### 统计代写|实验设计作业代写experimental design代考|ASSESSING THE TREATMENT MEANS

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计experimental designatistical Modelling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experimental design代写方面经验极为丰富，各种代写实验设计experimental design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|实验设计作业代写experimental design代考|ASSESSING THE TREATMENT MEANS

In the last chapter we desoribed the linear model for a simple experiment, found estimates of the parameters, and described a test for the hypothesis that there $1 s$ no overall treatment effect. In this chapter we cover the next step of examining more closely the pattern of differences among the treatment means. There are a number of approaches, One extreme is to test only the hypotheses framed before the experiment was carried out, but this approach wastes much of the information from the experiment. On the other hand, to carry out conventional hypothesis tests on every effect that looks interesting can be very misleading, for reasons which we now examine.
There are three main difflculties. First, two tests based on the same experiment are unlikely to be independent. Tests will usually involve the same estimate of variance, and if this estimate happens to be too small, every test will be too significant. Further, any comparisons involving the same means will be affected the same way by chance differences between estimate and parameter. As an example consider a case where there are three treatments assessing a new drug. Treatment “A” is the placebo, treatment ” $B^{H}$ the drug administered in one big dose and treatment “C” the orug administered in two half doses. If chance variation happens to make the number of cures on the experimental units using the placebo (A) rather low, the differences between $A$ and $B$, and $A$ and $C$ will both be overstated in the same way. Therefore two significant t-tests, one between $A$ and $B$, the other between $A$ and $C$, cannot be taken as independent corroboration of the effectiveness of the drug.

## 统计代写|实验设计作业代写experimental design代考|SPECIFIC HYPOTHESES

Any experiment should be designed to answer specif ic questions. If these questions are stated clearly it will be possible to construct a single linear function of the treatment means which answers each question. It can be a difficult for the statistician to discover what these questions are, but this type of problem is beyond the scope of this book. We will present some examples.
Example 6.2+1 Drug comparison example
In the drug comparison experiment mentioned in Section 1 one question might be, is the drug effective? Rather than doing two separate

tests ( $A \vee B$ and A $\vee$ C), a single test of $A$ against the average of $B$ and $C$ gives an unambiguous answer which uses all the relevant data. That is use
$\bar{y}{A}-\left(\bar{y}{B}+\bar{y}{C}\right) / 2$ with variance $\left[1 / r{A}+\left(1 / r_{B}+1 / r_{B}\right) / 4\right] \sigma^{2}$
Having decided that the drug has an effect the next question may be, how much better is two half doses than one complete dose. This will be estimated by the difference between treatment means for $B$ and C. For inferences remember that $\sigma^{2}$ is estimated by $s^{2}$, and this appears with its degrees of freedom in the ANOVA table.

## 统计代写|实验设计作业代写experimental design代考|Exper imentwise Error Rate

The above are examples of inferences to answer specific questions. Each individual inference will be correot, but there are several inferences being made on each experiment. If all four suggested comparisons were made on the fertilizer experiment, the probability of making at least one type I error will be much higher than the signif icance level of an individual test. If the traditional $5 \%$ level is used, and there are no treatment effeots at all, and the individual tests were independent, the number of significant results from the experiment would be a binomial random variable with $n=4$ and $p=.05$. The probability of no significant results will be $(1-0.05)^{4}$, so that the probability of at least one will be $1-(1-0.05)^{4}=$ 0.185. If one really wanted to have the error rate per experiment equal to $0.05$ each individual test would have to use a significance level, $p$, satisfying
\begin{aligned} 1-(1-p)^{4} &=0.05 \ \text { or } & p=0.013 \end{aligned}

Unfortunately, the underlying assumptions are false because, as we noted in Section 1, each inference is not independent. The correlation between test statistics will usually be positive because each depends on the same variance estimate, and so the probability of all four being nonsignificant w1ll be greater than that calculated above and so the value of p given above will be too low. If the error rate per experiment is important, the above procedure at least provides a lower bound. Usually though it is suffleient to be suspicious of experiments producing many significant results, particularly if the var fance estimate $1 s$ based on rather few degrees of freedom and is smaller than is usually found in similar experiments. Experimenters should not necessarily be congratulated on obtaining many significant results.

In section 1, another source of dependence was mentioned. This results from the same treatment means being used in different conparisons. If the questions being asked are themselves not independent, the inferences cannot be either. However, it is possible to design a treatment structure so that independent questions can be assessed independently. This will be the topic of the next section.

## 统计代写|实验设计作业代写experimental design代考|Exper imentwise Error Rate

1−(1−p)4=0.05  或者 p=0.013

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## 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。