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# 统计代写| 假设检验作业代写Hypothesis testing代考|Sample Size Considerations

##### 空白假设的早期选择

Paul Meehl认为，无效假设的选择在认识论上的重要性基本上没有得到承认。当无效假设是由理论预测的，一个更精确的实验将是对基础理论的更严格的检验。当无效假设默认为 “无差异 “或 “无影响 “时，一个更精确的实验是对促使进行实验的理论的一个较不严厉的检验。

1778年：皮埃尔-拉普拉斯比较了欧洲多个城市的男孩和女孩的出生率。他说 “很自然地得出结论，这些可能性几乎处于相同的比例”。因此，拉普拉斯的无效假设是，鉴于 “传统智慧”，男孩和女孩的出生率应该是相等的 。

1900: 卡尔-皮尔逊开发了卡方检验，以确定 “给定形式的频率曲线是否能有效地描述从特定人群中抽取的样本”。因此，无效假设是，一个群体是由理论预测的某种分布来描述的。他以韦尔登掷骰子数据中5和6的数量为例 。

1904: 卡尔-皮尔逊提出了 “或然性 “的概念，以确定结果是否独立于某个特定的分类因素。这里的无效假设是默认两件事情是不相关的（例如，疤痕的形成和天花的死亡率）。[16] 这种情况下的无效假设不再是理论或传统智慧的预测，而是导致费雪和其他人否定使用 “反概率 “的冷漠原则。

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## 统计代写| 假设检验作业代写Hypothesis testing代考|Degrees of Freedom

In statistics, the degrees of freedom (DF) indicate the number of independent values that can vary in an analysis without breaking any constraints. It’s related to sample size, but it’s not directly equal to it. Degrees of freedom is an essential but slippery idea that appears in all hypothesis tests. Learn how this fundamental concept affects the power and precision of your statistical analysis!

In this section, I bring this concept to life in an intuitive manner. I’ll start by defining degrees of freedom. However, I’ll quickly move on to practical examples in various contexts because they make this concept easier to understand.

Degrees of freedom are the number of independent values that a statistical analysis can estimate. You can also think of it as the number of values that are free to vary as you estimate parameters. I know, it’s starting to sound a bit murky!

Degrees of freedom encompasses the notion that the amount of independent information you have limits the number of parameters that you can estimate. Typically, the degrees of freedom equal your sample size minus the number of parameters you need to calculate during an analysis. It is usually a positive whole number.

Degrees of freedom is a combination of how much data you have and how many parameters you need to estimate. It indicates how much independent information goes into a parameter estimate. In this vein, it’s easy to see that you want a lot of information to go into parameter estimates to obtain more precise estimates and more powerful hypothesis tests. So, you want many degrees of freedom!
Independent Information and Constraints on Values
The definitions talk about independent information. You might think this refers to the sample size, but it’s a little more complicated than that. To understand why, we need to talk about the freedom to vary. The best way to illustrate this concept is with an example.

Suppose we collect the random sample of observations shown below. Now, imagine that we know the mean, but we don’t know the value of an observation-the $\mathrm{X}$ in the table below.

## 统计代写|假设检验作业代写HYPOTHESIS TESTING代考|Central Limit Theorem

The central limit theorem is a crucial concept in statistics that affects hypothesis testing. This theorem states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable’s distribution in the population.

Unpacking the meaning from that complex definition can be difficult. That’s the topic for this section! I’ll walk you through the various aspects of the central limit theorem (CLT) definition and show you why it is vital in statistics.
Distribution of the Variable in the Population
Part of the definition for the central limit theorem relates to “the variable’s distribution in the population.” This part is easy! In a population, the values of a variable can follow different probability distributions. These distributions can range from normal, left-skewed, right-skewed, and uniform among others.

This part of the definition refers to the distribution of the variable’s values in the population from which you draw a random sample.
The central limit theorem applies to almost all types of probability distributions, but there are exceptions. For example, the population must have a finite variance. That restriction rules out the Cauchy distribution because it has infinite variance.

Additionally, the central limit theorem applies to independent, identically distributed variables. In other words, the value of one observation does not depend on the value of another observation. And, the distribution of that variable must remain constant across all measurements.

## 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。