### 统计代写|数据可视化代写Data visualization代考|DESN6003

statistics-lab™ 为您的留学生涯保驾护航 在代写数据可视化Data visualization方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写数据可视化Data visualization代写方面经验极为丰富，各种代写数据可视化Data visualization相关的作业也就用不着说。

• 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|数据可视化代写Data visualization代考|Confidence Intervals

Confidence intervals are likely one of the most abstract and misinterpreted concepts in traditional statistics. Assume we want to compare two groups and estimate the difference between them. We could simply collect one sample of data from each group and calculate the difference in means between the samples. But we don’t know for sure the real difference between the two populations, because we are only working with samples. Confidence intervals give us a range of plausible values for the real difference based on the data we observe in our samples-this is preferred and more generalizable relative to a single number representing the difference in the samples.

If you repeated an experiment comparing two groups several times, each time would give you a slightly different difference in means, as well as a different confidence interval. Ninety-five percent of all such intervals would contain the true parameter value of interest (i.e., the true difference between the two populations under examination). You can see that the notion of confidence intervals rests on the assumption that you will repeat an experiment-which is not what typically happens in real life, unfortunately (hence the importance of replication studies). When we normally just run a single experiment, we cannot tell whether the only confidence interval that we have is the lucky interval to include the true parameter value.

Let’s go back to our example earlier where we considered whether recording classes could be useful to students. The difference between the two groups, $\mathcal{T}$ and $\mathcal{C}$, was $2.06$ points: $\bar{x}{\mathcal{C}}=83.05$ and $\bar{x}{\mathcal{T}}=85.11$. This difference was the effect size in our samples (i.e., the quantified impact of recording our classes using the original unit of the variable in question). What if we could have access to the true population means? Let’s pretend we do: assume that the true difference between $\mathcal{T}$ and $\mathcal{C}$ is $1.98: \mu_{T}=82.97$ and $\mu_{T}=84.95$ (in reality, of course, we wouldn’t know these means). So the true difference in means is $\mu_{T}-\mu_{c}=1.98$, which is not too far from $2.06$, our sample means difference. As mentioned in $\S 1.3 .2$, a $t$-test comparing both groups gives us a $p$-value $<0.0001$, which means we reject the null hypothesis that the groups come from the same population. This is correct, since we generated them from different population means. The $95 \%$ confidence interval for the difference in means between the two groups is $[1.13,3.00]$.

## 统计代写|数据可视化代写Data visualization代考|Standard Errors

To calculate a confidence interval, we need to know the standard enror of the sample mean $(S E)$, which is computed by dividing the standard deviation of the sample (s) by the square root of the sample size $(n): S E=\frac{s}{\sqrt{n}}$. Once we know the $S E$, our confidence interval is defined as $C I=[\bar{x}-1.96 \cdot S E, \bar{x}+1.96 \cdot S E]^{4}$-later in this book we will use a function in $\mathrm{R}$ that calculates confidence intervals for us using a better method. When you collect data from a sample of participants, the mean of that sample $(\bar{x})$ will deviate from the true mean of the population $(\mu)$-to which we have no access. As a result, there’s always some degree of uncertainty when we infer the population mean from the sample mean. To estimate that uncertainty, we calculate the standard error of the sample mean.

The standard error is essentially the standard deviation of the sampling distribution of the sample mean. Let’s unpack that. Imagine you collect test scores from five learners of English-so your sample size $(n)$ is 5 . This is a tiny sample of the entire population of all learners of English. You calculate the sample mean of the scores and you come to $\bar{x}=84.2$. You then calculate the standard deviation of the sample $(s)$, which in this hypothetical example is $s=7.66$. As we know, the standard deviation quantifies the variation in the data. In our sample, students deviate $7.66$ points from the mean in question (on average).

You now decide to repeat your data collection four times, where each time you collect scores from five different students. At the end, you will have five samples of the population of learners of English, each of which contains five scores. Each sample will in turn have its own mean and standard deviation. As a result, we will have five means. Assume that they are $84.2,84.8,77.4$, 87.0, and 78.0. This is our sampling distribution of the sample mean. This distribution will be normal even if our population distribution is not normal, as long as the sample size is sufficiently large and the population has a mean (this is known as the Central Limit Theorem). If you compute the mean of these means, you will estimate the true mean of the population $(\mu)$. And if you compute the standard deviation of these means, you’ll get the standard error of the sample mean, which quantifies the variation in the means from multiple samples. The larger the sample size of our samples (here $n=5$ ), the lower the standard error will tend to be. ${ }^{5}$ The more data you collect from a population, the more accurate your estimate will be of the true mean of that population, because the variation across sample means will decrease.

If you feel anxious about math in general and think you need to review basic statistical concepts in a little more detail, there are numerous options online these days. You may want to start with brief video tutorials, and then decide whether it’s necessary to consult textbooks to understand different concepts in more detail. I recommend the following YouTube channels: Statisticsfun (http://www.youtube.com/user/statisticsfun/) and StatQuest with Josh Starmer (https://www.youtube.com/joshstarmer/). Both channels offer a wide range of short and intuitive videos on basic statistics.

You are probably already familiar with different statistics textbooks (there are hundreds out there), so you may want to try Wheelan (2013), which provides a more user-friendly take on important statistical concepts. I will make more specific and advanced reading suggestions throughout this book, once you’re more familiarized with $\mathrm{R}$. Finally, a recent and detailed review of key statistical concepts discussed earlier can be found in Greenland et al. (2016) and in numerous references therein-Greenland et al. provide all you need for the present book.

## 有限元方法代写

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## 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。