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# 统计代写| 假设检验作业代写Hypothesis testing代考|t-Distributions and Statistical Significance

##### 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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• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验作业代写Hypothesis testing代考|t-Distributions and Statistical Significance

The term “t-test” refers to the fact that these hypothesis tests use tvalues to evaluate your sample data. T-values are a test statistic that factors in the effect size, sample size, and variability. Hypothesis tests use the test statistic that is calculated from your sample to compare your sample to the null hypothesis. If the test statistic is extreme enough, this indicates that your data are so incompatible with the null hypothesis that you can reject the null.

Don’t worry. I find these technical definitions of statistical terms are easier to explain with graphs, and we’ll get to that!

The tricky thing about $\mathrm{t}$-values is that they are difficult to interpret on their own. Imagine we performed a t-test, and it produced a t-value of 2. What does this t-value mean exactly?

We know that the sample mean doesn’t equal the null hypothesis value because this t-value doesn’t equal zero. We can also state that the effect is twice the variability. However, we don’t know how exceptional our value is if the null hypothesis is correct.

To be able to interpret individual t-values, we must place them in a larger context. T-distributions provide this broader context so we can determine the unusualness of an individual t-value.

A single t-test produces a single t-value. Now, imagine the following process. First, let’s assume that the null hypothesis is true for the population. Now, suppose we repeat our study many times by drawing numerous random samples of the same size from this population. Next, we perform t-tests on all the samples and plot the distribution of the t-values. This distribution is known as a sampling distribution, which is a type of probability distribution.

If we follow this procedure, we produce a graph that displays the distribution of t-values that we obtain from a population where the null hypothesis is true. We use sampling distributions to calculate probabilities for how unusual our sample statistic is if the null hypothesis is true.

Luckily, we don’t need to go through the hassle of collecting numerous random samples to create this graph! Statisticians understand the properties of t-distributions so we can estimate the sampling distribution using the t-distribution and our sample size.

The degrees of freedom (DF) for the statistical design define the tdistribution for a particular study. We’ll go over degrees of freedom in more detail in a later chapter. For now, understand that degrees of freedom are closely related to the sample size. For t-tests, there is a different t-distribution for each sample size.

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|t-Distributions and Sample Size

The sample size for a t-test determines the degrees of freedom (DF) for that test, which specifies the t-distribution. The overall effect is that as the sample size decreases, the tails of the t-distribution become thicker. Thicker tails indicate that t-values are more likely to be far from zero even when the null hypothesis is correct. The changing shapes are how t-distributions factor in the greater uncertainty when you have a smaller sample.

You can see this effect in the probability distribution plot below that displays t-distributions for 5 and 30 DF.

Sample means from smaller samples tend to be less precise. In other words, with a smaller sample, it’s less surprising to have an extreme tvalue, which affects the probabilities and p-values. A t-value of 2 has a p-value of $10.2 \%$ and $5.4 \%$ for 5 and $30 \mathrm{DF}$, respectively. Use larger samples!

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|Z-tests versus t-tests

Z-tests are very similar to t-tests. You use both kinds of tests fo same reasons-comparing means. Both types of tests have one-sample, two-sample, and paired versions. They even have the same assumptions-with one major exception. That difference determines when you’ll use a Z-test versus t-test.

• Z-test: Use when you know the population standard deviation.
• t-Test: Use when you have an estimate of the population standard deviation.

I’m not covering Z-tests in this book for one excellent reason. You’ll never use one in practice!

Think about it. The Z-test assumes that you know the population standard deviation. That rarely happens. In what situation would you not know the population mean (hence, the need to test it), but yet you do know the population standard deviation? As I discussed earlier, these parameters are generally unknowable.

Despite this critical limitation, many statistics students learn about Ztests. Why is that? Many statistics textbooks use Z-tests because it is easier for students to calculate manually. However, the t-test is more accurate, particularly for smaller sample sizes. For more information about manually calculating Z-scores and using them to calculate probabilities, read my Introduction to Statistics ebook.

Z-tests use the standard normal distribution (mean $=0$, standard deviation $=1$ ) to calculate p-values while t-tests use the t-distribution. However, the t-distribution can approximate the normal distribution.
When statisticians say that a particular distribution approximates the normal distribution, it simply means that they have very similar shapes under certain conditions. T-distributions with at least 30 degrees of freedom will closely follow the normal distribution, as shown in the probability plot below. Using either of these distributions to calculate p-values will produce similar results.

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|T-DISTRIBUTIONS AND SAMPLE SIZE

t 检验的样本量决定了自由度DF对于该测试，它指定了 t 分布。总体效果是随着样本量的减小，t 分布的尾部变得更粗。较粗的尾巴表明即使原假设正确，t 值也更有可能远离零。当样本较小时，变化的形状是 t 分布如何影响较大的不确定性。

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|Z-TESTS VERSUS T-TESTS

Z 检验与 t 检验非常相似。您出于相同的原因使用这两种测试 – 比较方法。两种类型的测试都有单样本、双样本和配对版本。他们甚至有相同的假设——除了一个主要的例外。这种差异决定了您何时使用 Z 检验与 t 检验。

• Z 检验：当您知道总体标准差时使用。
• t 检验：当您估计总体标准差时使用。

Z 检验使用标准正态分布米和一种n$=0$,s吨一种nd一种rdd和v一世一种吨一世○n$=1$在 t 检验使用 t 分布时计算 p 值。但是，t 分布可以逼近正态分布。

## 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。