# 统计代写|生物统计分析代写Biological statistic analysis代考|STA310

## 统计代写|生物统计分析代写Biological statistic analysis代考|Analysis of Variance in R

The aov () function provides all the necessary functionality for calculating complex ANOVAs and for estimating the model parameters of the corresponding linear models. It requires two arguments: data= indicates a data-frame with one column for each variable in the model, and aov () uses the values in these columns as the input data. The model is specified with the formula argument using a formula. This formula describes the factors in the model and their crossing and nesting relationships, and can be derived directly from the experiment diagram.

For our first example, the data is stored in a data-frame called drugs which consists of 32 rows and three columns: $y$ contains the observed enzyme level, drug the drug ( $D 1$ to $D 4)$, and mouse the number of the corresponding mouse ( $1 \ldots 32)$. Our data are then analyzed using the command aov (formula=y 1+drug+Error (mouse), data=drugs).

The corresponding formula has three parts: on the left-hand side, the name of the column containing the observed response values $(\mathrm{y}$ ), followed by a tilde. Then, a part describing the fixed factors, which we can usually derive from the treatment structure diagram: here, it contains the special symbol 1 for the grand mean $\mu$ and the term drug encoding the four parameters $\alpha_i$. Finally, the Error () part describes the random factors and is usually equivalent to the unit structure of the experiment. Here, it contains only mouse. An R formula can often be further simplified; in particular, aov () will always assume a grand mean 1 , unless it is explicitly removed from the model, and will always assume that each row is one observation relating to the lowest random factor in the diagram. Both parts can be skipped from the formula and are implicitly added; our formula is thus equivalent to $\mathrm{y} \sim \mathrm{drug}$. We can read a formula as an instruction: explain the observations $y_{i j}$ in column y by the factors on the right: a grand mean $1 / \mu$, the refinements drug/ $\alpha_i$ that give the group means when added to the grand mean, and the residuals mouse $/ e_{i j}$ that cover each difference between group mean and actual observation.

## 统计代写|生物统计分析代写Biological statistic analysis代考|From Hasse Diagram to Model Specification in R

From the Hasse diagrams, we construct the formula for the ANOVA as follows:

• There is one variable for each factor in the diagram;
• terms are added using +;
• $\mathrm{R}$ adds the factor $\mathbf{M}$ implicitly; we can make it explicit by adding 1 ;
• if factors $A$ and $B$ are crossed, we write $A \star B$ or equivalently $A+B+A: B$;
• if factor $B$ is nested in $A$, we write $A / B$ or equivalently $A+A: B$;
• the formula has two parts: one for the random factors inside the Error () term, and one for the fixed factors outside the $\operatorname{Error}()$ term;
• in most cases, the unit structure describes the random factors and we can use its diagram to derive the Error () formula;
• likewise, the treatment structure usually describes the fixed factors, and we can use its diagram to derive the remaining formula.

In our sub-sampling example (Fig. 4.5), the unit structure contains (Sample) nested in (Mouse), and we describe this nesting by the formula mouse/sample. The formula for the model is thus $y^1 1+$ drug+Error (mouse/sample), respectively, $y \sim$ drug+Error (mouse).

The aov () function does not directly provide estimates of the group means, and an elegant way of estimating them in $\mathrm{R}$ is the emmeans () function from the emmeans package. ${ }^1$ It calculates the expected marginal means (sometimes confusingly called least squares means) as defined in (Searle and Milliken 1980) for any combination of experiment factors using the model found by aov ( ). In our case, we can request the estimated group averages $\hat{\mu}_i$ for each level of drug, which emmeans () calculates from the model as $\hat{\mu}_i=\hat{\mu}+\hat{\alpha}_i$ :
$\mathrm{em}=$ emmeans $(\mathrm{m}, \sim$ drug $)$
This yields the estimates, their standard errors, degrees of freedom, and $95 \%$ confidence intervals in Table 4.3.

# 生物统计分析代考

## 统计代写|生物统计分析代写生物统计分析代考| R的方差分析

aov()函数为计算复杂anova和估计相应线性模型的模型参数提供了所有必要的功能。它需要两个参数:data=表示模型中每个变量都有一个列的数据框架，而aov()使用这些列中的值作为输入数据。模型通过使用公式的公式参数指定。该公式描述了模型中的各因素及其交叉嵌套关系，可直接从实验图中推导出来

## 统计代写|生物统计分析代写生物统计分析代考|从哈塞图到R中的模型规范

• 图中每个因子都有一个变量;
• 项使用+添加;
• $\mathrm{R}$ 加上因子 $\mathbf{M}$ 含蓄地;我们可以通过添加1使其显式化;
• if factors $A$ 和 $B$ 是交叉，我们写 $A \star B$ 或者等价地 $A+B+A: B$
• if factor . $B$ 嵌套在 $A$，我们写道 $A / B$ 或者等价地 $A+A: B$
• 公式有两部分:一部分用于Error()项内的随机因素，另一部分用于 $\operatorname{Error}()$
• 在大多数情况下，单位结构描述的是随机因素，我们可以用它的图表推导出Error()公式;
• 同样，处理结构通常描述的是固定因素，我们可以用它的图表推导出剩下的公式 在我们的子采样示例(图4.5)中，单元结构包含(Sample)嵌套在(Mouse)中，我们通过公式Mouse / Sample来描述这种嵌套。因此，模型的公式分别为$y^1 1+$ drug+Error (mouse/sample)， $y \sim$ drug+Error (mouse).
aov()函数不直接提供组均值的估计值，在$\mathrm{R}$中，emmeans()函数提供了一种很好的估计值方法。${ }^1$它计算期望边际均值(有时被称为最小二乘均值)，如(Searle和Milliken 1980)中定义的，使用aov()发现的模型对任何实验因子的组合进行计算。在我们的例子中，我们可以请求每个药物水平的估计组平均值$\hat{\mu}_i$, emmeans()从模型中计算为$\hat{\mu}_i=\hat{\mu}+\hat{\alpha}_i$:
$\mathrm{em}=$ emmeans $(\mathrm{m}, \sim$药物$)$
这产生了表4.3中的估计、它们的标准误差、自由度和$95 \%$置信区间

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