## 统计代写|生物统计代写Biostatistics代考|MPH203

statistics-lab™ 为您的留学生涯保驾护航 在代写生物统计Biostatistics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。我们的专家在代写生物统计Biostatistics代写方面经验极为丰富，各种生物统计Biostatistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|生物统计代写Biostatistics代考|Proportions and Percentiles

Populations are often summarized by listing the important percentages or proportions associated with the population. The proportion of units in a population having a particular characteristic is a parameter of the population, and a population proportion will be denoted by $p$. The population proportion having a particular characteristic, say characteristic $\mathrm{A}$, is defined to be
$$p=\frac{\text { number of units in population having characteristic A }}{N}$$
Note that the percentage of the population having characteristic A is $p \times 100 \%$. Population proportions and percentages are often associated with the categories of a qualitative variable or with the values in the population falling in a specific range of values. For example, the distribution of a qualitative variable is usually displayed in a bar chart with the height of a bar representing either the proportion or percentage of the population having that particular value.
Example $2.12$
The distribution of blood type according to the American Red Cross is given in Table $2.4$ in terms of proportions.

An important proportion in many biomedical studies is the proportion of individuals having a particular disease, which is called the prevalence of the disease. The prevalence of a disease is defined to be
Prevalence $=$ The proportion of individuals in a well-defined population having the disease of interest
For example, according to the Centers for Disease Control and Prevention (CDC) the prevalence of smoking among adults in the United States in January through June 2005 was $20.9 \%$. Proportions also play important roles in the study of survival and cure rates, the occurrence of side effects of new drugs, the absolute and relative risks associated with a disease, and the efficacy of new treatments and drugs.

A parameter that is related to a population proportion for a quantitative variable is the pth percentile of the population. The pth percentile is the value in the population where $p$ percent of the population falls below this value. The pth percentile will be denoted by $x_p$ for values of $p$ between 0 and 100 .

## 统计代写|生物统计代写Biostatistics代考|Parameters Measuring

The two parameters in the population of values of a quantitative variable that summarize how the variable is distributed are the parameters that measure the typical or central values in the population and the parameters that measure the spread of the values within the population. Parameters describing the central values in a population and the spread of a population are often used for summarizing the distribution of the values in a population; however, it is important to note that most populations cannot be described very well with only the parameters that measure centrality and the spread of the population.

Measures of centrality, location, or the typical value are parameters that lie in the “center” or “middle” region of a distribution. Because the center or middle of a distribution is not easily determined due to the wide range of different shapes that are possible with a distribution, there are several different parameters that can be used to describe the center of a population. The three most commonly used parameters for describing the center of a population are the mean, median, and mode. For a quantitative variable $X$.

• The mean of a population is the average of all of the units in the population, and will be denoted by $\mu$. The mean of a variable $X$ measured on a population consisting of $N$ units is
$$\mu=\frac{\text { sum of the values of } X}{N}=\frac{\sum X}{N}$$
• The median of a population is the 50 th percentile of the population, and will be denoted by $\tilde{\mu}$. The median of a population is found by first listing all of the values of the variable $X$, including repeated $X$ values, in ascending order. When the number of units in the population (i.e., $N$ ) is an odd number, the median is the middle observation in the list of ordered values of $X$; when $N$ is an even number, the median will be the average of the two observations in the middle of the ordered list of $X$ values.
• The mode of a population is the most frequent value in the population, and will be denoted by $M$. In a graph of the probability density function, the mode is the value of $X$ under the peak of the graph, and a population can have more than one mode as shown in Figure 2.8.

The mean, median, and mode are three different parameters that can be used to measure the center of a population or to describe the typical values in a population. These three parameters will have nearly the same value when the distribution is symmetric or mound shaped. For long-tailed distributions, the mean, median, and mode will be different, and the difference in their values will depend on the length of the distribution’s longer tail. Figures $2.12$ and $2.13$ illustrate the relationships between the values of the mean, median, and mode for long-tail right and long-tail left distributions.

## 统计代写|生物统计代写Biostatistics代考|Proportions and Percentiles

p= 人口中具有特征 A 的单位数 ñ

## 统计代写|生物统计代写Biostatistics代考|Parameters Measuring

• 总体的平均值是总体中所有单位的平均值，表示为米. 变量的平均值X在由以下人员组成的总体上测量ñ单位是
米= 的值的总和 Xñ=∑Xñ
• 人口的中位数是人口的第 50 个百分位，表示为米~. 通过首先列出变量的所有值来找到总体的中位数X，包括重复X值，按升序排列。当人口中的单位数（即，ñ) 是奇数，中位数是 的有序值列表中的中间观察值X; 什么时候ñ是偶数，中位数将是有序列表中间的两个观察值的平均值X价值观。
• 人口的众数是人口中出现频率最高的值，记为米. 在概率密度函数图中，众数是X如图 2.8 所示，一个总体可以有多个众数。

## 有限元方法代写

tatistics-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|生物统计代写Biostatistics代考|MPH701

statistics-lab™ 为您的留学生涯保驾护航 在代写生物统计Biostatistics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。我们的专家在代写生物统计Biostatistics代写方面经验极为丰富，各种生物统计Biostatistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|生物统计代写Biostatistics代考|Quantitative Variables

A quantitative variable is a variable that takes only numeric values. The values of a quantitative variable are said to be measured on an interval scale when the difference between two values is meaningful; the values of a quantitative variable are said to be measured on a ratio scale when the ratio of two values is meaningful. The key difference between a variable measured on an interval scale and a ratio scale is that on a ratio scale there is a “natural zero” representing absence of the attribute being measured, while there is no natural zero for variables measured on only an interval scale. Some scales of measurement will have natural zero and some will not. When a measurement scale has a natural zero, then the ratio of two measurements is a meaningful measure of how many times larger one value is than the other. For example, the variable Fat that represents the grams of fat in a food product is measured on a ratio scale because the value Fat $=0$ indicates that the unit contained absolutely no fat. When a scale of measurement does not have a natural zero, then only the difference between two measurements is a meaningful comparison of the values of the two measurements. For example, the variable Body Temperature is measured on a scale that has no natural zero since Body Temperature $=0$ does not indicate that the body has no temperature.

Since interval scales are ordered, the difference between two values measures how much larger one value is than another. A ratio scale is also an interval scale but has the additional property that the ratio of two values is meaningful. Thus, for a variable measured on an interval scale the difference of two values is the meaningful way to compare the values, and for a variable measured on a ratio scale both the difference and the ratio of two values are meaningful ways to compare difference values of the variable. For example, body temperature in degrees Fahrenheit is a variable that is measured on an interval scale so that it is meaningful to say that a body temperature of $98.6$ and a body temperature of $102.3$ differ by $3.7$ degrees; however, it would not be meaningful to say that a temperature of $102.3$ is $1.04$ times as much as a temperature of $98.6$. On the other hand, the variable weight in pounds is measured on a ratio scale, and therefore, it would be proper to say that a weight of $210 \mathrm{lb}$ is $1.4$ times a weight of $150 \mathrm{lb}$; it would also be meaningful to say that a weight of $210 \mathrm{lb}$ is $60 \mathrm{lb}$ more than a weight of $150 \mathrm{lb}$.

## 统计代写|生物统计代写Biostatistics代考|POPULATION DISTRIBUTIONS AND PARAMETERS

For a well-defined population of units and a variable, say $X$, the collection of all possible values of the variable $X$ formed by measuring all of the units in the target population forms the population associated with the variable $X$. When multiple variables are recorded, each of the variables will generate its own population. Furthermore, since a variable may take on many different values, an important question concerning the population of values of the variable is “How can the population of values of a variable be described or summarized?” The two different approaches that can be used to describe the population of values of the variable are (1) to describe explicitly how the variable is distributed over its values and (2) to describe a set of characteristics that summarize the distribution of the values in the population.

A statistical analysis of a population is centered on how the values of a variable are distributed, and the distribution of a variable or population is an explicit description of how the values of the variable are distributed often described in terms of percentages. The distribution of a variable is also called a probability distribution because it describes the probabilities that each of the possible values of the variable will occur. Moreover, the distribution of a variable is often presented in table or chart or modeled with a mathematical equation that explicitly determines the percentage of the population taking on each possible value of the variable. The total percentage in a probability distribution is $100 \%$. The distribution of a qualitative or a discrete variable is generally displayed in a bar chart or in a table, and the distribution of a continuous variable is generally displayed in a graph or is represented by a mathematical function.

## 有限元方法代写

tatistics-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|生物统计代写Biostatistics代考|STA310

statistics-lab™ 为您的留学生涯保驾护航 在代写生物统计Biostatistics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。我们的专家在代写生物统计Biostatistics代写方面经验极为丰富，各种生物统计Biostatistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|生物统计代写Biostatistics代考|POPULATIONS AND VARIABLES

In a properly designed biomedical research study, a well-defined target population and a particular set of research questions dictate the variables that should be measured on the units being studied in the research project. In most research problems, there are many variables that must be measured on each unit in the population. The outcome variables that are of primary interest are called the response variables, and the variables that are believed to explain the response variables are called the explanatory variables or predictor variables. For example, in a clinical trial designed to study the efficacy of a specialized treatment designed to reduce the size of a malignant tumor, the following explanatory variables might be recorded for each patient in the study: age, gender, race, weight, height, blood type, blood pressure, and oxygen uptake. The response variable in this study might be change in the size of the tumor.

Variables come in a variety of different types; however, each variable can be classified as being either quantitative or qualitative in nature. A variable that takes on only numeric values is a quantitative variable, and a variable that takes on non-numeric values is called a qualitative variable or a categorical variable. Note that a variable is a quantitative or qualitative variable based on the possible values the variable can take on.
Example $2.1$
In a study of obesity in the population of children aged 10 or less in the United States, some possible quantitative variables that might be measured include age, height, weight, heart rate, body mass index, and percent body fat; some qualitative variables that might be measured on this population include gender, eye color, race, and blood type. A likely choice for the response variable in this study would be the qualitative variable Obese defined by
$$\text { Obese }= \begin{cases}\text { Yes } & \text { for a body mass index of }>30 \ \text { No } & \text { for a body mass index of } \leq 30\end{cases}$$

## 统计代写|生物统计代写Biostatistics代考|Qualitative Variables

Qualitative variables take on nonnumeric values and are usually used to represent a distinct quality of a population unit. When the possible values of a qualitative variable have no intrinsic ordering, the variable is called a nominal variable; when there is a natural ordering of the possible values of the variable, then the variable is called an ordinal variable. An example of a nominal variable is Blood Type where the standard values for blood type are $\mathrm{A}, \mathrm{B}, \mathrm{AB}$, and $\mathrm{O}$. Clearly, there is no intrinsic ordering of these blood types, and hence, Blood Type is a nominal variable. An example of an ordinal variable is the variable Pain where a subject is asked to describe their pain verbally as

• No pain,
• Mild pain,
• Discomforting pain,
• Distressing pain,
• Intense pain,
• Excruciating pain.
In this case, since the verbal descriptions describe increasing levels of pain, there is a clear ordering of the possible values of the variable Pain levels, and therefore, Pain is an ordinal qualitative variable.
Example 2.2
In the Framingham Heart Study of coronary heart disease, the following two nominal qualitative variables were recorded:
$$\text { Smokes }=\left{\begin{array}{l} \text { Yes } \ \text { No } \end{array}\right.$$ and
• $$• \text { Diabetes }=\left{\begin{array}{l} • \text { Yes } \ • \text { No } • \end{array}\right. •$$
• Example $2.3$
• An example of an ordinal variable is the variable Baldness when measured on the Norwood-Hamilton scale for male-pattern baldness. The variable Baldness is measured according to the seven categories listed below:
• I Full head of hair without any hair loss.
• II Minor recession at the front of the hairline.
• III Further loss at the front of the hairline, which is considered “cosmetically significant.”
• IV Progressively more loss along the front hairline and at the crown.
• V Hair loss extends toward the vertex.
• VI Frontal and vertex balding areas merge into one and increase in size.
• VII All hair is lost along the front hairline and crown.
• Clearly, the values of the variable Baldness indicate an increasing degree of hair loss, and thus, Baldness as measured on the Norwood-Hamilton scale is an ordinal variable. This variable is also measured on the Offspring Cohort in the Framingham Heart Study.

## 统计代写|生物统计代写Biostatistics代考|POPULATIONS AND VARIABLES

肥胖 ={ 是的  对于体重指数 >30  不  对于体重指数 ≤30

## 统计代写|生物统计代写Biostatistics代考|Qualitative Variables

• 不痛，
• 轻微的疼痛，
• 令人不适的疼痛，
• 让人心疼的痛，
• 剧烈的疼痛，
• 难以忍受的疼痛。
在这种情况下，由于口头描述描述了疼痛程度的增加，变量疼痛水平的可能值有一个明确的顺序，因此，疼痛是一个有序的定性变量。
例 2.2
在冠心病的弗雷明汉心脏研究中，记录了以下两个名义上的定性变量：
$$\text { Smokes }=\left{ 是的 不 \正确的。$$ 和
• $$• \text { 糖尿病 }=\left{\begin{array}{l} • \文本{是} \ • \文本{没有} • \end{数组}\对。 •$$
• 例子2.3
• 序数变量的一个例子是变量 Baldness，当用 Norwood-Hamilton 量表测量男性型秃发时。变量秃头根据以下列出的七个类别进行测量：
• 我满头的头发没有任何脱发。
• II 发际线前部的轻微后退。
• III 发际线前部的进一步损失，这被认为是“具有美容意义的”。
• IV 沿着前发际线和头顶逐渐减少。
• V 脱发向顶点延伸。
• VI 前额和头顶秃发区域合并为一个并增加大小。
• VII 所有的头发都沿着前发际线和头顶脱落。
• 显然，变量秃头的值表明脱发程度的增加，因此，在诺伍德-汉密尔顿量表上测量的秃头是一个序数变量。该变量也在弗雷明汉心脏研究的后代队列中进行测量。

## 有限元方法代写

tatistics-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|生物统计分析代写Biological statistic analysis代考|BIOL220

statistics-lab™ 为您的留学生涯保驾护航 在代写生物统计分析Biological statistic analysis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。我们的专家在代写生物统计分析Biological statistic analysis代写方面经验极为丰富，各种生物统计分析Biological statistic analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|生物统计分析代写Biological statistic analysis代考|Degrees of Freedom

Associated with each sum of squares term are its degrees of freedom, the number of independent components used to calculate it.

The total degrees of freedom for $\mathrm{SS}{\text {tot }}$ are $\mathrm{df}{\mathrm{tot}}=N-1$, because we have $N$ response values, and need to compute a single value $\bar{y}$.. to find the sum of squares.
The treatment degrees of freedom are $\mathrm{df}_{\text {trt }}=k-1$, because there are $k$ treatment means, estimated by $\bar{y}_i$., but the calculation of the sum of squares requires the overall average $\bar{y} \ldots$

Finally, there are $N$ residuals, but we used up 1 degree of freedom for the overall average, and $k-1$ for the group averages, leaving us with $\mathrm{df}{\mathrm{res}}=N-k$ degrees of freedom. The degrees of freedom then decompose as $$\mathrm{df}{\mathrm{tot}}=\mathrm{df}{\mathrm{trt}}+\mathrm{df}{\mathrm{res}} .$$
This decomposition tells us how much of the data we ‘use up’ for calculating each sum of squares component.

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

Dividing a sum of squares by its degrees of freedom gives the corresponding mean squares, which are exactly our two variance estimates. The treatment mean squares are given by
$$\mathrm{MS}{\mathrm{trt}}=\frac{\mathrm{SS}{\mathrm{trt}}}{\mathrm{df}{\mathrm{trt}}}=\frac{\mathrm{SS}{\mathrm{trt}}}{k-1}=\tilde{\sigma}e^2$$ and are our first variance estimate based on group means and grand mean, while the residual mean squares $$\mathrm{MS}{\mathrm{res}}=\frac{\mathrm{SS}{\mathrm{res}}}{\mathrm{df}{\mathrm{res}}}=\frac{\mathrm{SS}{\mathrm{res}}}{N-k}=\hat{\sigma}_e^2$$ are our second independent estimator for the within-group variance. We find $\mathrm{MS}{\text {res }}=$ $41.37 / 28=1.48$ and $\mathrm{MS}_{\mathrm{trt}}=155.89 / 3=51.96$ for our example.

In contrast to the sum of squares, the mean squares do not decompose by factor and $\mathrm{MS}{\mathrm{tot}}=\mathrm{SS}{\text {tot }} /(N-1)=6.36 \neq \mathrm{MS}{\text {trt }}+\mathrm{MS}{\text {res }}=53.44$.

Our $F$-statistic for testing the omnibus hypothesis $H_0: \mu_1=\cdots=\mu_k$ is then $$F=\frac{\mathrm{MS}{\mathrm{trt}}}{\mathrm{MS}{\mathrm{res}}}=\frac{\mathrm{SS}{\mathrm{trt}} / \mathrm{df}{\mathrm{trt}}}{\mathrm{SS}{\mathrm{res}} / \mathrm{df}{\mathrm{res}}} \sim F_{\mathrm{df}{\mathrm{tr}}, \mathrm{df} \mathrm{res}},$$ and we reject $H_0$ if the observed $F$-statistic exceeds the (1- $\alpha$ )-quantile $F{1-\alpha, \mathrm{df}{\mathrm{fr}}, \mathrm{df}{\mathrm{res}}}$.
Based on the sum of squares and degrees of freedom decompositions, we again find the observed test statistic of $F=51.96 / 1.48=35.17$ on $\mathrm{df}{\text {trt }}=3$ and $\mathrm{df}{\mathrm{res}}=28$ degrees of freedom, corresponding to a $p$-value of $p=1.24 \times 10^{-9}$.

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

$$\text { dftot }=\text { dftrt }+\text { dfres. }$$

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

$$\mathrm{MStrt}=\frac{\text { SStrt }}{\text { dftrt }}=\frac{\text { SStrt }}{k-1}=\tilde{\sigma} e^2$$

$$\text { MSres }=\frac{\text { SSres }}{\text { dfres }}=\frac{\text { SSres }}{N-k}=\hat{\sigma}e^2$$ 是我们对组内方差的第二个独立估计量。我们发现MSres $=41.37 / 28=1.48$ 和 $\mathrm{MS}{\mathrm{trt}}=155.89 / 3=51.96$ 对于我们的例子。

$$F=\frac{\text { MStrt }}{\text { MSres }}=\frac{\text { SStrt } / \text { dftrt }}{\text { SSres } / \text { dfres }} \sim F_{\text {dftr,dfres }},$$

## 有限元方法代写

tatistics-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|生物统计分析代写Biological statistic analysis代考|STAT201

statistics-lab™ 为您的留学生涯保驾护航 在代写生物统计分析Biological statistic analysis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。我们的专家在代写生物统计分析Biological statistic analysis代写方面经验极为丰富，各种生物统计分析Biological statistic analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|生物统计分析代写Biological statistic analysis代考|Analysis of Variance

Our derivation of the omnihus $F$-test used the decomposition of the data into a between-groups and a within-groups component. We can exploit this decomposition further in the (one-way) analysis of variance (ANOVA) by directly partitioning the overall variation in the data via sums of squares and their associated degrees of freedom. In the words of its originator: The arithmetic advantages of the analysis of variance are no longer relevant today, but the decomposition of the data into various parts for explaining the observed variation remains an easily interpretable summary of the experimental results.

To stress that ANOVA decomposes the variation in the data, we first write each datum $y_{i j}$ as a sum of three components: the grand mean, deviation of group mean to grand mean, and deviation of datum to group mean:
$$y_{i j}=\bar{y}{. .}+\left(\bar{y}{i .}-\bar{y}{. .}\right)+\left(y{i j}-\bar{y}{i .}\right) \text {, }$$ where $\bar{y}_i=\sum_j y{i j} / n$ is the average of group $i, \bar{y}{. .}=\sum_i \sum_j y{i j} / n k$ is the grand mean, and a dot indicates summation over the corresponding index.

For example, the first datum in the second group, $y_{21}=13.56$, is decomposed into the grand mean $\bar{y}{. .}=11.43$, the deviation from group mean $\bar{y}_2 .=12.81$ to grand mean $\left(\bar{y}{2 .}-\bar{y}{. .}\right)=1.38$, and the residual $y{21}-\bar{y}_{2 .}=0.75$.

## 统计代写|生物统计分析代写Biological statistic analysis代考|Sums of Squares

We quantify the overall variation in the observations by the total sum of squares, the summed squared distances of each datum $y_{i j}$ to the estimated grand mean $\bar{y}_{\ldots} .$.

Following the partition of each datum, the total sum of squares is also partitioned into two parts: (i) the treatment (or between-groups) sum of squares which measures the variation between group means and captures the variation explained by the systematic differences between the treatments, and (ii) the residual (or within-groups) sum of squares which measures the variation of responses within each group and thus captures the unexplained random variation:
$$\mathrm{SS}{\mathrm{tot}}=\sum{i=1}^k \sum_{j=1}^n\left(y_{i j}-\bar{y}{. .}\right)^2=\underbrace{\sum{i=1}^k n \cdot\left(\bar{y}i-\bar{y}{. .}\right)^2}{\mathrm{SS}{\mathrm{tt}}}+\underbrace{\sum_{i=1}^k \sum_{j=1}^n\left(y_{i j}-\bar{y}{i .}\right)^2}{\mathrm{SS}{\mathrm{ta}}} .$$ The intermediate term $2 \sum_i \sum_j\left(y{i j}-\bar{y}i\right)\left(\bar{y}{i .}-\bar{y} ..\right)=0$ vanishes because $\mathrm{SS}{\mathrm{trt}}$ is based on group means and grand mean, while $\mathrm{SS}{\text {res }}$ is independently based on observations and group means; the two are orthogonal.

For our example, we find a total sum of squares of $\mathrm{SS}{\mathrm{tot}}=197.26$, a treatment sum of squares $\mathrm{SS}{\mathrm{trt}}=155.89$, and a residual sum of squares $\mathrm{SS}{\text {res }}=41.37$ : as expected. the latter two add precisely to $\mathrm{SS}{\mathrm{tot}}$. Thus, most of the observed variation in the data is due to systematic differences between the treatment groups.

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

$$y_{i j}=\bar{y} . .+(\bar{y} i .-\bar{y} . .)+(\text { yij }-\bar{y} i .),$$

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

$$\mathrm{SStot}=\sum i=1^k \sum_{j=1}^n\left(y_{i j}-\bar{y} . .\right)^2=\underbrace{\sum i=1^k n \cdot(\bar{y} i-\bar{y} . .)^2} \mathrm{SStt}+\underbrace{\sum_{j=1}^k\left(y_{i j}-\bar{y} i .\right)^2 \mathrm{SSta}}_{i=1}$$

SSres $=41.37$ : 符合预期。后两者恰好相加SStot. 因此，大多数观察到的数据变化是由于治疗组之间的系统差 异造成的。

## 有限元方法代写

tatistics-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|生物统计分析代写Biological statistic analysis代考|BIOL6610

statistics-lab™ 为您的留学生涯保驾护航 在代写生物统计分析Biological statistic analysis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。我们的专家在代写生物统计分析Biological statistic analysis代写方面经验极为丰富，各种生物统计分析Biological statistic analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|生物统计分析代写Biological statistic analysis代考|Experiment and Data

We consider investigating four drugs for their properties to alter the metabolism in mice, and we take the level of a liver enzyme as a biomarker to indicate this alteration, where higher levels are considered ‘better’. Metabolization and elimination of the drugs might be affected by the fatty acid metabolism, but for the moment we control this aspect by feeding all mice with the same low-fat diet and return to the diet effect in Chap. 6.

The data in Table $4.1$ and Fig. 4.1 A show the observed enzyme levels for $N=n$. $k=32$ mice, with $n=8$ mice randomly assigned to one of the $k=4$ drugs $D 1, D 2$, $D 3$, and $D 4$. We denote the four average treatment group responses as $\mu_1, \ldots, \mu_4$; we are interested in testing the omnibus hypothesis $H_0: \mu_1=\mu_2=\mu_3=\mu_4$ that the group averages are identical and the four drugs therefore all have the same effect on the enzyme levels.

Other interesting questions regard the estimation and testing of specific treatment group comparisons, which we postpone to Chap. 5.

In a balanced completely randomized design, we randomly allocate $k$ treatments on $N=n \cdot k$ experimental units. We assume that the response $y_{i j} \sim N\left(\mu_i, \sigma_e^2\right)$ of the $j$ th experimental unit in the $i$ th treatment group is normally distributed with groupspecific expectation $\mu_i$ and common variance $\sigma_e^2$, with $i=1 \ldots k$ and $j=1 \ldots n$; each group then has $n$ experimental units.

## 统计代写|生物统计分析代写Biological statistic analysis代考|Testing Equality of Means by Comparing Variances

For $k=2$ treatment groups, the omnibus null hypothesis is $H_0: \mu_1=\mu_2$ and can be tested using a $t$-test on the group difference $\Delta=\mu_1-\mu_2$. For $k>2$ treatment groups, the corresponding omnibus null hypothesis is $H_0: \mu_1=\cdots=\mu_k$, and the idea of using a single difference for testing does not work.

The crucial observation for deriving a test statistic for the general omnibus null hypothesis comes from changing our perspective on the problem: if the treatment group means $\mu_i \equiv \mu$ are all equal, then we can consider their estimates $\hat{\mu}i=\sum{j=1}^n y_{i j} / n$ as independent ‘samples’ from a normal distribution with mean $\mu$ and variance $\sigma_e^2 / n$ (Fig. 4.1B). We can then estimate their variance using the usual formula
$$\widehat{\operatorname{Var}}\left(\hat{\mu}i\right)=\sum{i=1}^k\left(\hat{\mu}i-\hat{\mu}\right)^2 /(k-1),$$ where $\hat{\mu}=\sum{i=1}^k \hat{\mu}i / k$ is an estimate of the grand mean $\mu$. Since $\operatorname{Var}\left(\hat{\mu}_i\right)=\sigma_e^2 / n$, this provides us with an estimator $$\tilde{\sigma}_e^2=n \cdot \widehat{\operatorname{Var}}\left(\hat{\mu}_i\right)=n \cdot \sum{i=1}^k\left(\hat{\mu}i-\hat{\mu}\right)^2 /(k-1)$$ for the variance $\sigma_e^2$ that only considers the dispersion of group means around the grand mean and is independent of the dispersion of individual observations around their group mean. On the other hand, our previous estimator pooled over groups is $$\hat{\sigma}_e^2=(\underbrace{\frac{\sum{j=1}^n\left(y_{1 j}-\hat{\mu}1\right)^2}{n-1}}{\text {variance group 1 }}+\cdots+\underbrace{\frac{\sum_{j=1}^n\left(y_{k j}-\hat{\mu}k\right)^2}{n-1}}{\text {variance group k }}) / k=\sum_{i=1}^k \sum_{j=1}^n \frac{\left(y_{i j}-\hat{\mu}_i\right)^2}{N-k}$$
and also estimates the variance $\sigma_e^2$ (Fig.4.1C). It only considers the dispersion of observations around their group means and is independent of the $\mu_i$ being equal. For example, we could add a fixed number to all measurements in one group and this would affect $\tilde{\sigma}_e^2$ but not $\hat{\sigma}_e^2$.

## 统计代写|生物统计分析代写Biological statistic analysis代考|比较方差检验均数相等性

$$\widehat{\operatorname{Var}}(\hat{\mu} i)=\sum i=1^k(\hat{\mu} i-\hat{\mu})^2 /(k-1),$$

## 有限元方法代写

tatistics-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。