统计代写|Generalized linear model代考广义线性模型代写|Null Hypothesis Statistical Significance Testing
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广义线性模型（GLiM，或GLM）是John Nelder和Robert Wedderburn在1972年提出的一种高级统计建模技术。它是一个包括许多其他模型的总称，它允许响应变量y具有正态分布以外的误差分布。
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我们提供的Generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:
- Statistical Inference 统计推断
- Statistical Computing 统计计算
- Advanced Probability Theory 高等概率论
- Advanced Mathematical Statistics 高等数理统计学
- (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|Generalized linear model代考广义线性模型代写|Null Hypothesis Statistical Significance Testing
The main purpose of this chapter is to transition from the theory of inferential statistics to the application of inferential statistics. The fundamental process of inferential statistics is called null hypothesis statistical significance testing (NHST). All procedures in the rest of this textbook are a form of NHST, so it is best to think of NHSTs as statistical procedures used to draw conclusions about a population based on sample data.
There are eight steps to NHST procedures:
- Form groups in the data.
- Define the null hypothesis $\left(\mathrm{H}_{0}\right)$. The null hypothesis is always that there is no difference between groups or that there is no relationship between independent and dependent variables.
- Set alpha $(\alpha)$. The default alpha $=.05$.
- Choose a one-tailed or a two-tailed test. This determines the alternative hypothesis $\left(\mathrm{H}_{\mathrm{l}}\right)$.
- Find the critical value, which is used to define the rejection region. Calculate the observed value.
- Compare the observed value and the critical value. If the observed value is more extreme than the critical value, then the null hypothesis should be rejected. Otherwise, it should be retained.
- Calculate an effect size.
- Readers who have had no previous exposure to statistics will find these steps confusing and abstract right now. But the rest of this chapter will define the terminology and show how to put these steps into practice. To reduce confusion, this book starts with the simplest possible NHST: the $z$-test.
统计代写|Generalized linear model代考广义线性模型代写|z-Test
Recall from the previous chapter that social scientists are often selecting samples from a population that they wish to study. However, it is usually impossible to know how representative a single sample is of the population. One possible solution is to follow the process shown at the end of Chapter 6 where a researcher selects many samples from the same population in order to build a probability distribution. Although this method works, it is not used in the real world because it is too expensive and time-consuming. (Moreover, nobody wants to spend their life gathering data from an infinite number of populations in order to build a sampling distribution.) The alternative is to conduct a $z$-test. A z-test is an NHST that scientists use to determine whether their sample is typical or representative of the population it was drawn from.
In Chapter 6 we learned that a sample mean often is not precisely equal to the mean of its parent population. This is due to sampling error, which is also apparent in the variation in mean values from sample to sample. If several samples are taken from the parent population, the means from each sample could be used to create a sampling distribution of means. Because of the principles of the central limit theorem (CLT), statisticians know that with an infinite number of sample means, the distribution will be normally distributed (if the $n$ of each sample is $\geq 25$ ) and the mean of means will always be equal to the population mean.
Additionally, remember that in Chapter 5 we saw that the normal distribution theoretically continues on from $-\infty$ to $+\infty$. This means that any $\bar{X}$ value is possible. However, because the sampling distribution of means is tallest at the population mean and shortest at the tails, the sample means close to the population mean are far more likely to occur than sample means that are very far from $\mu$.
Therefore, the question of inferential statistics is not whether a sample mean is possible but whether it is likely that the sample mean came from the population of interest. That requires a researcher to decide the point at which a sample mean is so different from the population mean that obtaining that sample mean would be highly unlikely (and, therefore, a more plausible explanation is that the sample really does differ from the population). If a sample mean $(\bar{X})$ is very similar to a population mean ( $\mu$ ), then the null hypothesis $(\bar{X}=\mu)$ is a good model for the data. Conversely, if the sample mean and population mean are very different, then the null hypothesis does not fit the data well, and it is reasonable to believe that the two means are different.
This can be seen in Figure 7.1, which shows a standard normal distribution of sampling means. As expected, the population mean $(\mu)$ is in the middle of the distribution, which is also the peak of the sampling distribution. The shaded regions in the tails are called the rejection region. If, when we graph the sample mean, it falls within the rejection region, the sample is so different from the mean that it is unlikely that sampling error alone could account for the differences between $\bar{X}$
and $\mu$ – and it is more likely that there is an actual difference between $\bar{X}$ and $\mu$. If the sample mean is outside the rejection region, then $\bar{X}$ and $\mu$ are similar enough that it can be concluded that $\bar{X}$ is typical of the population (and sampling error alone could possibly account for all of the differences between $\bar{X}$ and $\mu$ ).
Judging whether differences between $\bar{X}$ and $\mu$ are “close enough” or not due to just sampling error requires following the eight steps of NHST. To show how this happens in real life, we will use an example from a UK study by Vinten et al. (2009).
统计代写|Generalized linear model代考广义线性模型代写|Cautions for Using NHSTs
NHST procedures dominate quantitative research in the behavioral sciences (Cumming et al., 2007; Fidler et al., 2005; Warne, Lazo, Ramos, \& Ritter, 2012). But it is not a flawless procedure, and NHST is open to abuse. In this section, we will explore three of the main problems with NHST: (1) the possibility of errors, (2) the subjective decisions involved in conducting an NHST, and (3) NHST’s sensitivity to sample size.
Type I and Type II Errors. In the Vinten et al. (2009) example, we rejected the null hypothesis because the $z$-observed value was inside the rejection region, as is apparent in Figure $7.4$ (where the z-observed value was so far below zero that it could not be shown on the figure). But this does not mean that the null hypothesis is definitely wrong. Remember that theoretically – the probability distribution extends from $-\infty$ to to . Therefore, it is possible that a random sample could have an $\bar{X}$ value as low as what was observed in Vinten et al.’s (2009) study. This is clearly an unlikely event – but, theoretically, it is possible. So even though we rejected the null hypothesis and the $\bar{X}$ value in this example had a very extreme z-observed value, it is still possible that Vinten et al. just had a weird sample (which would produce a large amount of sampling error). Thus, the results of this z-test do not prove that the anti-seizure medication is harmful to children in the womb.
Scientists never know for sure whether their null hypothesis is true or not – even if that null is strongly rejected, as in this chapter’s example (Open Science Collaboration, 2015; Tukey, 1991). There is always the possibility (no matter how small) that the results are just a product of sampling error. When researchers reject the null hypothesis and it is true, they have made a Type I error. We can use the $z$-observed value and Appendix Al to calculate the probability of Type I error if the null hypothesis were perfectly true and the researcher chose to reject the null hypothesis (regardless of the $\alpha$ level). This probability is called a $p$-value (abbreviated as $p$ ). Visually, it can be represented, as in Figure $7.6$, as the region of the sampling distribution that starts at the observed value and includes everything beyond it in the tail.
To calculate $p$, you should first find the $z$-observed value in column $\mathrm{A}$. (If the $z$-observed value is not in Appendix A1, then the Price Is Right rule applies, and you should select the number in column A that is closest to the $z$-observed value without going over it.) The number in column $\mathrm{C}$ in the same row will be the $p$-value. For example, in a one-tailed test, if $z$-observed were equal to $+2.10$, then the $p$-value (i.e., the number in column $\mathrm{C}$ in the same row) would be 0179 . This $p$-value means that in this example the probability that these results could occur through purely random sampling error is .0179 (or $1.79 \%$ ). In other words, if we selected an infinite number of samples from the population, then $1.79 \%$ of $\bar{X}$ values would be as different as or more different than $\mu$. But remember that this probability only applies if the null hypothesis is perfectly true (see Sidebar 10.3).
In the Vinten et al. $(2009)$ example, the $z$-observed value was $-9.95$. However, because Appendix Al does not have values that high, we will select the last row (because of the Price Is Right rule), which has the number $\pm 5.00$ in column A. The number in column $\mathrm{C}$ in the same row is $.0000003$, which is the closest value available for the $p$-value. In reality, $p$ will be smaller than this tiny number. (Notice how the numbers in column $C$ get smaller as the numbers in column $A$ get bigger. Therefore, a $z$-observed value that is outside the $\pm 5.00$ range will have smaller $p$-values than the values in the table.) Thus, the chance that – if the null hypothesis were true – Vinten et al. (2009) would obtain a random sample of 41 children with such low VABS scores is less than .0000003-or less than 3 in 10 million. Given this tiny probability of making a Type I error if the null hypothesis were true, it seems more plausible that these results are due to an actual difference between the sample and the population – and not merely to sampling error.
广义线性模型代写
统计代写|Generalized linear model代考广义线性模型代写|Null Hypothesis Statistical Significance Testing
本章的主要目的是从推论统计理论过渡到推论统计的应用。推论统计的基本过程称为零假设统计显着性检验 (NHST)。本教科书其余部分中的所有程序都是 NHST 的一种形式，因此最好将 NHST 视为统计程序，用于根据样本数据得出关于总体的结论。
NHST 程序有八个步骤：
- 在数据中形成组。
- 定义零假设(H0). 零假设始终是组之间没有差异，或者自变量和因变量之间没有关系。
- 设置阿尔法(一种). 默认阿尔法=.05.
- 选择单尾或双尾测试。这决定了备择假设(Hl).
- 找到用于定义拒绝区域的临界值。计算观察值。
- 比较观察值和临界值。如果观测值比临界值更极端，则应拒绝原假设。否则，应保留。
- 计算效应量。
- 以前没有接触过统计数据的读者现在会发现这些步骤令人困惑和抽象。但本章的其余部分将定义术语并展示如何将这些步骤付诸实践。为了减少混淆，本书从最简单的 NHST 开始：和-测试。
统计代写|Generalized linear model代考广义线性模型代写|z-Test
回想一下前一章，社会科学家经常从他们希望研究的人群中选择样本。然而，通常不可能知道单个样本在总体中的代表性。一种可能的解决方案是遵循第 6 章末尾显示的过程，在该过程中，研究人员从同一总体中选择许多样本以构建概率分布。虽然这种方法有效，但它并没有在现实世界中使用，因为它太昂贵且耗时。（此外，没有人愿意花费一生的时间从无数人口中收集数据以建立抽样分布。）另一种方法是进行和-测试。z 检验是一种 NHST，科学家们使用它来确定他们的样本是典型的还是代表样本的人群。
在第 6 章中，我们了解到样本均值通常不完全等于其父总体的均值。这是由于抽样误差，这在样本间平均值的变化中也很明显。如果从父总体中抽取多个样本，则每个样本的均值可用于创建均值的抽样分布。由于中心极限定理 (CLT) 的原理，统计学家知道，对于无限数量的样本均值，分布将是正态分布的（如果n每个样本的≥25) 并且均值的平均值将始终等于总体均值。
此外，请记住，在第 5 章中，我们看到理论上正态分布从−∞到+∞. 这意味着任何X¯值是可能的。但是，由于均值的抽样分布在总体均值处最高而在尾部最短，因此接近总体均值的样本均值比远离总体均值的样本均值更容易出现。μ.
因此，推论统计的问题不是样本均值是否可能，而是样本均值是否可能来自感兴趣的总体。这需要研究人员确定样本均值与总体均值如此不同的点，因此获得该样本均值的可能性极小（因此，更合理的解释是样本确实与总体不同）。如果样本均值(X¯)与总体平均值非常相似（μ)，然后是原假设(X¯=μ)是一个很好的数据模型。反之，如果样本均值和总体均值相差很大，则原假设不能很好地拟合数据，有理由相信这两个均值不同。
这可以在图 7.1 中看到，它显示了采样均值的标准正态分布。正如预期的那样，人口平均(μ)处于分布的中间，也是采样分布的峰值。尾部的阴影区域称为拒绝区域。如果当我们绘制样本均值时，它落在拒绝区域内，则样本与均值的差异如此之大，以至于仅靠抽样误差不可能解释两者之间的差异X¯
和μ– 更有可能两者之间存在实际差异X¯和μ. 如果样本均值在拒绝域之外，则X¯和μ足够相似，可以得出结论X¯是典型的总体（仅抽样误差就可能解释两者之间的所有差异X¯和μ ).
判断是否存在差异X¯和μ是否“足够接近”只是由于抽样误差需要遵循 NHST 的八个步骤。为了说明这在现实生活中是如何发生的，我们将使用 Vinten 等人的英国研究中的一个例子。（2009 年）。
统计代写|Generalized linear model代考广义线性模型代写|Cautions for Using NHSTs
NHST 程序主导了行为科学的定量研究（Cumming 等人，2007；Fidler 等人，2005；Warne，Lazo，Ramos，\& Ritter，2012）。但这不是一个完美的程序，NHST 很容易被滥用。在本节中，我们将探讨 NHST 的三个主要问题：(1) 错误的可能性，(2) 进行 NHST 所涉及的主观决定，以及 (3) NHST 对样本量的敏感性。
I 型和 II 型错误。在文滕等人。（2009）的例子，我们拒绝了原假设，因为和- 观察值在拒绝区域内，如图所示7.4（其中 z 观测值远低于零，无法在图中显示）。但这并不意味着零假设肯定是错误的。请记住，理论上——概率分布从−∞到 到 。因此，一个随机样本可能有一个X¯值与 Vinten 等人 (2009) 研究中观察到的值一样低。这显然是一个不太可能发生的事件——但从理论上讲，这是可能的。所以即使我们拒绝了原假设和X¯这个例子中的值有一个非常极端的 z 观察值，Vinten 等人仍然有可能。只是有一个奇怪的样本（这会产生大量的抽样误差）。因此，该 z 检验的结果并不能证明抗癫痫药物对子宫内的儿童有害。
科学家们永远无法确定他们的零假设是否正确——即使该零假设被强烈拒绝，如本章的示例所示（Open Science Collaboration，2015；Tukey，1991）。结果总是有可能（无论多么小）只是抽样误差的产物。当研究人员拒绝零假设并且它是真的时，他们犯了第一类错误。我们可以使用和- 观察值和附录 A 来计算如果原假设完全正确并且研究人员选择拒绝原假设（无论一种等级）。这个概率称为p-值（缩写为p）。视觉上可以表示，如图7.6，作为采样分布的区域，该区域从观察值开始，包括尾部之外的所有内容。
计算p, 你应该首先找到和- 列中的观察值一种. （如果和- 观察值不在附录 A1 中，则适用价格正确规则，您应选择 A 列中最接近和- 观察到的值，不经过它。）列中的数字C在同一行将是p-价值。例如，在单尾测试中，如果和- 观察到等于+2.10，那么p-value（即列中的数字C在同一行）将是 0179 。这p-value 表示在本例中，这些结果可能通过纯随机抽样误差出现的概率为 0.0179（或1.79%）。换句话说，如果我们从总体中选择了无限个样本，那么1.79%的X¯值将与以下相同或更多不同μ. 但请记住，这种概率仅适用于原假设完全正确的情况（见侧边栏 10.3）。
在文滕等人。(2009)例如，和-观察值是−9.95. 但是，由于附录 A 没有那么高的值，我们将选择最后一行（因为价格正确规则），它的编号为±5.00在 A 列中。列中的数字C在同一行是.0000003，这是可用的最接近的值p-价值。事实上，p将小于这个微小的数字。（注意列中的数字C随着列中的数字变小一种变得更大。因此，一个和- 观察值之外±5.00范围会更小p-值比表中的值。）因此，如果零假设为真，Vinten 等人的机会。（2009 年）将获得 41 名儿童的随机样本，这些儿童的 VABS 分数低于 0.0000003 或低于 1000 万分之三。鉴于如果原假设为真，犯 I 类错误的可能性很小，这些结果似乎更合理的是，这些结果是由于样本和总体之间的实际差异——而不仅仅是抽样误差。
统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。
金融工程代写
金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。
非参数统计代写
非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。
广义线性模型代考
广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。
术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。
有限元方法代写
有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。
有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。
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随机分析代写
随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。
时间序列分析代写
随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。
回归分析代写
多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。
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，工具箱允许您学习和应用专业技术。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。
