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# 统计代写|回归分析代写Regression Analysis代考|Hypothesis Testing and $p$-Values: Is the Observed Effect of $X$ on $Y$ Explainable by Chance Alone?

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## 统计代写|回归分析代写Regression Analysis代考|Hypothesis Testing and $p$-Values: Is the Observed Effect of $X$ on $Y$ Explainable by Chance Alone?

Some researchers will do nearly anything to get a publication. The incentives are great: Fame, tenure, promotion, annual salary, raises, prime class assignments, and clout in one’s department are a function of quality and quantity of publications.

Historically, statistical results were required to be “statistically significant” to be publishable. In terms of confidence intervals, this means that the interval for the effect (e.g., the $\beta$ ) in question must exclude 0 so that you can confidently state the direction of the effect (positive or negative) of the given $X$ variable on $Y$.

Researchers used the $p$-values that are reported routinely by regression software to determine “statistical significance.” But $p$-values are easily manipulated, and unscrupulous researchers can analyze data “creatively” to get nearly any $p$-value they would like to see. This has led to an unfortunate practice known as p-hacking, where researchers try analyses many different ways until they get a $p$-value that is statistically significant, and then try to publish the results. Because of their potential for misuse, there is a strong movement in the scientific community away from use of $p$-values, as well as the phrase “statistical significance,” in favor of other statistics and characterizations.

When interpreted correctly and not misused, the $p$-value does provide interesting and somewhat useful information. Thus, we insist that you understand $p$-values very well, so that you can use them correctly and effectively, and so that you will not become a ” $p$-hacker.”

To interpret the $p$-value correctly, you must consider the question, “Is the estimate of the effect of $X$ on $Y$ explainable by chance alone?” But to answer that question, you must first understand what it means for an estimated effect to be explained by chance alone. The following example explains this concept.

## 统计代写|回归分析代写Regression Analysis代考|Is the Last Digit of a Person’s Identification Number Related to Their Height?

On the surface of it, this is a silly question. But it provides a great example to help you to understand what it means for a phenomenon to be “explained by chance alone,” which is the first thing you need to know before you can ascertain whether a phenomenon is “explainable by chance alone.”

Suppose you have a data set containing heights of 100 adult males in the United States, along with the last digit of their social security number (SSN). Since adult male heights are approximately normally distributed with mean 70 inches and standard deviation 4 inches, and since the last digit of the SSN is uniformly distributed on the numbers $0,1,2, \ldots, 9$, the following code simulates a quite realistic example of how such a data set would look.
## Simulation of data relating Height to SSN
$\mathrm{n}=100$
set. seed(12345) # so that the results will replicate perfectly
height = round(rnorm( $100,70,4))$
ssn = sample $(0: 9,100$, replace=T)
ssn. data = data.frame(ssn, height)
## Simulation of data relating Height to SSN
$\mathrm{n}=100$
set.seed(12345) # so that the results will replicate perfectly
height = round $(\operatorname{rnorm}(100,70,4))$
$\mathrm{ssn}=$ sample $(0: 9,100$, replace $=T)$
ssn.data = data.frame (ssn, height)
This code gives you the following (hypothetical but realistic) data on last digit of social security number (SSN) and Height:
$\begin{array}{lrr} & \sin & \text { height } \ 1 & 5 & 72 \ 2 & 8 & 73 \ 3 & 1 & 70 \ 4 & 5 & 68 \ 5 & 6 & 72 \ 6 & 7 & 63\end{array}$

## 统计代写|回归分析代写Regression Analysis代考|Is the Last Digit of a Person’s Identification Number Related to Their Height?

＃＃模拟高度与SSN相关的数据
$\mathrm{n}=100$

ssn = sample $(0: 9,100$, replace=T)
ssn. ssn.Data = Data .frame(ssn, height)

＃＃模拟高度与SSN相关的数据
$\mathrm{n}=100$

$\mathrm{ssn}=$样品$(0: 9,100$，替换$=T)$
ssn. ssn.Data = Data .frame (ssn, height)

$\begin{array}{lrr} & \sin & \text { height } \ 1 & 5 & 72 \ 2 & 8 & 73 \ 3 & 1 & 70 \ 4 & 5 & 68 \ 5 & 6 & 72 \ 6 & 7 & 63\end{array}$

## 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。