crop three densities vary in the same way but vertically, with highest combined densities being in the lower right-hand corner of an experimental unit. The experimenter would divide each experimental unit into $n_{2} n_{3}$ equal-sized rectangles and obtain the response for each of these rectangles. The density level for each rectangle would be the average density in that rectangle. The $n_{1}$ experimental units are randomly allocated in each replicate in the experiment and the crop two and crop three densities are systematically increasing within the experimental unit. Thus, the crop one density levels are somewhat akin to a “whole plot” and the density levels of crops two and three are somewhat like “split plots.” A response function, e.g., a second-degree polynomial, would be fitted, the maximum value on the response surface, and/or the area under the response function could be used as the response for the experimental unit (see Federer and Scully, 1993). The selection of which crop to use as crop one is important, but probably one crop would be an obvious candidate. For the first example above, cassava would be crop one because a large experimental unit relative to the one needed for maize or beans would be required. In other situations, one of the crops may utilize well-defined discrete levels and, hence, would be a candidate to be crop one. There should be no gradients within each of the experimental units in order that a gradient effect does not become confounded with the effect of density level on the response.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|All Crops in a Mixture

(i) 主要作物的密度可以变化，而次要作物的密度保持不变。
(ii) 主要作物的密度可以保持不变，而次要作物的部分或全部密度可以变化。
(iii) 混合物中所有作物的密度可以变化。

78

1. 改变混合物中某些或所有作物
的密度 (i) 混合物中所有主要作物的密度可以改变。
(ii) 两种或多种主要作物的密度可以保持不变，而其余作物的密度可以变化。
(iii) (i) 或 (ii) 中包括的任何次要作物的密度可以变化或保持不变。
2. 正如第一卷第 5 章所讨论的，需要认真注意为每种作物选择不同的密度水平。实验者需要决定是否使为一种作物选择的水平依赖于或独立于为混合物中的其余作物选择的水平。接近混合物中所有作物的最大密度可能是有意义的，因为无论作物如何，植物的总数是总人口水平，超过该水平就不会增加产量。水分、植物养分、阳光等的量可能决定了一块土地上可以支持的最大人口水平。众所周知，人口过剩会导致产量减少甚至为零。为了确定产生最大或接近最大响应的密度水平，建议选择的电平略高于给出最大响应的电平。例如，玉米的最大产量可以达到每公顷 60,000 株。每公顷 70,000 株甚至 80,000 株植物的水平应该会导致产量下降，并且应该包括在实验中进行研究。在确定响应曲线时，实验者经常犯的错误是只包括“将在实践中使用”的水平。包含超出实践中通常使用的水平的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。玉米的最高产量可以达到每公顷 60,000 株。每公顷 70,000 株甚至 80,000 株植物的水平应该会导致产量下降，并且应该包括在实验中进行研究。在确定响应曲线时，实验者经常犯的错误是只包括“将在实践中使用”的水平。包含超出实践中通常使用的水平的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。玉米的最高产量可以达到每公顷 60,000 株。每公顷 70,000 株甚至 80,000 株植物的水平应该会导致产量下降，并且应该包括在实验中进行研究。在确定响应曲线时，实验者经常犯的错误是只包括“将在实践中使用”的水平。包含超出实践中通常使用的水平的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。每公顷植物应导致产量下降，并应包括在实验中进行研究。在确定响应曲线时，实验者经常犯的错误是只包括“将在实践中使用”的水平。包含超出实践中通常使用的水平的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。每公顷植物应导致产量下降，并应包括在实验中进行研究。在确定响应曲线时，实验者经常犯的错误是只包括“将在实践中使用”的水平。包含超出实践中通常使用的水平的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。” 包含超出实践中通常使用的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。” 包含超出实践中通常使用的水平会导致更准确的响应曲线显示响应和密度水平之间的关系。如果响应曲线在最高密度处未显示下降，则不清楚是否已达到最大值以及是否应包括更高的密度水平。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考| Literature Cited

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Literature Cited

Aidar, H. (1978). Estudo sobre populacoes de plants emdois de culturas associades de milho e feijao. Viscosa, M.G., Tese de Doutorada, Universidade Federalde Vicosa.
Federer, W.T. (1987). Statistical analyses for intercropping experiments. Proc., Thirty-Second Conference on the Design of Experiments in Army Research Development and Testing, ARO Report 87-2, pp. 1-29.
Federer, W.T. and S.J. Schwager (1982). On the distribution of land equivalent ratios. BU-777-M in the Technical Report Series of the Biometrics Unit, Cornell University, Ithaca, NY.
Grimes, B.A. and W.T. Federer (1984). Comparison of means from populations with unequal variances. In W.G. Cochran’s Impact on Statistics (Editors: P.S.R.S. Rao and J. Sedransk), John Wiley \& Sons, Inc., New York, pp. 353-374. Mead, R. and J. Riley (1981). A review of statistical ideas relevant to intercropping research (with discussion). J. Roy. Statist. Soc., Ser. A 144, 462-509.
Mead, R. and R. Willey (1980). The concept of ‘Land equivalent ratio’ and advantages in yields from intercropping. Exp. Agric. 16, 217-228.
Riley, J. (1984). A general form of the ‘Land Equivalent Ratio.’ Exp. Agric. 20, 19-29.
Srivastava, J.N. (1968). On a general class of designs for multiresponse experiments. Ann. Math. Statist. 39, 1825-1843.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Equations for a 12-Plant Basis

For the experiment and data of Example 13.5, let us consider the response equations to be (for cultivar A)
Sole crop for A (yield from 12 plants):
$$Y_{h A}=\mu+\tau_{A}+\rho_{h t}+\epsilon_{h A} .$$
Mixture of three crops, $A$ with $j$ and $g \neq A$ (yields from four plants):
\begin{aligned} Y_{h A(j g)}=& \frac{1}{3}\left(\mu+\tau_{A}+\rho_{h A}\right)+\frac{2}{3}\left(\delta_{A(j)}+\delta_{A(g)}\right) \ &+\pi_{A(j g)}+\epsilon_{h A(j g)} . \end{aligned}
Mixture of six crops, A with five others (yields from two plants):
\begin{aligned} Y_{h t A(B C D E F)}=& \frac{1}{6}\left(\mu+\tau_{A}+\rho_{h A}\right)+\frac{1}{3} \sum_{j=B}^{F} \delta_{A(j)} \ &+\beta_{A(B C D E F)}+\epsilon_{h A(B C D E F)} . \end{aligned}
The coefficient of $1 / 3$ in (13.47) is to put $\mu+\tau_{A}+\rho_{h A}$ on the same basis as in (13.46). The coefficient of $2 / 3$ in (13.47) is used because $\delta_{A(j)}$ should have been derived from 8 instead of 12 plants in order to be on the same basis as $\mu+\tau_{A}$. A similar explanation holds for the coefficients in (13.48).

For the above response equations, a set of normal equations after applying the parameter constraints
$$0=\sum_{h=1}^{r} \rho_{h t}=\sum_{\substack{j=1 \ \neq A_{, g}}}^{v} \pi_{A(j g)}=\sum_{\substack{j=1 \ \neq A, j}}^{v} \pi_{A(j g)}, \sum_{\substack{j=1 \ \neq A}}^{v} \delta_{A(j \cdot)}=(v-1) \bar{\delta}{A(\cdot)}$$ and $v=6$ is \begin{aligned} \sum{h} Y_{h A} &=Y_{\cdot A}=r\left(\mu+\tau_{A}\right) \ \sum_{h} \sum_{g \neq j, A} Y_{h A(j g)} &=Y_{\cdot A(j \cdot)}=\frac{r(v-2)}{3}\left(\mu+\tau_{A}\right) \ \sum_{h} \sum_{j} \sum_{g} Y_{h A(j g)} &=\frac{2 r(v-3)}{3} Y_{A(j)}+\frac{2 r(v-1)}{3} \bar{\delta}{A(\cdot)} \ &=\frac{r(v-1)(v-2)}{2(3)}\left(\mu+\tau{A}+4 \bar{\delta}_{A(\cdot)}\right) \end{aligned}

\begin{aligned} \sum_{h=1}^{r} Y_{h A(B C D E F)} &=Y_{\cdot A(B C D E F)} \ &=\frac{r}{6}\left(\mu+\tau_{A}\right)+\frac{r(v-1)}{3} \bar{\delta}{A}+r \beta{A(B C D E F)} . \end{aligned}

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Equations on a Four-Plant Basis

If it is desired to analyze the data from the three types of mixtures jointly in one analysis, the yields would need to be put all on the same number of plants basis as was done in Example 13.5, that is, e.g., $Y_{h A / 3}^{\prime}, Y_{h A(j g)}^{\prime}$, and $2 Y_{h A(B C D E F)}^{\prime}$ would all be on a four-plant basis. $Y_{h A}$ is the yield from 12 plants and $Y_{h A(B C D E F)}$ is the yield from 2 plants. On this four-plant basis, one could reparameterize the response equations as follows:
Sole crop A
$$Y_{h A / 3}^{\prime}=Y_{h A}=\mu+\tau_{A}+\rho_{h A}+\epsilon_{h A} .$$
Mixture of three crops, A with $\mathrm{j}$ and $g$
$$Y_{h A(j g)}^{\prime}=Y_{h A(j g)}=\mu+\tau_{A}+\rho_{h A}+\frac{1}{2}\left(\delta_{A(j)}+\delta_{A(g)}\right)+\pi_{A(j g)}+\epsilon_{h A(j g)} .$$
Mixture of all six crops, yield for crop A
\begin{aligned} 2 Y_{h A(B C D E F)}^{\prime}=& Y_{h A(B C D E F)}=\mu+\tau_{A}+\rho_{h A} \ &+\frac{2}{(v-1)} \sum \delta_{A(j)}+2 \beta_{A(B C D E F)}+\epsilon_{h A(B C D E F)} \ =& \mu+\tau_{A}+\rho_{h A}+2 \bar{\delta}{A(\cdot)}+2 \beta{A(B C D E F)} \ &+\epsilon_{h A(B C D E F) .} \end{aligned}
Using the parameterization for the response equations can be rationalized as follows. If there were no effects from the mixture, the expected value of $Y_{h A}, Y_{h A(j g)}$, and $Y_{h A(B C D E F)}$ should be $\mu+\tau_{A}+\rho_{h A}$, since all responses are for four plants. Likewise, one would say, with less credibility, that $\epsilon_{h A}, \epsilon_{h A(j g)}$, and $\epsilon_{h A(B C D E F)}$, as defined directly above, all have mean zero and common variance $\hat{\sigma}{e A}^{2}$. The last statement can only be approximately correct since $\epsilon{h A} / 3$ from the 12 -plant response equation is equal to the $\epsilon_{h A}$ from the 4-plant response equations above. Thus, one would suspect that $\epsilon_{h A}$ as defined above would have a smaller variance
Appendix 13.1 71
than the $\epsilon_{h A(j g)}$ and that $\epsilon_{h A(B C D E F)}$ would have a larger variance. If the component of variance due to variation among plants within an experimental unit is small relative to the component of variance among experimental units treated alike, then the inequality of variances will be small and, hence, can be ignored. This is what was assumed for the analyses given in Example 13.5. Thus, we shall use equations (13.59) to $(13.60)$ for analyses of the data.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Literature Cited

Grimes, BA 和 WT Federer (1984)。比较具有不等方差的总体的平均值。在 WG Cochran 对统计的影响（编辑：PSRS Rao 和 J. Sedransk）中，John Wiley \& Sons, Inc.，纽约，第 353-374 页。Mead, R. 和 J. Riley (1981)。回顾与间作研究相关的统计思想（带讨论）。J.罗伊。统计学家。社会党，爵士。144, 462-509。
Mead, R. 和 R. Willey (1980)。“土地当量比”的概念和间作产量的优势。经验。农业。16, 217-228。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Equations for a 12-Plant Basis

0=∑H=1rρH吨=∑j=1 ≠一种,Gv圆周率一种(jG)=∑j=1 ≠一种,jv圆周率一种(jG),∑j=1 ≠一种vd一种(j⋅)=(v−1)d¯一种(⋅)和v=6是∑H是H一种=是⋅一种=r(μ+τ一种) ∑H∑G≠j,一种是H一种(jG)=是⋅一种(j⋅)=r(v−2)3(μ+τ一种) ∑H∑j∑G是H一种(jG)=2r(v−3)3是一种(j)+2r(v−1)3d¯一种(⋅) =r(v−1)(v−2)2(3)(μ+τ一种+4d¯一种(⋅))

∑H=1r是H一种(乙CD和F)=是⋅一种(乙CD和F) =r6(μ+τ一种)+r(v−1)3d¯一种+rb一种(乙CD和F).

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Equations on a Four-Plant Basis

\begin{aligned} 2 Y_{h A(BCDEF)}^​​{\prime}=& Y_{h A(BCDEF)}=\mu+\tau_{A}+ \rho_{h A} \ &+\frac{2}{(v-1)} \sum \delta_{A(j)}+2 \beta_{A(BCDEF)}+\epsilon_{h A(BCDEF) } \ =& \mu+\tau_{A}+\rho_{h A}+2 \bar{\delta} {A(\cdot)}+2 \beta {A(BCDEF)} \ &+\epsilon_{h A(BCDEF) .} \end{aligned}

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Combined Responses for Three or More Crops

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Combined Responses for Three or More Crops

As stated in Chapter 4 of Volume I, the grower of crops in a farming system would be interested in some linear combination of crop responses. In most cases, the responses will be weights of fruit, grain, fodder, biomass, or some other characteristic. In some cases, the response could involve numbers rather than weight, e.g., oranges, ears of sweet corn, etc. Whatever the response of interest, it will appear in the weighted total response for the system. For $v$ crops in mixtures of size $k$, $k=1, \ldots, v$, and responses $Y_{h i j}$, the linear combination would be
$$\sum_{h=1}^{v} a_{h t} Y_{h i j}=Z_{i j}$$
where $a_{h}$ is a weighting factor for crop $h$ in block $j$ in the $i$ th mixture of size $k$; all crops not appearing in the mixture will have $a_{h}=0$. Thus, for a sole crop, all $a_{h}=0$ except one, for a mixture of two crops, only two of the $a_{h}$ will be nonzero. Equation (13.43) is a generalization of the results in Chapter 4 of Volume I (also, see Federer, 1987, Riley, 1984).

From an economic point of view, $a_{h}$ is the value of crop $h$. From a nutritional point of view, $a_{h}$ would represent a calorie or a protein conversion factor. From a land use point of view, $a_{h}$ would be the reciprocal of the sole crop yield and $Y_{h}$ would be the yield of crop $h$ in the mixture. From a statistical viewpoint, (13.43) could be
54

1. Three or More Main Crops-Density Constant
the linear combination maximizing the variance of the linear combination or which maximized the treatment sum of squares divided by the treatment plus error sums of squares. The statistical view does not lend itself to practical interpretation and, hence, would not ordinarily be of use in an experiment on intercropping. Since ratios of prices and ratios of sole crop yields are much more stable than are prices or yields themselves, it is recommended that one crop be selected as a base crop and that the coefficients for all crops be divided by this coefficient. Thus, if $h=1$ is the base crop, then (13.43) becomes
$$\sum_{h=1}^{v} \frac{a_{h} Y_{h}}{a_{1}}=\sum_{h=1}^{v} b_{h} Y_{h}$$
where $b_{h}=a_{h} / a_{1}$. When $a_{h}$ is the reciprocal of the sole crop yields, say $Y_{s h}$, then (13.44) becomes
$$\mathrm{LER}^{*}=\sum_{h=1}^{v} Y_{s 1} Y_{h} / Y_{s h}=Y_{s 1} \sum_{h=1}^{v} L_{h}$$
where $L_{h}=Y_{h} / Y_{s h}, Y_{s h}$ is the sole crop yield for crop $h, Y_{s 1}$ is the yield for the base sole crop, and $Y_{h}$ is the yield of crop $h$ in the mixture. Equations (13.44) and (13.45) would be called relative linear combinations, e.g., relative economic values, relative land use or land equivalent ratios, relative calories or protein, etc. For comparative purposes of cropping systems, such relative values are useful and, as shown in Chapter 4 of Volume I and Chapter 11, they can be discussed together simply by changing the values for $a_{h}$ or $b_{h}$.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Some Comments

The examples presented demonstrate the diversity in types of intercropping experiments and in types of statistical analyses that are useful in eliciting the information contained in the experiments. Sole cropping ideas and goals need to be extended considerably in order to provide appropriate analyses and interpretations for intercropping experiments. From Chapter 11, we reiterate that the investigator should “expect the unexpected” from an intercropping experiment. Several results which were unusual and unexpected to the writer occurred in the examples here, just as they did in the preceding chapter. The large difference in bean yields at the two locations in Example $13.3$ is striking. Such differences appear to be extraordinarily large. The investigator should provide an explanation as to why the differences were so large. Also, bean and cowpea yields were reduced more when grown with maize than with sorghum. Is this a varietal or species phenomenon? Why?

In Example 13.4, cotton yields were relatively unaffected when fertilized. This would mean that any additional yield from the intercrops is obtained as anditional bonus. Why would cotton yields be unaffected when intercropped in this manner? What is the nature and physiology of cotton which allows this to happen? Why would maize yields be lower (or the same) on fertilized than on unfertilized plots?

Example $13.5$ had considerable variation among the experimental units treated alike. The large coefficients of variation indicate that experimental technique needs to be reconsidered. The size of the experimental unit (see Figure 13.1) immediately comes to mind.

Many of the computations described in this chapter are programmable using such software packages as SAS or GENSTAT. It is suggested that the computations be done on a pocket or desk calculator until the analyst becomes familiar with the statistical models and analyses. Then, the packages may be used for calculations.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Problems

$13.1$ For crop D, recompute the analysis using $0.27$ rather than $0.22$ (Table 13.2) for combination ADF in block three.
$13.2$ Obtain the analyses described in this chapter after making the transformation $\log ($ yield $+1)$ for the data in Table 13.2. Note that 1 is added to the yield of cultivars D and $F$ since some of the values are near zero. Do this for all cultivars.
13.3 For the data of Table $13.2$ corrected as in Problem 1, compute the residuals and determine if there are possible outliers. If so, one would need to question the experimenter as to possible reasons for this.
13.4 Select a multiple comparisons procedure and make the appropriate comparisons and interpretations for the data of Example 13.6.
13.7 Literature Cited
67
13.5 Partition the treatment sum of squares with 26 degrees of freedom as suggested in the text following Table 13.12. Do likewise with the error sum of squares. Make the appropriate interpretations.
13.6 For the data following equation (13.48), verify that equations (13.49) through (13.57) are correct by performing the calculations.
$13.7$ Verify that equations (13.61) to $(13.70$ ) hold for the parameter values in the text following equations (13.58) $-(13.60)$. Verify the totals following equation (13.70).
$13.8$ Given a canonical variate $Y_{1}+b Y_{2}+c Y_{3}$, show how to extend the computer program in Chapter 4 of Volume I to obtain values of $b$ and $c$ which maximize (treatment sums of squares)/(treatment $+$ error sum of squares). How would you extend this to include four variables?
13.9 What effect does removing the value of 207 for treatment $B$ for $Z_{1 i j}$ have on the analysis of variance and on $F$-tests? Are there more outliers for these data?

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Combined Responses for Three or More Crops

∑H=1v一种H吨是H一世j=从一世j

54

1. 三种或更多主要作物-密度常数
线性组合使线性组合的方差最大化或使处理平方和最大化除以处理加上误差平方和。统计观点不适合实际解释，因此通常不会用于间作试验。由于价格比率和单一作物产量比率比价格或产量本身稳定得多，因此建议选择一种作物作为基础作物，并将所有作物的系数除以该系数。因此，如果H=1是基础作物，则 (13.43) 变为
∑H=1v一种H是H一种1=∑H=1vbH是H
在哪里bH=一种H/一种1. 什么时候一种H是唯一作物产量的倒数，比如说是sH，则 (13.44) 变为
大号和R∗=∑H=1v是s1是H/是sH=是s1∑H=1v大号H
在哪里大号H=是H/是sH,是sH是作物的唯一作物产量H,是s1是基础单一作物的产量，并且是H是作物的产量H在混合物中。等式 (13.44) 和 (13.45) 将被称为相对线性组合，例如，相对经济价值、相对土地利用或土地当量比率、相对卡路里或蛋白质等。对于种植系统的比较目的，这些相对值是有用的，并且，如第一卷第 4 章和第 11 章所示，只需更改一种H或者bH.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Problems

13.1对于作物 D，使用重新计算分析0.27而不是0.22（表 13.2）用于块 3 中的组合 ADF。
13.2转换后得到本章描述的分析日志⁡(屈服+1)对于表 13.2 中的数据。请注意，将 1 添加到品种 D 的产量和F因为有些值接近于零。对所有品种都这样做。
13.3 对于表中的数据13.2按照问题 1 进行校正，计算残差并确定是否存在可能的异常值。如果是这样，则需要向实验者询问可能的原因。
13.4 选择多重比较程序并对例 13.6 的数据进行适当的比较和解释。
13.7 引用的文献
67
13.5 按照表 13.12 后面的文本中的建议，对具有 26 个自由度的平方和进行划分。对误差平方和做同样的事情。做出适当的解释。
13.6 对于方程（13.48）后的数据，通过计算验证方程（13.49）到（13.57）是否正确。
13.7验证方程 (13.61) 到(13.70) 对文本中的参数值保持以下等式 (13.58)−(13.60). 验证以下等式 (13.70) 的总数。
13.8给定一个规范变量是1+b是2+C是3，展示如何扩展第一卷第 4 章中的计算机程序以获得b和C最大化（治疗平方和）/（治疗+误差平方和）。您将如何扩展它以包含四个变量？
13.9 去掉207的值进行治疗有什么作用乙为了从1一世j有关于方差分析和关于F-测试？这些数据是否存在更多异常值？

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Three or More Main Crops

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Density Constant

In many situations involving intercropping, three or more of the crops in a mixture may be considered to be the main crops. The grower is interested in a farming system and not necessarily in how each crop in the mixture performs. A desirable system would be one yielding the highest return in calories, in protein, in land use, in crop value (monetary or otherwise), and/or in some other evaluation of the system. From this point of view, all crops in a mixture would be considered to be main crops. Considering crops to be main crops need not imply that they are equal in value but that the grower will use these crops in a farming system.

There are many types of systems, as is partially demonstrated by the five examples given in the following sections. Great variation in systems exists. The experimenter should always ascertain which set of response model equations and which statistical analyses are appropriate to meet the type and goals of the particular experiment involved.

In Section 13.2, some comments on treatment design are given and illustrated with four examples. Treatment designs are different for the four examples and even more so for Example 13.5. Response model equations for each crop are given in Section 13.3. Estimators for the various parameters are presented along with an analysis of variance. The results are applied to a set of data from a mixture experiment. These analyses are for the yields of the individual crops in the spirit of the previous chapter.

Since a grower would be interested in a system, methods of combining the crop responses are given in Section 13.4. These results are applied to the data
$13.2$ Treatment Design 35
from Examples $13.3$ and $13.5$ and for a set of data for all possible combinations of three crops. Land equivalent ratios are generalized from two to $v$ crops. Also, other created variables such as total calories, total protein, and total value are given for $v$ crops. This is a generalization of the results presented in Chapter 4 of Volume I. Rather than use actual conversion factors, a ratio of coefficients is used which largely eliminates year-to-year variation in variables such as price. This requires selecting one of the crops as a base crop and the created variables will then be relative land equivalent ratios, relative values, etc. For comparative purposes, these relative variables are appropriate, and the ratios of yields, prices, etc. are considerably less variable than are actual values.

Some comments on the results from the experiments are given in Section 13.5. Some results are expected and others not. The last section is a derivation of some of the results in Section $13.3$ and was relegated to an appendix rather than including it in the text.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Treatment Design

The treatment design given in Chapter 12, or subsets of it, may be used in this chapter as well. However, there are many variations that are used in intercropping experiments. Four other examples are described below. These have been reported by Aidar (1978) in his thesis and were made available through the courtesy of $\mathrm{J}$. G. de Silva, EMBRAPA, in 1980 .

Example 13.1. The treatment design consisted of the following eight treatments:
A cotton grown in sole crop
B cotton $+2$ rows of maize
C cotton $+2$ rows of beans
D cotton $+1$ row of maize $+1$ row of beans
E cotton $+2$ rows of maize $+2$ rows of beans
F cotton $+1$ row of maize
$\mathrm{G}$ cotton $+1$ row of beans
$\mathrm{H}$ cotton $+1$ row of maize $+1$ row of beans
Treatment H was different from $\mathrm{D}$ in that the bean plants were planted in with the maize plants, whereas, in D, there was one row of maize and one row of beans. This example could have been used in Chapter 12 if cotton was the main crop, say, and maize and beans, say, were the supplementary crops.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Model Equations and Analyses

For the following discussion, we shall consider the situation where the treatments are in a randomized complete block design and are included only once in each block. The results are easily generalizable to other experiment designs; the fol-
13.3 Response Model Equations
39
lowing equations may be considered to be appropriate for the $v=3$ sole crop yields:
\begin{aligned} \text { Crop one } & Y_{1 h i} &=\mu_{1}+\rho_{1 h}+\tau_{1 i}+\epsilon_{1 h i}, \ \text { Crop two } & Y_{2 h i} &=\mu_{2}+\rho_{2 h}+\tau_{2 i}+\epsilon_{2 h i}, \ \text { Crop three } & Y_{3 h i} &=\mu_{3}+\rho_{3 h t}+\tau_{3 i}+\epsilon_{3 h i}, \end{aligned}
where $Y_{f h i}$ is the response for the $f$ th crop, $f=1,2,3=v$, in the $h$ th block, $h=1,2, \ldots, r$, for the $i$ th line of crop $f, i=1,2, \ldots, c_{f}, \mu_{f}$ is an overall mean effect for crop $f, \rho_{f h}$ is the $h$ th block effect for crop $f, \tau_{f i}$ is the $i$ th line effect for crop $f$, and $\epsilon_{f h i}$ is a normal independent random variable with mean zero and variance $\sigma_{f e}^{2}$. A straightforward extension results in $v$ equations for the $v$ sole crop responses.

The following response model equations may be appropriate for mixtures of lines of three main crops. Generalization to $v$ main crops is straightforward. The crops are assumed to be in a 1:1:1 ratio, i.e., one-third of the area for a sole crop would be devoted to each crop. Certain crops might have an equal number of plants/ha as well as equal areas. The response model equations for mixtures of three crops are
\begin{aligned} Y_{1 h i(j g)}=&\left(\mu_{1}+\rho_{1 h}+\tau_{1 i}+\delta_{1 i}\right) / 3+2\left(\gamma_{i(j)}+\gamma_{i(g)}\right) / 3 \ &+\pi_{i(j g)}+\epsilon_{1 h i(j g)} \ Y_{2 h(i) j(g)}=&\left(\mu_{2}+\rho_{2 h}+\tau_{2 j}+\delta_{2 j}\right) / 3+2\left(\gamma_{(i) j}+\gamma_{j(g)}\right) / 3 \ &+\pi_{(i) j(g)}+\epsilon_{2 h(i) j(g),} \end{aligned}
and
\begin{aligned} Y_{3 h(i j) g}=&\left(\mu_{3}+\rho_{3 h}+\tau_{3 g}+\delta_{3 g}\right) / 3+2\left(\gamma_{(i) g}+\gamma_{(j) g}\right) / 3 \ &+\pi_{(i j) g}+\epsilon_{3 h(i j) g}, \end{aligned}

13.2处理设计 35

A 单一作物种植的

C棉行+2排豆
D棉+1一排玉米+1排豆
E棉+2一排排玉米+2排豆
F棉+1一排玉米
G棉布+1一排豆子
H棉布+1一排玉米+1排豆

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Model Equations and Analyses

39

作物一 是1H一世=μ1+ρ1H+τ1一世+ε1H一世,  作物二 是2H一世=μ2+ρ2H+τ2一世+ε2H一世,  作物三 是3H一世=μ3+ρ3H吨+τ3一世+ε3H一世,

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Several Cultivars of Primary Interest

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Example

S. Kaffka, Cornell University, conducted an experiment in large containers in a greenhouse at the University of Hohenheim, Stuttgart, West Germany, during March to July of 1980. A uniform stockpiled Filder clay-loam soil mixed with small amounts of peat moss and sand was used to fill the containers (boxes). All boxes were sown with sufficient barley seeds and seeds of the other six secondary species to establish a stand of 20 uniformly spaced barley plants and undersown plants according to the following pattern in one block of a randomized complete block design with $r=3$ blocks (see Figure 12.2):
(i) 1 box with 20 barley plants and no secondary species,
(ii) 6 boxes in which 1 box contained 20 barley plants and 12 plants of 1 of the 6 species,
(iii) 20 boxes with 20 barley plants and 12 other plants which consisted of 4 plants (randomly allotted) from each of 3 of the 6 species and which was 1 of the 20 possible combinations of 6 species taken 3 at a time, and
(iv) 1 box which contained 20 barley plants and 2 plants of each of the 6 species.
All seeds were sown on one planting date, thinned to a single plant per position, and watered as necessary throughout the growing season. At the end of the growing season, 6 barley plants from the center of each box and all 12 plants of the secondary species were harvested and dry weights taken. A yield-density trial for barley and a replacement series of barley and lentils were also included in the experiment as a partial check on the model employed. The data for seed weight of the six barley

The seed weight in grams of six barley plants is presented in Table 12.2. The treatment and block totals and means are also given. From these, one may compute residuals for a two-way array as
$$Y_{i j}-\bar{y}{i \cdot}-\bar{y}{\cdot j}+\bar{y}{. .}=\hat{e}{i j}$$
or
$$\left(r v Y_{i j}-r Y_{i,}-v Y_{\cdot j}+Y_{. .}\right) / r v=\hat{e}{i j} .$$ The first formula is subject to rounding errors, whereas the second form is not. The residuals times $r v$ sum to zero exactly in any row or any column of the table using the second form. The frequency distribution of the $84 \hat{e}{i j}$ ‘s is given in Figure 12.3. A rather symmetrical distribution, 43 negatives and 41 positives, was obtained with no unusual outliers, although the 3 residuals greater than 6 accounted for $21 \%$ of the total residual sum of squares. One could check on the relation between treatment means, $\bar{y}{i}$, and sums of squares, $\sum{j=1}^{r} \hat{e}{i j}^{2}$, using Spearman’s rank correlation. (D.S. Robson, Cornell University, and C.L. Wood, University of Kentucky, have shown that this follows Spearman’s rank correlation.) First rank the means from 1 to 28 ; compute the $28 \sum{j=1}^{3} \hat{e}{i j}^{2}$ in Table 12.3, and then rank them. Take the difference $d{i}$ in ranks. Then, Spearman’s rank correlation is computed as
$$r_{S}=1-\frac{6 \sum_{i=1}^{n} d_{i}^{2}}{n\left(n^{2}-1\right)}=1-\frac{6 \sum_{i=1}^{28} d_{i}^{2}}{28\left(28^{2}-1\right)}=1-\frac{6(3004)}{28(783)}=0.18$$
$r_{S}=0.18$ is considerably smaller than $r_{.05}$ (26 d.f.) $=0.374$. Hence, the treatment means and variances are considered to be uncorrelated. In light of the above evidence, no transformation of seed weight was considered necessary to stabilize variances, which is required for $F$-tests.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Several Cultivars of Primary Interest

Suppose that $c$ lines or cultivars are of primary interest and that $v$ lines or cultivars of secondary interest are being considered. For example, suppose that $c$ lines of barley, which will be grown with $k$ of $v$ supplementary cultivars, $k=0,1,2, \ldots, v$, are of interest. A split plot experiment design could be used in which
(i) the $c$ lines or cultivars of primary interest form the whole plot or

The choice would depend on contrasts of primary interest. If a mixture combination for each cultivar of primary interest was desired, then use (i). If, on the other hand, it was desired to have more information on the $c$ cultivars of primary interest, then use (ii). If all contrasts were of equal interest, then a complete block or an incomplete block design would be indicated.

Analyses of variance for situations (i) and (ii) above are given in Tables $12.7$ and 12.8. It is recommended that analyses of variance of the form of Table $12.1$ be performed for each line of the main crop prior to combining results as in Table 12.7. For (ii), analyses of variance should be obtained for each whole plot treatment before combining the results for all whole plots. Standard statistical software for obtaining analyses for split plot designs may be used for these analyses. To obtain some of the sums of squares, a contrast statement is needed.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Some Comments

In the previous chapter, it was stated that one should not generalize from mixtures of two to mixtures of four, that one could expect surprises when analyzing data from a mixture experiment, and that one should not generalize from cultivar to cultivar. The example discussed in this chapter bears out these comments. When this particular barley variety was grown with one of the particular six cultivars, the yield was decreased for five of the six, relative to sole crop yield. The reverse was true for the barley variety grown with 3 of the 6 cultivars where 13 of the 20 mixtures of 4 outyielded the sole crop. Also, when averages of all mixtures of four in which one of the six cultivars was obtained, all six were above the sole crop average, $19.47$ (see Table $12.4$ and Figure 12.4). If a prediction had been made from mixtures of two for mixtures of four, it would have been predicted that mixtures of four would decrease yields. An error would have been made.

Such a result as discussed above for mixtures of two versus mixtures of four crops came as a surprise. Another surprise was that when the mixture contained barley plus all six cultivars, the barley yields were below the sole crop mean, i.e., $18.93$ vs. 19.47. If these results are repeatable, they are interesting biological phenomena concerning species competition and ecology. Another surprise was that the 12 extra plants did not always decrease the yield of barley as this author would have presumed. The 12 extra plants should have exerted considerable stress on the barley plants, but this did not always materialize.

Even if these results are repeatable when the experiment is repeated, it would not be correct to generalize to other barley varieties and to other cultivars. The results are specific for this particular barley variety and the particular collection of the six supplementary crops used in the experiment. It is possible that the results are more general than indicated, but experiments should be conducted to confirm this.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Example

i) 1 盒 20 株大麦植物，无次生物种，
(ii) 6 盒，其中 1 盒包含 20 株大麦植物和 6 种中 1 株的 12 株，
(iii) 20 盒20 株大麦植物和 12 株其他植物，由来自 6 种中的 3 种的 4 株植物（随机分配）组成，是 6 种植物的 20 种可能组合中的 1 株，一次取 3 株，和
(iv) 1 个盒子，其中包含大麦植物 20 株，6 种各 2 株。

(rv是一世j−r是一世,−v是⋅j+是..)/rv=和^一世j.第一个公式会出现舍入误差，而第二个公式则不会。残差次数rv使用第二种形式在表格的任何行或任何列中精确地求和为零。频率分布84和^一世j’s 在图 12.3 中给出。尽管大于 6 的 3 个残差占了21%的总残差平方和。可以检查治疗手段之间的关系，是¯一世, 和平方和,∑j=1r和^一世j2，使用 Spearman 等级相关性。（康奈尔大学的 DS Robson 和肯塔基大学的 CL Wood 表明，这遵循 Spearman 的等级相关性。）首先对 1 到 28 的平均值进行排序；计算28∑j=13和^一世j2在表 12.3 中，然后对它们进行排名。拿差价d一世在行列中。然后，Spearman 的秩相关计算为
r小号=1−6∑一世=1nd一世2n(n2−1)=1−6∑一世=128d一世228(282−1)=1−6(3004)28(783)=0.18
r小号=0.18远小于r.05(26 自由度)=0.374. 因此，处理均值和方差被认为是不相关的。鉴于上述证据，种子重量的变换被认为是稳定方差所必需的，这是F-测试。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Several Cultivars of Primary Interest

(i)C主要兴趣的线或品种形成整个地块或

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考| One Main Crop Grown

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|One Supplementary Crop

In Chapter 2 of Volume I, we discussed the situation for which there was one main crop grown with one supplementary crop. In this chapter, we consider the situation where $1,2, \ldots, v$ cultivars of a secondary crop or crops are grown with one main crop. For example, consider one line or variety of sugarcane which does not “close in,” that is, form a canopy of shade, for 4 months after planting; when the sugarcane plants are small, within the first 4 months after planting, the plants do not fully utilize all the available space, water, and nutrients. In order to utilize this material more fully, short-season annuals are planted between the rows of sugarcane. Such crops as onions, cowpeas, beans, radishes, potatoes, and melons, alone or in combinations, have been used successfully with sugarcane. The supplementary crops must be such that the yield of the main crop is either relatively unaffected or is enhanced. Short-season crops may be grown simultaneously or in sequence during the first months of the sugarcane crop.

Another example where short-season annuals may be grown with a main crop is cassava (manioc, yucca). Since cassava plants start off slowly and the plants are relatively far apart, the land is not fully utilized during the first few months after the cassava has been planted. Greens, melons, cowpeas, beans, potatoes, etc., alone or in mixtures, have been used successfully as supplementary intercrops with the main crop cassava. Another example is using a grain crop, e.g., oats, in a grass-legume mixture. The grain crop has been called a “nurse crop,” while the grass is included with the main crop legume to have a grass-legume hay. When paddy rice is the main crop, the edges around the paddy have been used to grow

a variety of crops, including mixtures of crops. When rubber trees were the main crop, beans, cotton, and maize, alone and in mixtures, have been grown during the first year or two while the rubber trees in the plantation were being established. Legume-grass mixtures are grown as secondary crops in various types of fruit orchards.

In many situations, the correct choice and density of the supplementary crops will leave the main crop yield relatively unaffected. The benefit then would be the value of the supplementary crops, as no extra land is utilized. It is possible and not infrequent that the main crop yields may be increased by the presence of the supplementary crops. For example, in Nigeria, when cassava is intercropped with melons, its yield is actually increased. The reason is that the melons prevent erosion over and above that found in the sole crop cassava. The erosion-control aspects of melons more than offset any competition between melons and cassava for space, water, and nutrients. Thus, intercropping cassava with melons not only produces a partial crop of melons but it actually increases the yield of the main crop cassava. With long-season crops like sugarcane and cassava, legumes with nitrogen-fixation qualities forming nodules on the roots should be successful in enhancing the yields of cassava and sugarcane. These main crops would be able to utilize the nitrogen nodules left in the soil as they decomposed. The fertilizer replacement qualities of the legume may be quite beneficial for crops of this nature.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Some Statistical Design Considerations

One possible treatment design for one main crop cultivar and $v$ supplementary crops follows:
main crop grown as a sole crop,
main crop grown with each one of the $v$ supplementary crops,
main crop grown with each of the $v(v-1) / 2$ pairs of supplementary crops,
main crop grown with each of the $v(v-1)(v-2) / 6$ triples of supplementary crops,
main crop grown with each set of $v-1$ of the supplementary crops, and main crop grown with all $v$ supplementary crops.
The total number of treatments would be $\sum_{k=0}^{v}\left(\begin{array}{c}v \ k\end{array}\right)=2^{v}=N$. The experimenter would usually eliminate certain values of $k$ and/or other combinations to reduce $N$ considerably and would often know that certain combinations were undesirable or would not be used in practice. These usually would not be included in the experiment. There are many possible subsets of $N$ and the experimenter should determine which subset to use to meet the goals of the experiment. For example, the treatment design could be a sole main crop, the main crop with each of the $v$ supplementary crops, and the main crop with all possible pairs of the $v$ supplementary crops for a total of $1+v+v(v-1) / 2$ treatments. Results from fractional replication may be of use here (see, e.g., Cochran and Cox, 1957, Federer, 1967, Raktoe et al., 1981). As an example, interest could center on only mixtures of size four and only main effects and two-factor interactions. Then, only $v(v-1) / 2$ mixtures of the total number of combinations of $v(v-1)(v-2)(v-3) / 24$ would be used. For $v=8$, the fraction would be 28 out of 70 possible mixtures. Examples of fractional replicates appear in Chapters 15 and $16 .$

Also, it is possible that it would be desirable to replicate the sole crop treatment more frequently than the others. If all comparisons are to be made with the sole crop, then for $r$ replications of each of the other treatments, the number of replications for the sole crop could be $\sqrt{N}$ to the nearest integer in each of $r$ blocks in order to optimize variance considerations. If the experiment design were an incomplete block, the $\sqrt{N}$ sole crop experimental units would be scattered over the incomplete blocks, such that sole crop (experimental units) would appear $m$ or $m+1$ times in an incomplete block, $m=0,1,2, \ldots$. Such an arrangement would decrease the variance between sole crop and other combinations.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Model Equations

Consider an experiment involving a single cultivar, e.g., a given barley variety, for which the experiment design is a randomized complete blocks design (RCBD) with $r$ blocks; the treatment design consists of the sole crop of the cultivar and mixtures of $k$ of $v$ additional lines, cultivars, or crop species with $k=1,2, \ldots, v$. The simplest possible response equations for the main crop, e.g., barley, would appear to be of the following form $h=1, \cdots, r$ :
$\text { Sole crop cultivar }$
$$Y_{h 0}=\mu+\tau+\rho_{h}+\epsilon_{h}$$
Cultivar plus one additional line (i)
$$Y_{h i 1}=\mu+\tau+\rho_{h}+\delta_{i}+\epsilon_{h i}$$
Cultivar plus two additional lines ( $i$ and $j$ )
$$Y_{h i j 2}=\mu+\tau+\rho_{h}+\frac{1}{2}\left(\delta_{i}+\delta_{j}\right)+\gamma_{i j}+\epsilon_{h i j}$$
Cultivar plus three additional lines $(i, j$, and $g$ )
$$Y_{h i j g 3}=\mu+\tau+\rho_{h}+\frac{1}{3}\left(\delta_{i}+\delta_{j}+\delta_{g}\right)+\lambda_{i j g}+\epsilon_{h i j g}$$
Cultivar with all $v$ additional lines
$$Y_{h i j, v}=\mu+\tau+\rho_{h}+\delta .+\pi_{12 \cdots v}+\epsilon_{h i j \cdots \cdot}$$
$\mu+\tau$ is the mean of the barley cultivar (main crop) when grown as a sole crop; $\rho_{h t}$ is the $h$ th replicate effect for the RCBD; $\delta_{i}$ is the effect on the barley cultivar when grown in a mixture with supplementary crop line $i ; \gamma_{i j}$ is the bi-specific mixing effect of lines $i$ and $j$ on the response for the barley cultivar; $\gamma_{i j}$ is the tri-specific mixing effect of lines $i, j$, and $g$ on the response for the barley cultivar; $\delta$, is the average of the δi; γ·· is the average of the γij ; λ… is the average of the λijg

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Response Model Equations

$\text { 单一作物品种 }是H0=μ+τ+ρH+εHC你一世吨一世v一种rp一世你s这n和一种dd一世吨一世这n一种一世一世一世n和(一世)是H一世1=μ+τ+ρH+d一世+εH一世C你一世吨一世v一种rp一世你s吨在这一种dd一世吨一世这n一种一世一世一世n和s(一世一种ndj)是H一世j2=μ+τ+ρH+12(d一世+dj)+C一世j+εH一世jC你一世吨一世v一种rp一世你s吨Hr和和一种dd一世吨一世这n一种一世一世一世n和s(i, j,一种ndG)是H一世jG3=μ+τ+ρH+13(d一世+dj+dG)+λ一世jG+εH一世jGC你一世吨一世v一种r在一世吨H一种一世一世v一种dd一世吨一世这n一种一世一世一世n和s是H一世j,v=μ+τ+ρH+d.+圆周率12⋯v+εH一世j⋯⋅\mu+\tau一世s吨H和米和一种n这F吨H和b一种r一世和是C你一世吨一世v一种r(米一种一世nCr这p)在H和nGr这在n一种s一种s这一世和Cr这p;\rho_{ht}一世s吨H和H吨Hr和p一世一世C一种吨和和FF和C吨F这r吨H和RC乙D;\参加}一世s吨H和和FF和C吨这n吨H和b一种r一世和是C你一世吨一世v一种r在H和nGr这在n一世n一种米一世X吨你r和在一世吨Hs你pp一世和米和n吨一种r是Cr这p一世一世n和一世 ; \gamma_{ij}一世s吨H和b一世−sp和C一世F一世C米一世X一世nG和FF和C吨这F一世一世n和s一世一种ndj这n吨H和r和sp这ns和F这r吨H和b一种r一世和是C你一世吨一世v一种r;\gamma_{ij}一世s吨H和吨r一世−sp和C一世F一世C米一世X一世nG和FF和C吨这F一世一世n和s我, j,一种ndG这n吨H和r和sp这ns和F这r吨H和b一种r一世和是C你一世吨一世v一种r;\delta$, 是 δi 的平均值；γ··是γij的平均值；λ… 是 λijg 的平均值

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考| Statistical Considerations

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Statistical Considerations

The topic of experiment design, the arrangement of treatments in an experiment, has been covered in Chapter 10 of Volume I. The experiment design is for $v$ treatments for whatever treatment design is used. The control of experimental heterogeneity by blocking or covariance is a topic independent of the treatments included in an experiment. Treatment design, the selection of treatments to be used in an experiment, in intercropping studies is vital in reaching desired goals. Since there are many goals and situations, there will be a variety of treatment designs. Since the number of treatments $v$ in an intercropping experimment can become large quickly, it is necessary to select minimal treatment designs (TDs). Minimal TDs which contain as many treatments as there are independent parameters to estimate are called saturated designs. If all independent parameters are estimable, the TD is said to be connected. Thus, saturated designs which are minimal and connected are desired. TDs are needed for the situation where a response for each member of a mixture of $n$ crops is available and when only one response is available for the mixture. As will be demonstrated in the following chapters, many and diverse TDs are required in intercropping investigations. Experiment design

theory involving balanced incomplete block, partially balanced incomplete block, Youden, and supplemented block designs is utilized to construct the various and diverse TDs. Methods other than trial and error are needed for construction of some of the saturated TDs.

In general, any mixture of $n$ crops of interest qualifies for inclusion in an intercropping investigation. For certain goals and analyses, it may be necessary to include sole crops and all possible mixtures of size $n$ of $m$ cultivars. The particular treatment design selected needs to be done considering the precisely defined goals of the experiment. If, e.g., the goal is to compare $v$ mixtures with a standard sole crop or mixture, this is only possible when the standard or appropriate sole crop is included. Appropriate standards as points of reference should be included in the TD. In selecting a TD, the experimenter should consider the following rules:

1. Precisely define the goals of the investigation.
2. Select treatments allowing accomplishment of stated goals.
3. Consider the TD in light of the anticipated statistical analyses.
4. Decide in light of steps 1,2 , and 3 if the required comparisons are possible.
5. Revise steps 1,2 , and 3 , if step 4 is not answered in the affirmative.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Scope of Volume

Modeling yield-density relations for sole crops is much simpler than modeling yield-density relations for the $n$ cultivars in the mixture. It is necessary to determine which, if any, of the cultivars in a mixture are to have density varied. Varying densities for all $n$ crops in mixture will necessarily require many experimental units (e.u.s). Hence, the experimenter should only include enough densities to model the yield-density relationships. In addition to density considerations, spatial and intimacy (the nearness of cultivars in a mixture) of the $n$ cultivars in the mixture need to be taken into account. Are the cultivars to be in separate rows, mixed together in the same row, some combination of the previous two, or to be in a broadcast arrangement? Are cultivars included in a mixture at different times? Is every cultivar bordered by every other cultivar and on one side, or all sides? These are items of importance in intercropping studies and require the attention of the intercrop researcher. Plot technic regarding shape and size of an e.u. is also

important. From an experiment design standpoint, long narrow e.u.s over all types of gradients are more efficient than square e.u.s. For intercropping studies, long narrow e.u.s may be ineffective because of the intimacy, competition, and mixing ability characteristics required to evaluate a mixture to be used in practice.

The linear combination of responses for the $n$ cultivars in a mixture discussed in Sections 11.2, 11.3, and $11.4$ are reminicent of canonical variates in multivariate analyses. The statistician unfarnilar with intercropping might think that multivariate statistical techniques would satisfy the needs of statistical analysis. However, as Federer and Murty (1987) have pointed out, multivariate techniques have very limited usefulness in this area. One use for mixtures of size two has been demonstrated by Pearce and Gilliver $(1978,1979)$. The multivariate analysis mathematical criterion used to a canonical variate is to select a linear combination of the responses for the $n$ items, say,
$$\text { first canonical variate }=\sum_{i=1}^{n} a_{i} Y_{m i} \text {, }$$
in such a way that no other selection of the $a_{i}$ has a larger ratio of the treatment sum of squares to the treatment sum of squares plus error sum of squares. Then, to the residuals from the first canonical variate, a second canonical variate, say, is constucted as
$$\text { second canonical variate }=\sum_{i=1}^{n} b_{i} Y_{m i} \text {, }$$
where the $b_{i}$ are selected in the same manner as the $a_{i}$, and so forth, until $n$ canonical variates are obtained. As pointed out by Federer and Murty (1987), the $a_{i}$ and $b_{i}$ have no practical interpretation and, hence, are of no use to the experimenter. These authors also describe other difficulties in trying to apply standard mutivariate techniques to the results from intercropping experiments.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Literature Cited

Aina, P. O., R. Lal, and G. S. Tyler (1977). Soil and crop management in relation to soil erosion in rainforest of Western Nigeria. In Soil Erosion Prediction and Control (Editor: G. R. Foster), Special Publication 21, Soil and Water Conservation Society, Ankeny, IA, pp. 75-84.
Anonymous (1989). Decision reached on sustainable agriculture. Agronomy News, January, p. $15 .$
Balaam, L. N. (1986). Intercropping-past and present. In Statistical DesignsTheory and Practice. Proceedings of a Conference in Honor of Walter T. Federer (Editors: C. E. McCulloch, S. J. Schwager, G. Casella, and S. R. Searle), Biometrics Unit, Cornell University, Ithaca, NY, pp. 141-150.
de Wit, C. T. and J. P. van den Bergh (1965). Competition among herbage plants. Netherlands J. Agric. Sci. 13, 212-221.
Ezumah, H. C. and W. T. Federer (1991). Intercropping cassava and grain legumes in humid Africa. 2. Cassava root yield, energy, monetary, and protein returns of system. BU-1115-M in the Technical Report Series of the Biometrics Unit, Cornell University, Ithaca, NY.
Ezumah, H. C. and N. R. Hullugalle (1989). Studies on cassava-based rotation systems in tropical Alfisol. Agronomy Abstracts, ASA, Madison, WI, pp. $53 .$
Federer, W. T. (1987). Statistical analysis for intercropping experiments. Proceedings, Thirty-Second Conference on the Design of Experimnts in Army Research Development and Testing, ARO-87-2, pp. 1-29.
Federer, W. T. (1989). Intercropping, developing countries, and tropical agriculture. Biometrics Bull. 6, 22-24.
Federer, W. T. (1993a). Statistical design and analysis of intercropping experiments. In Crop Improvement for Sustainable Agriculture (Editors: M. B.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Statistical Considerations

1. 准确定义调查目标。
2. 选择能够实现既定目标的治疗方法。
3. 根据预期的统计分析考虑 TD。
4. 根据步骤 1,2 和 3 确定是否可以进行所需的比较。
5. 如果第 4 步没有得到肯定回答，请修改第 1,2 和 3 步。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Scope of Volume

第一个典型变量 =∑一世=1n一种一世是米一世,

第二典型变量 =∑一世=1nb一世是米一世,

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Literature Cited

Aina、PO、R. Lal 和 GS Tyler (1977)。与尼日利亚西部雨林土壤侵蚀有关的土壤和作物管理。在土壤侵蚀预测和控制（编辑：GR Foster）中，特别出版物 21，水土保持协会，爱荷华州安克尼，第 75-84 页。

de Wit, CT 和 JP van den Bergh (1965)。草本植物之间的竞争。荷兰 J. Agric。科学。13, 212-221。
Ezumah, HC 和 WT Federer (1991)。在潮湿的非洲间作木薯和谷物豆类。2. 系统的木薯根产量、能量、金钱和蛋白质回报。BU-1115-M 属于纽约州伊萨卡康奈尔大学生物识别部门技术报告系列。
Ezumah, HC 和 NR Hullugalle (1989)。热带 Alfisol 中木薯轮作系统的研究。农学文摘，ASA，威斯康星州麦迪逊，第53.

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Nutritional Goals

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Nutritional Goals

In subsistence farming areas of the world, the number of calories provided by the crops grown on the farm is of vital importance. Insufficient calories in the diet leads to dietary difficulties and to starvation in extreme cases. Protein content is also important for a proper diet. Palatability of the foods produced is of concern, as it will not matter how many calories are produced if the produce is unpalatable and cannot be used for sale or barter. In intercropping experiments, it is necessary to assess the caloric and protein content of mixtures and sole crops and the palatability of the foods produced.

For comparative purposes, calorie conversion factors for the various crops in a mixture are available. These conversion factors may vary widely between crops and less so among cultivars within crops. After selection of appropriate conversion factors for each of the crop cultivars in the mixture of $n$ cultivars, the total calories, protein, or other measure is
$$C=\sum_{i=1}^{n} C_{i} Y_{m i},$$
where $C_{i}$ is the conversion factor for cultivar $i$ and for the characteristic under consideration. A relative total calorie, total protein, total fiber, total vitamin, etc., for crop 1 as the base crop is
$$\mathrm{RC}=\sum_{i=1}^{n} C_{i} Y_{m i} / C_{1}=\sum_{i=1}^{n} R_{i} Y_{m i} .$$

An RV or RC may not appear appropriate at first glance, but using only relative measures RLER, RV, and RC affords ease of presentation of the several analyses used, e.g., putting results on the same graph.

Note that the $C_{i}$ in (11.5) and (11.6) could be of a complex form if it were decided to combine nutritional measures. Suppose the relative importance of protein conversion factor $C_{p i}$ to the carbohydrate conversion factor $C_{c i}$ is $R_{p / c i}$, of the fiber conversion $C_{f i}$ to carbohydrate is $R_{f / c i}$, of the vitamin conversion factor $C_{v i}$ to carbohydrate is $R_{v / c i}$, etc., then the conversion factor for all components could be of the form
$$C_{i} Y_{m i} / C_{c i}=\left(1+R_{p / c i}+R_{f / c i}+R_{v / c i}+\cdots\right) Y_{m i}$$
where $C_{i}$ in (11.5) and (11.7) is equal to
$$C_{i}=C_{c i}+C_{p i}+C_{f i}+C_{v i}+\cdots$$
This form of $C_{i}$ could be used in (11.5) and (11.6). Also, different weights could be added to take into account the relative importance of carbohydrates, protein, fiber, vitamins, and other dietary components as a measure of the nutritional value of a mixture.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Sustainability of a System

The term sustainability has many and diverse meanings in published literature. Therefore, it behooves the author to state which definition is being used. For example, does sustainability mean

• constant crop yields year after year,
• fluctuations in yearly yields but no downward or upward trends in yield,
• the above two situations but crop value replacing yield,
• a system that has survived through time, or
• yield to meet population nutritional requirements over time?
Or does it follow the definition
A sustainable agriculture is one that, over the long term, enhances environmental quality and the resource base on which agriculture depends; provides for basic human food and fiber needs; is economically viable; and enhances the quality of life for farmers and society as a whole. (Anon., 1989)

Does it follow the definition in the 1990 Farm Bill which mandated the USDA to support research and extension in sustainable agriculture defined as

An integrated system of plant and animal production practices having a site-specific application that will over the long term: (i) satisfy human and fiber needs; (ii) enhance environmental quality and the natural resources base upon which the agricultural economy depends; (iii) make the most efficient use of nonrenewable resources and on-farm resources, and integrate,

where appropriate, the natural biological cycles and controls; (iv) sustain the economic viability of farm operations; and (v) enhance the quality of life for farmers and society as a whole.
Weil (1990) prefers the following definition
An agricultural program, policy, or practice contributes to agricultural sustainability if it:

1. Enhances, or maintains, the number, quality, and long-term economic viability of farming and other agricultural business opportunities in a community or region.
2. Enhances, rather than diminishes, the integrity, diversity, and longterm productivity of both the managed agricultural ecosystem and the surrounding ecosystems.
3. Enhances, rather than threatens, the health, safety, and aesthetic satisfaction of agricultural producers and consumers alike.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Biological Goals and Considerations

In addition to agronomic, economic, and nutritional considerations in analyzing data from an intercropping experiments, it is often important to determine the nature of biological phenomena involved in intercropping systems. The determination and measurement of how well cultivars mix or compete, how mixtures respond to density changes and spatial arrangements and why, synergistic relationships and mechanisms, and possibly new biological concepts are some of the biological considerations required when interpreting the results from an intercropping experiment. Yield-density relationships need to be modeled. Measures of mixing ability need to be developed. Competition models for various situations need to be available. Knowledge of the biological processes governing the responses of why some systems or mixtures perform as they do is necessary in order to develop methods for producing the desirable systems or mixtures in an efficient manner. Knowing the theory behind a system is helpful to the researcher in producing a more desirable system. This situation has precedence in plant breeding where diallel crossing, top-crossing, single-crossing, double-crossing, and multiple-crossing theory and procedures were developed and applied to develop the desired cultivars. The concepts and results of Chapters 5,6 , and 7 in Volume I are extended to mixtures of more than two cultivars in the following chapters.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Nutritional Goals

C=∑一世=1nC一世是米一世,

RC=∑一世=1nC一世是米一世/C1=∑一世=1nR一世是米一世.

RV 或 RC 乍一看可能不合适，但仅使用相对测量 RLER、RV 和 RC 可以轻松呈现所使用的几种分析，例如将结果放在同一图表上。

C一世是米一世/CC一世=(1+Rp/C一世+RF/C一世+Rv/C一世+⋯)是米一世

C一世=CC一世+Cp一世+CF一世+Cv一世+⋯

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Sustainability of a System

• 年复一年的稳定作物产量，
• 年收益率波动，但收益率没有下降或上升趋势，
• 以上两种情况，但作物价值代替产量，
• 一个在时间中幸存下来的系统，或
• 随着时间的推移，产量能否满足人口营养需求？
或者它是否遵循定义
可持续农业是一种从长远来看可以提高环境质量和农业所依赖的资源基础的农业；提供人类基本的食物和纤维需求；经济上可行；并提高农民和整个社会的生活质量。（匿名，1989）

Weil (1990) 更喜欢以下定义

1. 提高或保持社区或地区农业和其他农业商业机会的数量、质量和长期经济可行性。
2. 增强而不是削弱管理的农业生态系统和周围生态系统的完整性、多样性和长期生产力。
3. 增强而非威胁农业生产者和消费者的健康、安全和审美满意度。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Experiments Involving Comparisons

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计与分析Design and Analysis of Experiments方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计与分析Design and Analysis of Experiments方面经验极为丰富，各种代写实验设计与分析Design and Analysis of Experiments相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Agricultural Systems

Experiments involving the comparison of systems, such as agricultural systems, medical treatments systems, educational systems, etc., require a multi-faceted approach for setting up the goals of the investigation, in designing the experiment, and in performing the necessary statistical analyses. (See, e.g., Kass, 1978, Mead and Riley, 1981, Balaam, 1986, Federer, 1987, 1989, 1993a, 1993b, hereafter referred to as Volume I, and references therein.) When performing experiments comparing agricultural systems, the researcher needs to consider goals involving efficiency of land use, nutritional values, economic values, sustainablity of yields in the system, insect and disease control, soil structure and erosion, spatial arrangements of the system, density and intimacy considerations, competition, mixing abilities of components of the system, and/or perhaps other characteristics. In most cases, it is not be possible to generalize from monocultures to polycultures, from pairs of cultivars to mixtures of more than two, and so forth. Four rules to keep in mind when conducting intercropping experiments are as follows:

Rule 1. Understand the concepts, design, and analyses for mixtures of two crops before proceeding to mixtures of three or more cultivars.
Rule 2. Do not attempt to generalize from monocultures to pairs of cultivars, from pairs to triplets of cultivars, from triplets to quartets of cultivars, from one set of cultivars to another, and so on, as this may lead to gross errors.

Experiments need to be conducted for the specific mixture size and the specific cultivars under study.
Rule 3. Be prepared for the increasing difficulty of design, analysis, and interpretation involved, as the degree of difficulty increases by an order of magnitude in going from monocrops to mixtures of two, by another order of magnitude in going from pairs to triplets, etc.
Rule 4. Be prepared for and look for surprises, as many intercropping experiments produce quite unexpected results, as was exhibited in the examples in Volume I and in the examples presented herein.

Intercropping is an age-old practice going back at least to early Biblical times (The Holy Bible, 1952). It is a farming system that is popular in many areas of planet Earth, especially in tropical agriculture but is present in some form all over the world. Even in temperate zone agriculture, intercropping is common in hay crops, in orchard cover crops, in crop rotations, and in cover crops for such crops as alfalfa. Many gardeners use crop mixtures and sequences for a variety of reasons, one being insect and disease control. In making comparisons among agricultural systems, a variety of statistical designs and analyses will be required and will be demonstrated in the following chapters. But first let us consider some of the goals, uses, and other considertions of intercropping systems investigations.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Land Use and Agronomic Goals

As Earth’s populations tend to increase and with agricultural land area being depleted by urbanization and salinization, it is necessary to make more and more efficient use of the available agricultural land area. A measure for efficiency of land use is the relative yield (de Wit and van den Bergh, 1965) or land equivalent ratio (Willey and Osiru, 1972). A land equivalent ratio (LER) is an agronomic characteristic of an intercropping experiment. It is the sum of ratios of yields of a crop, say $i$, in a mixture, say $Y_{m i}$, to its yield as a sole crop, say $Y_{s i}$. Then, for $n$ crops, an LER is
$$\mathrm{LER}=\sum_{i=1}^{n} Y_{m i} / Y_{s i}=\sum_{i=1}^{n} \mathrm{LER}{i}$$ Instead of using the yield of the sole as the denominator, another form of an LER could be obtained by using the yield of crop $i$ in a standard mixture. A variety of other values could be used for $Y{s i}$ in (11.1) such as

• individual plot yields of the sole crop,
• mean yields from $r$ replicates for the sole crop,
• a theoretical “optimum value” for the sole crop,
• farmer’s yields averaged over y years or for a single year for the sole crop, or
• some other value.

As is obvious, there are many possible LERs. Therefore, it is imperative that the experimenter understands the properties of and consequences of using the LER selected for the determination of land use efficiency of a cropping system.

When only the numerators in an LER are random variables and the denominators are fixed constants, then standard statistical procedures are available for use as explained in Volume I. When both numerators and denominators in the LER are random variables, little is known about the statistical distribution of the LERs. If the numerators and denominators are random normal deviates from a multivariate normal distribution, then the statistic in (11.1) has a Cauchy distribution (Federer and Schwager, 1982) which has infinite variance. If the numerators and denominators come from log-normal distributions, Morales (1993) has obtained the statistical distribution for two crops in the mixture. Presently, work is being done considering the distributions of sums of ratios of gamma-distributed random variables, but at this writing, this research is not at the stage of practical usefulness. A normal distribution ranges from plus to minus infinity. Hence, crop responses not having this range as a possibility cannot be normally distributed. Gamma random variables range from zero to plus infinity, which has a realistic starting point, zero, for yield, counts, etc.

As described in Volume I, one way out of this dilemma is when one sole crop can be used as a base sole crop, say $Y_{s 1}$. Then, use ratios of yields of sole crops to the base sole crop, say crop 1, as follows to obtain a relative land equivalent ratio (RLER):
$$\mathrm{RLER}=\sum_{i=1}^{n} Y_{s 1} Y_{m i} / Y_{s i}=\sum_{i=1}^{n} R_{i} Y_{m i}=\sum_{i=1}^{n} \operatorname{RLER}{i}$$ A RLER is useful in comparing cropping systems and statistical analyses but needs to be converted to an LER for actual land-use considerations. Ratios of yields and prices, e.g., are much more stable than are actual yields and prices (Ezumah and Federer, 1991). Since this is true, the ratios $R{i}$ may be regarded as fixed constants rather than as random variables, and the problem of the distribution of sums of ratios of random variables is bypassed to one which is simply a linear combination of random variables.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Crop Value and Economic Goals

Various values may be assigned to the yield of each crop in a mixture. For many people, value means monetary value. For others, value could be related to how well dietary goals of a family are satisfied with regard to taste and variety of foods in a diet. Crop value for others could be related to frequency of produce for sale or barter throughout the year. Whatever value system is used, consider the value, monetary or otherwise, of crop $i$ to be $P_{i}$ per crop unit, such as a kilogram or individual fruit. The value of a crop will then be $P_{i} Y_{m i}$, where $Y_{m i}$ is the total yield or number of fruit per experimental unit (e.u.). Then, the value of the crops in a
4 11. Introduction to Volume II
mixture of $n$ crops is
$$\text { Crop value }=V=\sum_{i=1}^{n} P_{i} Y_{m i} \text {. }$$
Although prices or other crop values may fluctuate considerably from year to year, ratios of prices or values may not (Ezumah and Federer, 1991). Hence, for comparative purposes, relative crop values may be used and the difficulties of random fluctuations in prices avoided. As for RLER, a base crop price is selected, say $P_{1}$, and ratios of crop values are used to obtain a relative crop value, RV, for a mixture of $n$ crops as
$$\mathrm{RV}=\sum_{i=1}^{n}\left(P_{i} / P_{1}\right) Y_{m i} .$$
The goal would be to select that mixture maximizing $V$ or, equivalently, RV. In making comparisons of the $v$ mixtures in an experiment, it is recommended that RLER and RV be utilized in order to circumvent statistical distribution problems. Their use will also ease presentation problems of the several analyses required to summarize the information from intercropping experiments.

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Agricultural Systems

4. 准备好并寻找惊喜，因为许多间作试验会产生非常意想不到的结果，正如第一卷中的示例和本文介绍的示例中所展示的那样。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Land Use and Agronomic Goals

• 单一作物的个别地块产量，
• 平均产量r复制单一作物，
• 单一作物的理论“最佳值”，
• 农民 y 年或单一作物一年的平均单产，或
• 一些其他的价值。

R大号和R=∑一世=1n是s1是米一世/是s一世=∑一世=1nR一世是米一世=∑一世=1nRLER⁡一世RLER 在比较种植系统和统计分析时很有用，但需要根据实际土地利用考虑将其转换为 LER。例如，产量和价格的比率比实际产量和价格要稳定得多（Ezumah 和 Federer，1991）。既然这是真的，那么比率R一世可以将其视为固定常数而不是随机变量，并且将随机变量的比率之和的分布问题绕过到一个简单的随机变量线性组合的问题。

## 统计代写|实验设计与分析作业代写Design and Analysis of Experiments代考|Crop Value and Economic Goals

4 11。介绍卷二

作物价值 =五=∑一世=1n磷一世是米一世.

R五=∑一世=1n(磷一世/磷1)是米一世.

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。