### 统计代写|生物统计代写biostatistics代考|The Coefficient of Variation

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• 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|The Coefficient of Variation

The standard deviations of two populations resulting from measuring the same variable can be compared to determine which of the two populations is more variable. That is, when one standard deviation is substantially larger than the other (i.e., more than two times as large), then clearly the population with the larger standard deviation is much more variable than the other. It is also important to be able to determine whether a single population is highly variable or not. A parameter that measures the relative variability in a population is the coefficient of variation. The coefficient of variation will be denoted by CV and is defined to be
$$\mathrm{CV}=\frac{\sigma}{|\mu|}$$
The coefficient of variation is also sometimes represented as a percentage in which case
$$\mathrm{CV}=\frac{\sigma}{|\mu|} \times 100 \%$$

The coefficient of variation compares the size of the standard deviation with the size of the mean. When the coefficient of variation is small, this means that the variability in the population is relatively small compared to the size of the mean of the population. On the other hand, when the coefficient of variation is large, this indicates that the population varies greatly relative to the size of the mean. The standard for what is a large coefficient of variation differs from one discipline to another, and in some disciplines a coefficient of variation of less than $15 \%$ is considered reasonable, and in other disciplines larger or smaller cutoffs are used.

Because the standard deviation and the mean have the same units of measurement, the coefficient of variation is a unitless parameter. That is, the coefficient is unaffected by changes in the units of measurement. For example, if a variable $X$ is measured in inches and the coefficient of variation is $\mathrm{CV}=2$, then coefficient of variation will also be 2 when the units of measurement are converted to centimeters. The coefficient of variation can also be used to compare the relative variability in two different and unrelated populations; the standard deviation can only be used to compare the variability in two different populations based on similar variables.

## 统计代写|生物统计代写biostatistics代考|Parameters for Bivariate Populations

In most biomedical research studies, there are many variables that will be recorded on each individual in the study. A multivariate distribution can be formed by jointly tabulating, charting, or graphing the values of the variables over the $N$ units in the population. For example, the bivariate distribution of two variables, say $X$ and $Y$, is the collection of the ordered pairs
$$\left(X_{1}, Y_{1}\right),\left(X_{2}, Y_{2}\right),\left(X_{3}, Y_{3}\right), \ldots,\left(X_{N}, Y_{N}\right)$$
These $N$ ordered pairs form the units of the bivariate distribution of $X$ and $Y$ and their joint distribution can be displayed in a two-way chart, table, or graph.

When the two variables are qualitative, the joint proportions in the bivariate distribution are often denoted by $p_{a b}$, where
$$p_{a b}=\text { proportion of pairs in population where } X=a \text { and } Y=b$$
The joint proportions in the bivariate distribution are then displayed in a two-way table or two-way bar chart. For example, according to the American Red Cross, the joint distribution of blood type and Rh factor is given in Table $2.7$ and presented as a bar chart in Figure $2.21$.

## 统计代写|生物统计代写biostatistics代考|Basic Probability Rules

Determining the probabilities associated with complex real-life events often requires a great deal of information and an extensive scientific understanding of the structure of the chance experiment being studied. In fact, even when the sample space and event are easily identified, the determination of the probability of an event can be an extremely difficult task. For example, in studying the side effects of a drug, the possible side effects can generally be anticipated and the sample space will be known. However, because humans react differently to drugs, the probabilities of the occurrence of the side effects are generally unknown. The probabilities of the side effects are often estimated in clinical trials.

The following basic probability rules are often useful in determining the probability of an event.

1. When the outcomes of a random experiment are equally likely to occur, the probability of an event $A$ is the number of outcomes in $A$ divided by the number of simple events in $\mathcal{S}$. That is,
$$P(A)=\frac{\text { number of simple events in } A}{\text { number of simple events in } \mathcal{S}}=\frac{N(A)}{N(\delta)}$$
2. For every event $A$, the probability of $A$ is the sum of the probabilities of the outcomes comprising $A$. That is, when an event $A$ is comprised of the outcomes $O_{1}, O_{2}, \ldots, O_{k}$, the probability of the event $A$ is
$$P(A)=P\left(O_{1}\right)+P\left(O_{2}\right)+\cdots+P\left(O_{k}\right)$$
3. For any two events $A$ and $B$, the probability that either event $A$ or event $B$ occurs is
$$P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)$$
4. The probability that the event $A$ does not occur is 1 minus the probability that the event $A$ does occur. That is,
$$P(A \text { does not occur })=1-P(A)$$

C在=σ|μ|

C在=σ|μ|×100%

## 统计代写|生物统计代写biostatistics代考|Parameters for Bivariate Populations

(X1,是1),(X2,是2),(X3,是3),…,(Xñ,是ñ)

p一个b= 人口中对的比例 X=一个 和 是=b

## 统计代写|生物统计代写biostatistics代考|Basic Probability Rules

1. 当随机实验的结果同样可能发生时，事件发生的概率一个是结果的数量一个除以简单事件的数量小号. 那是，
磷(一个)= 简单事件的数量 一个 简单事件的数量 小号=ñ(一个)ñ(d)
2. 对于每一个事件一个, 的概率一个是结果的概率之和，包括一个. 也就是说，当一个事件一个由结果组成○1,○2,…,○ķ, 事件的概率一个是
磷(一个)=磷(○1)+磷(○2)+⋯+磷(○ķ)
3. 对于任意两个事件一个和乙, 任一事件的概率一个或事件乙发生是
磷(一个 或者 乙)=磷(一个)+磷(乙)−磷(一个 和 乙)
4. 事件发生的概率一个不发生是 1 减去事件发生的概率一个确实发生。那是，
磷(一个 不发生 )=1−磷(一个)

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## MATLAB代写

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