# 统计代写|线性回归代写linear regression代考|STAT452

## 统计代写|线性回归代写linear regression代考|Whole Plots Assigned to A as in a CRBD

Shown below is the split plot ANOVA table when the whole plots are assigned to factor $A$ and a blocking variable as in a completely randomized block design. The whole plot error is error(W) and can be obtained as a block*A interaction. The subplot error is error(S). $F_A=M S A / M S E W$, $F_B=M S B / M S E S$, and $F_{A B}=M S A B / M S E S$. Factor $A$ has a levels and factor $B$ has $b$ levels. There are $r$ blocks of $a$ whole plots. Each whole plot contains $b$ subplots, and each block contains $a$ whole plots and thus $a b$ subplots. Hence there are $r a$ whole plots and $r a b$ subplots.
$S A S$ computes the last two test statistics and pvalues correctly, and the last line of $S A S$ output gives $F_A$ and the pvalue $p_A$. The initial line of output for A is not correct. The output for blocks is probably not correct.

The tests of interest for this split plot design are nearly identical to those of a two way Anova model. $Y_{i j k}$ has $i=1, \ldots, a, j=1, \ldots, b$ and $k=1, \ldots, r$. Keep $A$ and $B$ in the model if there is an $A B$ interaction.
a) The 4 step test for $\mathrm{AB}$ interaction is
i) Ho: there is no interaction $H_A$ : there is an interaction.
ii) $F_{A B}$ is obtained from output.
iii) The pval is obtained from output.
iv) If pval $\leq \delta$ reject Ho and conclude that there is an interaction between $A$ and $B$, otherwise fail to reject Ho and conclude that there is no interaction between $A$ and $B$. (Or there is not enough evidence to conclude that there is an interaction.)
b) The 4 step test for A main effects is
i) Ho: $\mu_{100}=\cdots=\mu_{a 00} \quad H_A$ : not Ho.
ii) $F_A$ is obtained from output.
iii) The pval is obtained from output.
iv) If pval $\leq \delta$ reject Ho and conclude that the mean response depends on the level of $A$, otherwise fail to reject Ho and conclude that the mean response does not depend on the level of $A$. (Or there is not enough evidence to conclude that the response depends on the level of $A$.)
c) The 4 step test for B main effects is
i) Ho: $\mu_{010}=\cdots=\mu_{0 b 0} \quad H_A$ : not Ho.
ii) $F_B$ is obtained from output.
iii) The pval is obtained from output.
iv) If pval $\leq \delta$ reject Ho and conclude that the mean response depends on the level of $B$, otherwise fail to reject Ho and conclude that the mean response does not depend on the level of $B$. (Or there is not enough evidence to conclude that the response depends on the level of $B$.)

## 统计代写|线性回归代写linear regression代考|Review of the DOE Models

The three basic principles of DOE (design of experiments) are
i) use randomization to assign treatments to units.
ii) Use factorial crossing to compare the effects (main effects, pairwise interactions, $\ldots$, J-fold interaction) of $J \geq 2$ factors. If $A_1, \ldots, A_J$ are the factors with $l_i$ levels for $i=1, \ldots, J$; then there are $l_1 l_2 \cdots l_J$ treatments where each treatment uses exactly one level from each factor.
iii) Blocking is used to divide units into blocks of similar units where “similar” means the units are likely to have similar values of the response when given the same treatment. Within each block, randomly assign units to treatments.

Next the 10 designs of Chapter 5 to Section $9.1$ are summarized. If the randomization cannot be done as described, then much stronger assumptions on the data are needed for inference to be approximately correct. There are three common ways of assigning units. For inference, i) requires the least assumptions and iii) the most.
i) Experimental units are randomly assigned.
ii) Observational units are a random sample of units from a population of units. Each combination of levels determines a population. So a two way Anova design has $a b$ populations.
iii) Units (such as time slots) can be assigned systematically due to constraints (e.g., physical, cost, or time constraints).
I) One way Anova: Factor $A$ has $p$ levels.
a) For a fixed effects one way Anova model, the levels are fixed.

## 统计代写|线性回归代写线性回归代考|整个地块分配给A在CRBD

$S A S$正确计算最后两个测试统计信息和pvalue, $S A S$输出的最后一行给出$F_A$和pvalue $p_A$。A的初始输出行不正确。

a) 4步测试 $\mathrm{AB}$ i) Ho:没有相互作用 $H_A$ :有交互作用
ii) $F_{A B}$
iii) pval从输出中获取
iv)如果pval $\leq \delta$ 拒绝Ho，并得出结论，两者之间存在相互作用 $A$ 和 $B$，否则无法拒绝Ho，并得出结论，两者之间没有相互作用 $A$ 和 $B$。(或者没有足够的证据得出相互作用的结论)
b)主效应的4步测试是
i) Ho: $\mu_{100}=\cdots=\mu_{a 00} \quad H_A$ : not Ho.
ii) $F_A$
iii) pval从输出中获取
iv)如果pval $\leq \delta$ 否定Ho，得出平均响应取决于的水平 $A$，否则不能拒绝Ho，并得出平均响应不依赖于的水平的结论 $A$。(或者没有足够的证据得出结论，反应取决于……的水平 $A$)
c) B主效应的4步测试是
i) Ho: $\mu_{010}=\cdots=\mu_{0 b 0} \quad H_A$ : not Ho.
ii) $F_B$
iii) pval从输出中获取
iv)如果pval $\leq \delta$ 否定Ho，得出平均响应取决于的水平 $B$，否则不能拒绝Ho，并得出平均响应不依赖于的水平的结论 $B$。(或者没有足够的证据得出结论，反应取决于……的水平 $B$.)

## 统计代写|线性回归代写线性回归代考| DOE模型的回顾

DOE(实验设计)的三个基本原则是:i)使用随机化给单位分配处理。 $\ldots$， J-fold相互作用) $J \geq 2$ 因素。如果 $A_1, \ldots, A_J$ 这些因素 $l_i$ 级别 $i=1, \ldots, J$;然后是 $l_1 l_2 \cdots l_J$
iii)阻塞(Blocking)用于将单元划分为相似单元的块，其中“相似”意味着在给予相同的处理时，这些单元可能具有相似的响应值。在每个块中，随机分配单位给治疗

i)实验单位是随机分配的。
ii)观察单位是从单位总数中随机抽样的单位。每个水平的组合决定了一个种群。双向方差分析设计有 $a b$
iii)单位(如时间段)可以根据约束条件(如物理、成本或时间限制)进行系统分配 $A$ 有 $p$
a)对于一个固定效果的单向方差分析模型，水平是固定的

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