## 统计代写|Generalized linear model代考广义线性模型代写|Null Hypothesis Statistical Significance Testing

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|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:

1. Form groups in the data.
2. 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.
3. Set alpha $(\alpha)$. The default alpha $=.05$.
4. Choose a one-tailed or a two-tailed test. This determines the alternative hypothesis $\left(\mathrm{H}_{\mathrm{l}}\right)$.
5. Find the critical value, which is used to define the rejection region. Calculate the observed value.
6. 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.
7. Calculate an effect size.
8. 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.

## 统计代写|Generalized linear model代考广义线性模型代写|Null Hypothesis Statistical Significance Testing

NHST 程序有八个步骤：

1. 在数据中形成组。
2. 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。
3. 设置阿尔法(一种). 默认阿尔法=.05.
4. 选择单尾或双尾测试。这决定了备择假设(Hl).
5. 找到用于定义拒绝区域的临界值。计算观察值。
6. 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。
7. 计算效应量。
8. 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|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。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Probability and the Central Limit Theorem

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Basic Probability

Statistics is based entirely on a branch of mathematics called probability, which is concerned with the likelihood of outcomes for an event. In probability theory, mathematicians use information about

all possible outcomes for an event in order to determine the likelihood of any given outcome. The first section of this chapter will explain the basics of probability before advancing to the foundational issues of the rest of the textbook.

Imagine an event repeated 100 times. Each of these repetitions – called a trial – would be recorded. Mathematically, the formula for probability (abbreviated $p$ ) is:
$$p=\frac{\text { Number of trials with the same outcome }}{\text { Total number of trials }}$$
(Formula 6.1)
To calculate the probability of any given outcome, it is necessary to count the number of trials that resulted in that particular outcome and divide it by the total number of trials. Thus, if the 100 trials consisted of coin flips – which have two outcomes, heads and tails – and 50 trials resulted in “heads” and 50 trials resulted in “tails,” the probability of the coin landing heads side up would then be $\frac{50}{100}$ ” To simplify this notation, it is standard to reduce the fraction to its simplest form or to convert it to a decimal: $1 / 2$ or $.50$ in this example.

This is called the empirical probability because it is based on empirical data collected from actual trials. Some readers will notice that this is the same method and formula for calculating the relative frequency in a frequency table (see Chapter 3). Therefore, empirical probabilities have the same mathematical properties as relative frequencies. That is, probability values always range from 0 to 1 . A probability of zero indicates that the outcome never occurred, and a probability value of 1 indicates that the outcome occurred for every trial (and that no other outcome occurred). Also, all probabilities for a trial must add up to 1 – just as all relative frequencies in a dataset must add up to 1 .

Interpreting probability statistics only requires an understanding of percentages, fractions, and decimals. In the coin-flipping example, a probability of $.50$ indicates that we can expect that half of those trials would result in an outcome of “heads.” Similarly, the chances that any particular trial will result in an outcome of “heads” is $50 \%$. Mathematically, it really doesn’t matter whether probability values are expressed as percentages (e.g., $50 \%$ ), fractions (e.g., 1/2), or decimals (e.g., .50). Statisticians, though, prefer to express probabilities as decimals, and this textbook will stick to that convention.

## 统计代写|Generalized linear model代考广义线性模型代写|The Logic of Inferential Statistics and the CLT

The beginning of this book, especially Chapter 4, discussed descriptive statistics, which is the branch of statistics concerned with describing data that have been collected. Descriptive statistics are indispensable for understanding data, but they are often of limited usefulness because most social scientists wish to make conclusions about the entire population of interest – not just the subjects in the sample that provided data to the researcher. For example, in a study of bipolar mood disorders, Kupka et al. (2007) collected data from 507 patients to examine how frequently they were in manic, hypomanic, and depressed mood states. The descriptive statistics that Kupka et al. provided are interesting – but they are of limited use if they only apply to the 507 people in the study. The authors of this study – and the vast majority of researchers – want to apply their conclusions to the entire population of people they are studying, even people who are not in the sample. The process of drawing conclusions about the entire population based on data from a sample is called generalization, and it requires inferential statistics in order to be possible. Inferential statistics is the branch of statistics that builds on the foundation of probability in order to make generalizations.
The logic of inferential statistics is diagrammed in Figure 6.6. It starts with a population, which, for a continuous, interval- or ratio-level variable, has an unknown mean and unknown standard deviation (represented as the circle in the top left of Figure 6.6). A researcher then draws a random sample from the population and uses the techniques discussed in previous chapters to calculate a sample mean and create a sample histogram. The problem with using a single sample to learn about the population is that there is no way of knowing whether that sample is typical – or representative – of the population from which it is drawn. It is possible (although not likely if the

sampling method was truly random) that the sample consists of several outliers that distort the sample mean and standard deviation.

The solution to this conundrum is to take multiple random samples with the same $n$ from the population. Because of natural random variation in which population members are selected for a sample, we expect some slight variation in mean values from sample to sample. This natural variation across samples is called sampling error. With several samples that all have the same sample size, it becomes easier to judge whether any particular sample is typical or unusual because we can see which samples differ from the others (and therefore probably have more sampling error). However, this still does not tell the researcher anything about the population. Further steps are needed to make inferences about the population from sample data.

After finding a mean for each sample, it is necessary to create a separate histogram (in the middle of Figure 6.6) that consists solely of sample means. The histogram of means from a series of samples is called a sampling distribution of means. Sampling distributions can be created from

other sample statistics (e.g., standard deviations, medians, ranges), but for the purposes of this chapter it is only necessary to talk about a sampling distribution of means.

Because a sampling distribution of means is produced by a purely random process, its properties are governed by the same principles of probability that govern other random outcomes, such as dice throws and coin tosses. Therefore, there are some regular predictions that can be made about the properties of the sampling distribution as the number of contributing samples increases. First, with a large sample size within each sample, the shape of the sampling distribution of means is a normal distribution. Given the convergence to a normal distribution, as shown in Figures 6.4a-6.4d, this should not be surprising. What is surprising to some people is that this convergence towards a normal distribution occurs regardless of the shape of the population, as long as the $\mathrm{n}$ for each sample is at least 25 and all samples have the same sample size. This is the main principle of the CLT.

## 统计代写|Generalized linear model代考广义线性模型代写|Summary

The basics of probability form the foundation of inferential statistics. Probability is the branch of mathematics concerned with estimating the likelihood of outcomes of trials. There are two types of probabilities that can be estimated. The first is the empirical probability, which is calculated by conducting a large number of trials and finding the proportion of trials that resulted in each outcome, using Formula 6.1. The second type of probability is the theoretical probability, which is calculated by dividing the number of methods of obtaining an outcome by the total number of possible outcomes. Adding together the probabilities of two different events will produce the probability that either one will occur. Multiplying the probabilities of two events together will produce the joint probability, which is the likelihood that the two events will occur at the same time or in succession.
With a small or moderate number of trials, there may be discrepancies between the empirical and theoretical probabilities. However, as the number of trials increases, the empirical probability converges to the value of the theoretical probability. Additionally, it is possible to build a histogram of outcomes of trials from multiple events; dividing the number of trials that resulted in each outcome by the total number of trials produces an empirical probability distribution. As the number of trials increases, this empirical probability distribution gradually converges to the theoretical probability distribution, which is a histogram of the theoretical probabilities.

If an outcome is produced by adding together the results of multiple independent events, the theoretical probability distribution will be normally distributed. Additionally, with a large number of trials, the empirical probability distribution will also be normally distributed. This is a result of the CLT.

The CLT states that a sampling distribution of means will be normally distributed if the size of each sample is at least 25. As a result of the CLT, it is possible to make inferences about the population based on sample data – a process called generalization. Additionally, the mean of the sample means converges to the population mean as the number of samples in a sampling distribution increases. Likewise, the standard deviation of means in the sampling distribution (called the standard error) converges on the value of $\frac{\sigma}{\sqrt{n}}$.

## 统计代写|Generalized linear model代考广义线性模型代写|Basic Probability

p= 相同结果的试验次数  试验总数
（公式 6.1）

## 统计代写|Generalized linear model代考广义线性模型代写|Summary

CLT 指出，如果每个样本的大小至少为 25，则均值的抽样分布将呈正态分布。由于 CLT，可以根据样本数据对总体进行推断——这一过程称为泛化。此外，随着抽样分布中样本数量的增加，样本均值的均值会收敛到总体均值。同样，抽样分布中均值的标准差（称为标准误差）收敛于σn.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Linear Transformations and $z-S c o r e s$

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Linear Transformations

To perform a linear transformation, you need to take a dataset and either add, subtract, multiply, or divide every score by the same constant. (You may remember from Chapter 1 that a constant is a score that is the same for every member of a sample or population.) Performing a linear transformation is common in statistics. Linear transformations change the data, and that means they can have an impact on models derived from the data – including visual models and descriptive statistics.

Linear transformations allow us to convert data from one scale to a more preferable scale. For example, converting measurements recorded in inches into centimeters requires a linear transformation (multiplying by 2.54). Another common linear transformation is to convert Fahrenheit temperatures to Celsius temperatures (which requires subtracting 32 and then dividing by 1.8) or vice versa (which requires multiplying by $1.8$ and then adding 32 ). Sometimes performing a linear transformation is done to make calculations easier, as by eliminating negative numbers (by adding a constant so that all scores are positive) or eliminating decimals or fractions (by multiplying by a constant). As you will see in this chapter, making these changes in the scale of the data does not fundamentally alter the relative pattern of the scores or the results of many statistical analyses.

Linear transformations are common in statistics, so it is important to understand how linear transformations change statistics and data.

Impact of linear transformations on means. Chapter 4 showed how to calculate the mean (Formula 4.2) and standard deviation (Formulas 4.7-4.9). An interesting thing happens to these sample statistics when a constant is added to the data. If we use the Waite et al. (2015) data and add a constant of 4 to every person’s age, then the results will be as follows:
Finding the mean of these scores is as follows:
$$\begin{gathered} \bar{X}{\text {mew }}=\frac{22+23+24+25+27+27+28+28+29+35+37+39+42}{13} \ \bar{X}{\text {mew }}=\frac{386}{13}=29.69 \end{gathered}$$
The original mean (which we will abbreviate as $\bar{X}{\text {orig }}$ ) was 25.69, as shown in Guided Example 4.1. The difference between the original mean and the new mean is $4(29.69-25.69=4)$, which is the same value as the constant that was added to all of the original data. This is true for any constant that is added to every score in a dataset: $$\bar{X}{\text {orig }}+\text { constant }=\bar{X}_{\text {new }}$$
(Formula 5.1)

## 统计代写|Generalized linear model代考广义线性模型代写|A Special Linear Transformation

One common linear transformation in the social sciences is to convert the data to $z$-scores. A $z$-score is a type of data that has a mean of 0 and a standard deviation of 1 . Converting a set of scores to $z$ scores requires a formula:
$$z_{i}=\frac{x_{i}-\bar{X}}{s_{x}}$$
(Formula 5.7)
In Formula $5.7$ the $x_{i}$ refers to each individual score for variable $x, \bar{X}$ is the sample mean for variable $x$, and $s_{x}$ is the standard deviation for the same variable. The $i$ subscript in $z_{i}$ indicates that each individual score in a dataset has its own $z$-score.

There are two steps in calculating $z$-scores. The first step is in the numerator where the sample mean is subtracted from each score. (You may recognize this as the deviation score, which was discussed in Chapter 4 .) This step moves the mean of the data to 0 . The second step is to divide by the standard deviation of the data. Dividing by the standard deviation changes the scale of the data until the deviation is precisely equal to 1. Guided Practice $5.1$ shows how to calculate $z$-scores for real data.

The example $z$-score calculation in Guided Practice $5.1$ illustrates several principles of $z$-scores. First, notice how every individual whose original score was below the original mean (i.e., $\bar{X}=25.69$ ) has a negative $z$-score, and every individual whose original score was above the original mean has a positive $z$-score. Additionally, when comparing the original scores to the $z$-scores, it is apparent that the subjects whose scores are closest to the original mean also have $z$-scores closest to 0 which is the mean of the $z$-scores. Another principle is that the unit of $z$-scores is the standard deviation, meaning that the difference between each whole number is one standard deviation. Finally, in this example the person with the lowest score in the original data also has the lowest $z$-score – and the person with the highest score in the original data also has the highest $z$-score. In fact, the rank order of subjects’ scores is the same for both the original data and the set of $z$-scores because linear transformations (including converting raw scores to $z$-scores) do not change the shape of data or the ranking of individuals’scores. These principles also apply to every dataset that is converted to $z$-scores.
There are two benefits of $z$-scores. The first is that they permit comparisons of scores across different scales. Unlike researchers working in the physical sciences who have clear-cut units of

measurement (e.g., meters, grams, pounds), researchers and students in the social sciences frequently study variables that are difficult to measure (e.g., tension, quality of communication in a marriage). For example, a sociologist interested in gender roles may use a test called the Bem Sex Roles Inventory (Bem, 1974) to measure how strongly the subjects in a study identify with traditional masculine or feminine gender roles. This test has a masculinity subscale and a femininity subscale, each of which has scores ranging from 0 to 25 , with higher numbers indicating stronger identification with either masculine or feminine sex roles. A psychologist, though, may decide to use the Minnesota Multiphasic Personality Inventory’s masculinity and femininity subscales (Butcher, Dahlstrom, Graham, Tellegen, \& Kaemmer, 1989) to measure gender roles. Scores on these subscales typically range from 20 to 80 . Even though both researchers are measuring the same traits, their scores would not be comparable because the scales are so different. But if they convert their data to $z$-scores, then the scores from both studies are comparable.

Another benefit is that $z$-scores permit us to make comparisons across different variables. For example, an anthropologist can find that one of her subjects has a $z$-score of $+1.20$ in individualism and a $z$-score of $-0.43$ in level of cultural traditionalism. In this case she can say that the person is higher in their level of individualism than in their level of traditionalism. This example shows that comparing scores only requires that the scores be on the same scale. Because $z$-scores can be compared across scales and across variables, they function like a “universal language” for data of different scales and variables. For this reason $z$-scores are sometimes called standardized scores.

## 统计代写|Generalized linear model代考广义线性模型代写|Linear Transformations and Scales

In this chapter we have seen how linear transformations can be used to change the scale of the data. A common transformation is from the original data to $z$-scores, which have a mean of 0 and a standard deviation of 1 . We can change the scale into any form through applying linear transformations. Adding and subtracting a constant shifts data over to the desired mean, and multiplying and dividing by a constant condenses or expands the scale. This shows that all scales and axes in statistics are arbitrary (Warne, 2014a). This will be an important issue in later chapters. Regardless of how we change the scale, a linear transformation will never change the shape of the histogram of a dataset (and, consequently, its skewness and kurtosis).

We can change the scale of a distribution by performing a linear transformation, which is the process of adding, subtracting, multiplying, or dividing the data by a constant. Adding and subtracting a constant will change the mean of a variable, but not its standard deviation or variance. Multiplying and dividing by a constant will change the mean, the standard deviation, and the variance of a dataset. Table $5.1$ shows how linear transformations change the values of models of central tendency and variability.

One special linear transformation is the $z$-score, the formula for which is Formula 5.7. All $z$-score values have a mean of 0 and a standard deviation of 1 . Putting datasets on a common scale permits comparisons across different units. Linear transformations, like the $z$-score, force the data to have the mean and standard deviation that we want. Yet, they do not change the shape of the distribution – only its scale. In fact, all scales are arbitrary, and we can use linear transformations to give our data any mean and standard deviation we choose. We can also convert data from $z$-scores to any other scale using the linear transformation equation in Formula $5.8$.

## 统计代写|Generalized linear model代考广义线性模型代写|Linear Transformations

X¯喵喵 =22+23+24+25+27+27+28+28+29+35+37+39+4213 X¯喵喵 =38613=29.69

（公式 5.1）

(公式 5.7)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Models of Central Tendency and Variability

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Models of Central Tendency

Models of central tendency are statistical models that are used to describe where the middle of the histogram lies. For many distributions, the model of central tendency is at or near the tallest bar in the histogram. (We will discuss exceptions to this general rule in the next chapter.) These statistical models are valuable in helping people understand their data because they show where most scores tend to cluster together. Models of central tendency are also important because they can help us understand the characteristics of the “typical” sample member.

Mode. The most basic (and easiest to calculate) statistical model of central tendency is the mode. The mode of a variable is the most frequently occurring score in the data. For example, in the Waite et al. (2015) study that was used as an example in Chapter 3, there were four males (labeled as Group 1) and nine females (labeled as Group 2). Therefore, the mode for this variable is 2, or you could alternatively say that the mode sex of the sample is female. Modes are especially easy to find if the data are already in a frequency table because the mode will be the score that has the highest frequency value.

Calculating the mode requires at least nominal-level data. Remember from Chapter 2 that nominal data can be counted and classified (see Table 2.1). Because finding the mode merely requires counting the number of sample members who belong to each category, it makes sense that a mode can be calculated with nominal data. Additionally, any mathematical function that can be

performed with nominal data can be performed with all other levels of data, so a mode can also be calculated for ordinal, interval, and ratio data. This makes the mode the only model of central tendency that can be calculated for all levels of data, making the mode a useful and versatile statistical model.

One advantage of the mode is that it is not influenced by outliers. An outlier (also called an extreme value) is a member of a dataset that is unusual because its score is much higher or much lower than the other scores in the dataset (Cortina, 2002). Outliers can distort some statistical models, but not the mode because the mode is the most frequent score in the dataset. For an outlier to change the mode, there would have to be so many people with the same extreme score that it becomes the most common score in the dataset. If that were to happen, then these “outliers” would not be unusual.

The major disadvantage of the mode is that it cannot be used in later, more complex calculations in statistics. In other words, the mode is useful in its own right, but it cannot be used to create other statistical models that can provide additional information about the data.

## 统计代写|Generalized linear model代考广义线性模型代写|Models of Variability

Statistical models of central tendency are useful, but they only communicate information about one characteristic of a variable: the location of the histogram’s center. Models of central tendency say nothing about another important characteristic of distributions – their variability. In statistics variability refers to the degree to which scores in a dataset vary from one another. Distributions with high variability tend to be spread out, while distributions with low variability tend to be compact. In this chapter we will discuss four models of variability: the range, the interquartile range, the standard deviation, and the variance.

Range. The range for a variable is the difference between the highest and the lowest scores in the dataset. Mathematically, this is:
$$\text { Range }=\text { Highest Score – Lowest Score } \quad \text { (Formula 4.6) }$$
The advantage of the range is that it is simple to calculate. But the disadvantages should also be apparent in the formula. First, only two scores (the highest score and the lowest score) determine the range. Although this does provide insight into the span of scores within a dataset, it does not say much (if anything) about the variability seen among the typical scores in the dataset. This is especially true if either the highest score or the lowest score is an outlier (or if both are outliers).
The second disadvantage of the range as a statistical model of variability is that outliers have more influence on the range than on any other statistical model discussed in this chapter. If either the highest score or the lowest score (or both) is an outlier, then the range can be greatly inflated and the data may appear to be more variable than they really are. Nevertheless, the range is still a useful statistical model of variability, especially in studies of growth or change, where it may show effectively whether sample members become more alike or grow in their differences over time.
A statistical assumption of the range is that the data are interval-or ratio-level data. This is because the formula for the range requires subtracting one score from another – a mathematical operation that requires interval data at a minimum.

Interquartile Range. Because the mean is extremely susceptible to the influence of outliers, a similar model of variability was developed in an attempt to overcome these shortfalls: the interquartile range, which is the range of the middle $50 \%$ of scores. There are three quartiles in any dataset, and these three scores divide the dataset into four equal-sized groups. These quartiles are (as numbered from the lowest score to the highest score) the first quartile, second quartile, and third quartile. ${ }^{1}$ There are four steps to finding the interquartile range:

1. Calculate the median for a dataset. This is the second quartile.
2. Find the score that is halfway between the median and the lowest score. This is the first quartile.
3. Find the score that is halfway between the median and the highest score. This is the third quartile.
4. Subtract the score in the first quartile from the third quartile to produce the interquartile range.

## 统计代写|Generalized linear model代考广义线性模型代写|Using Models of Central Tendency and Variance Together

Models of central tendency and models of variance provide different, but complementary information. Neither type of model can tell you everything you need to know about a distribution. However, when combined, these models can provide researchers with a thorough understanding of their data. For example, Figure $4.2$ shows two samples with the same mean, but one has a standard deviation that is twice as large as the other. Using just the mean to understand the two distributions would mask the important differences between the histograms. Indeed, when reporting a model of central tendency, it is recommended that you report an accompanying model of variability (Warne et al., 2012; Zientek,Capraro, \& Capraro, 2008). It is impossible to fully understand a distribution of scores without a knowledge of the variable’s central tendency and variability, and even slight differences in these values across distributions can be important (Voracek, Mohr, \& Hagmann, 2013).

This chapter discussed two types of descriptive statistics: models of central tendency and models of variability. Models of central tendency describe the location of the middle of the distribution, and models of variability describe the degree that scores are spread out from one another.

There were four models of central tendency in this chapter. Listed in ascending order of the complexity of their calculations, these are the mode, median, mean, and trimmed mean. The mode is calculated by finding the most frequent score in a dataset. The median is the center score when the data are arranged from the smallest score to the highest score (or vice versa). The mean is calculated by adding all the scores for a particular variable together and dividing by the number of scores. To find the trimmed mean, you should eliminate the same number of scores from the top and bottom of the distribution (usually $1 \%, 5 \%$, or $10 \%$ ) and then calculate the mean of the remaining data.

There were also four principal models of variability discussed in this chapter. The first was the range, which is found by subtracting the lowest score for a variable from the highest score for that same variable. The interquartile range requires finding the median and then finding the scores that are halfway between (a) the median and the lowest score in the dataset, and (b) the median and the highest score in the dataset. Score (a) is then subtracted from score (b). The standard deviation is defined as the square root of the average of the squared deviation scores of each individual in the dataset. Finally, the variance is defined as the square of the standard deviation (as a result, the variance is the mean of the squared deviation scores). There are three formulas for the standard deviation and three formulas for the variance in this chapter. Selecting the appropriate formula depends on (1) whether you have sample or population data, and (2) whether you wish to estimate the population standard deviation or variance.

No statistical model of central tendency or variability tells you everything you may need to know about your data. Only by using multiple models in conjunction with each other can you have a thorough understanding of your data.

## 统计代写|Generalized linear model代考广义线性模型代写|Models of Variability

范围 = 最高分 – 最低分  （公式 4.6）

1. 计算数据集的中位数。这是第二个四分位数。
2. 找到中位数和最低分数之间的分数。这是第一个四分位数。
3. 找到中位数和最高分之间的分数。这是第三个四分位数。
4. 从第三个四分位数中减去第一个四分位数的分数以产生四分位数范围。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Describing Distribution Shapes: A Caveat

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Frequency Polygons

Another alternative to the histogram is a box plot (also called a box-and-whisker plot), which is a visual model that shows how spread out or compact the scores in a dataset are. An example of a box plot is shown in Figure 3.21, which represents the age of the subjects in the Waite et al. (2015) study. In a box plot, there are two components: the box (which is the rectangle at the center of the figure) and the fences (which are the vertical lines extending from the box). The middle $50 \%$ of scores are represented by the box. For the subject age data from the Waite et al. (2015) dataset, the middle $50 \%$ of scores range from 21 to 31 , so the box shown in Figure $3.21$ extends from 21 to 31 . Inside the box is a horizontal line, which represents the score that is in the exact middle, which is 24 . The lower

fence extends from the bottom of the box to the minimum score (which is 18). The upper fence extends from the top of the box to the maximum score (which is 38 ).

The example in Figure $3.21$ shows some useful characteristics of box plots that are not always apparent in histograms. First, the box plot shows the exact middle of the scores. Second, the box plot shows how far the minimum and maximum scores are from the middle of the data. Finally, it is easy to see how spread out the compact the scores in a dataset are. Figure $3.21$ shows that the oldest subjects in the Waite et al. (2015) study are further from the middle of the dataset than the youngest subjects are. This is apparent because the upper fence is much longer than the lower fence-indicating that the maximum score is much further from the middle $50 \%$ of scores than the minimum score is.
Like frequency polygons, box plots have the advantage of being useful for displaying multiple variables in the same picture. This is done by displaying box plots side by side. Formatting multiple box plots in the same figure makes it easy to determine which variable(s) have higher means and wider ranges of scores.

## 统计代写|Generalized linear model代考广义线性模型代写|Stem-and-Leaf Plots

Another visual model that some people use to display their data is the stem-and-leaf plot, an example of which is shown on the right side of Figure 3.23. This figure shows the age of the subjects from Table 3.1. The left column is the tens place (e.g., the 2 in the number 20 ), and the other columns represent the ones place (e.g., the 0 in the number 20) of each person’s age. Each digit on the right side of the visual model represents a single person. To read an individual’s score, you take the number in the left column and combine it with a number on the other side of the graph. For example, the youngest person in this sample was 18 years old, as shown by the 1 in the left column and the 8 on the right side of the model. The next youngest person was 19 years old (as represented by the 1 in the left column and the 9 in the same row on the right side of the visual model). The stem-and-leaf also shows that seven people were between 20 and 25 years old and that the oldest person was 38 years old. In a way, this stemand-leaf plot resembles a histogram that has been turned on its side, with each interval 10 years wide.

Stem-and-leaf plots can be convenient, but, compared to histograms, they have limitations. Large datasets can result in stem-and-leaf plots that are cumbersome and hard to read. They can also be problematic if scores for a variable span a wide range of values (e.g., some scores in single digits and other scores in double or triple digits) or precisely measured variables where a large number of subjects have scores that are decimals or fractions.

Before personal computers were widespread, stem-and-leaf plots were more common because they were easy to create on a typewriter. As computer software was created that was capable of generating histograms, frequency polygons, and box plots automatically, stem-and-leaf plots gradually lost popularity. Still, they occasionally show up in modern social science research articles (e.g., Acar, Sen, \& Cayirdag, 2016, p. 89; Linn, Graue, \& Sanders, 1990, p. 9; Paek, Abdulla, \& Cramond, 2016, p. 125).

## 统计代写|Generalized linear model代考广义线性模型代写|Line Graphs

Another common visual model for quantitative data is the line graph. Like a frequency polygon, line graphs are created by using straight-line segments to connect data points to one another. However, a line graph does not have to represent continuous values of a single variable (as in a frequency polygon and histogram) or begin and end with a frequency of zero. Line graphs can also be used to show trends and differences across time or across nominal or ordinal categories.

Since their invention over 200 years ago, line graphs have been recognized as being extremely useful for showing trends over time (Friendly \& Denis, 2005). When using it for this purpose, the creator of the line graph should use the horizontal axis to indicate time and the vertical axis to indicate the value of the variable being graphed. An example of this type of line graph is shown in Figure 3.24, which shows the murder rates in the five most populous Canadian provinces over the course of 5 years. Line graphs are also occasionally used to illustrate differences among categories or to display several variables at once. The latter purpose is common for line graphs because bar graphs and histograms can get too messy and complex when displaying more than one variable.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Visual Models

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Frequency Tables

One of the simplest ways to display data is in a frequency table. To create a frequency table for a variable, you need to list every value for the variable in the dataset and then list the frequency, which is the count of how many times each value occurs. Table 3.2a shows an example from Waite et al.’s (2015) study. When asked how much the subjects agree with the statement “I feel that my sibling understands me well,” one person strongly disagreed, three people disagreed, three felt neutral about the statement, five agreed, and one strongly agreed. A frequency table just compiles this information in an easy to use format, as shown below. The first column of a frequency table consists of the response label (labeled “Response”) and the second column is the number of each response (labeled “Frequency”).

Frequency tables can only show data for one variable at a time, but they are helpful for discerning general patterns within a variable. Table $3.2 \mathrm{a}$, for example, shows that few people in the Waite et al. (2015) study felt strongly about whether their sibling with autism understood them well. Most responses clustered towards the middle of the scale.

Table $3.2 \mathrm{a}$ also shows an important characteristic of frequency tables: the number of responses adds up to the number of participants in the study. This will be true if there are responses from everyone in the study (as is the case in Waite et al.’s study).

Frequency tables can include additional information about subjects’ scores in new columns. The first new column is labeled “Cumulative frequency,” which is determined by counting the number of people in a row and adding it to the number of people in higher rows in the frequency table. For example, in Table $3.2 \mathrm{~b}$, the cumulative frequency for the second row (labeled “Disagree”) is 4 – which was calculated by summing the frequency from that row, which was 3 , and the

frequency of the higher row, which was $1(3+1=4)$. As another example, the cumulative frequency column shows that, for example, 7 of the 13 respondents responded “strongly disagree,” “disagree,” or “neutral” when asked about whether their sibling with autism understood them well.

It is also possible to use a frequency table to identify the proportion of people giving each response. In a frequency table, a proportion is a number expressed as a decimal or a fraction that shows how many subjects in the dataset have the same value for a variable. To calculate the proportion of people who gave each response, use the following formula:
$$\text { Proportion }=\frac{f}{n} \quad \text { (Formula 3.1) }$$
In Formula $3.1, f$ is the frequency of a response, and $n$ is the sample size. Therefore, calculating the proportion merely requires finding the frequency of a response and dividing it by the number of people in the sample. Proportions will always be between the values of 0 to 1 .

Table $3.3$ shows the frequency table for the Waite et al. (2015) study, with new columns showing the proportions for the frequencies and the cumulative frequencies. The table nicely provides examples of the properties of proportions. For example, it is apparent that all of the values in both the “Frequency proportion” and “Cumulative proportion” columns are between 0 and 1.0. Additionally, those columns show how the frequency proportions were calculated – by taking the number in the frequency column and dividing by $n$ (which is 13 in this small study). A similar process was used to calculate the cumulative proportions in the far right column.

Table $3.3$ is helpful in visualizing data because it shows quickly which variable responses were most common and which responses were rare. It is obvious, for example, that “Agree” was the most common response to the question of whether the subjects’ sibling with autism understood them well, which is apparent because that response had the highest frequency (5) and the highest frequency proportion (.385). Likewise, “strongly disagree” and “strongly agree” were unusual responses because they tied for having the lowest frequency (1) and lowest frequency proportion (.077). Combined together, this information reveals that even though autism is characterized by pervasive difficulties in social situations and interpersonal relationships, many people with autism can still have a relationship with their sibling without a disability (Waite et al., 2015). This is important information for professionals who work with families that include a person with a diagnosis of autism.

## 统计代写|Generalized linear model代考广义线性模型代写|Histograms

Frequency tables are very helpful, but they have a major drawback: they are just a summary of the data, and they are not very visual. For people who prefer a picture to a table, there is the option of creating a histogram, an example of which is shown below in Figure 3.1.

A histogram converts the data in a frequency table into visual format. Each bar in a histogram (called an interval) represents a range of possible values for a variable. The height of the bar represents the frequency of responses within the range of the interval. In Figure $3.1$ it is clear that, for the second bar, which represents the “disagree” response, three people gave this response (because the bar is 3 units high).

Notice how the variable scores (i.e., 1, 2, 3, 4, or 5) are in the middle of the interval for each bar. Technically, this means that the interval includes more than just whole number values. This is illustrated in Figure 3.2, which shows that each interval has a width of 1 unit. The figure also annotates how, for the second bar, the interval ranges between $1.5$ and $2.5$. In Waite et al.’s study (2015), all of the responses were whole numbers, but this is not always true of social science data, especially for variables that can be measured very precisely, such as reaction time (often measured in milliseconds) or grade-point average (often calculated to two or three decimal places).

Figures $3.1$ and $3.2$ also show another important characteristic of histograms: the bars in the histogram touch. This is because the variable on this histogram is assumed to measure a continuous trait (i.e., level of agreement), even if Waite et al. (2015) only permitted their subjects to give five possible responses to the question. In other words, there are probably subtle differences in how much each subject agreed with the statement that their sibling with autism knows them well. If Waite et al. (2015) had a more precise way of measuring their subjects’ responses, it is possible that the data would include responses that were not whole numbers, such as $1.8,2.1$, and 2.3. However, if only whole numbers were permitted in their data, these responses would be rounded to 2. Yet, it is still possible that there are differences in the subjects’ actual levels of agreement. Having the histogram bars touch shows that, theoretically, the respondents’ opinions are on a continuum.

The only gaps in a histogram should occur in intervals where there are no values for a variable within the interval. An example of the types of gaps that are appropriate for a histogram is Figure $3.3$, which is a histogram of the subjects’ ages.

The gaps in Figure $3.3$ are acceptable because they represent intervals where there were no subjects. For example, there were no subjects in the study who were 32 years old. (This can be verified by checking Table 3.1, which shows the subjects’ ages in the third column.) Therefore, there is a gap at this place on the histogram in Figure 3.3.

Some people do not like having a large number of intervals in their histograms, so they will combine intervals as they build their histogram. For example, having intervals that span 3 years instead of 1 year will change Figure $3.3$ into Figure 3.4.

Combining intervals simplifies the visual model even more, but this simplification may be needed. In some studies with precisely measured variables or large sample sizes, having an interval for every single value of a variable may result in complex histograms that are difficult to understand. By simplifying the visual model, the data become more intelligible. There are no firm guidelines for choosing the number of intervals in a histogram, but I recommend having no fewer than five. Regardless of the number of intervals you choose for a histogram, you should always ensure that the intervals are all the same width.

## 统计代写|Generalized linear model代考广义线性模型代写|Number of Peaks

Another way to describe distributions is to describe the number of peaks that the histogram has. A distribution with a single peak is called a unimodal distribution. All of the distributions in the chapter so far (including the normal distribution in Figure $3.9$ and Quetelet’s data in Figure $3.10$ ) are unimodal distributions because they have one peak. The term “-modal” refers to the most common score in a distribution, a concept explained in further detail in Chapter $4 .$

Sometimes distributions have two peaks, as in Figure 3.17. When a distribution has two peaks, it is called a bimodal distribution. In the social sciences most distributions have only one peak, but bimodal distributions like the one in Figure $3.17$ occur occasionally, as in Lacritz et al.’s (2004) study that found that people’s test scores on a test of visual short-term memory were bimodal. In that case the peaks of the histograms were at the two extreme ends of the distribution – meaning people tended to have very poor or very good recognition of pictures they had seen earlier. Bimodal distributions can occur when a sample consists of two different groups (as when some members of a sample have had a treatment and the other sample members have not).

## 统计代写|Generalized linear model代考广义线性模型代写|Frequency Tables

部分 =Fn （公式 3.1）

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Reflection Questions: Comprehension

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Summary

Before conducting any statistical analyses, researchers must decide how to measure their variables. There is no obvious method of measuring many of the variables that interest social scientists. Therefore, researchers must give each variable an operationalization that permits them to collect numerical data.

The most common system for conceptualizing quantitative data was developed by Stevens (1946), who defined four levels of data, which are (in ascending order of complexity) nominal, ordinal, interval, and ratio-level data. Nominal data consist of mutually exclusive and exhaustive categories, which are then given an arbitrary number. Ordinal data have all of the qualities of nominal data, but the numbers in ordinal data also indicate rank order. Interval data are characterized by all the traits of nominal and ordinal data, but the spacing between numbers is equal across the entire length of the scale. Finally, ratio data are characterized by the presence of an absolute zero. This does not mean that a zero has been obtained in the data; it merely means that zero would indicate the total lack of whatever is being measured. Higher levels of data contain more information, although it is always possible to convert from one level of data to a lower level. It is not possible to convert data to a higher level than it was collected at.

It is important for us to recognize the level of data because, as Table $2.1$ indicates, there are certain mathematical procedures that require certain levels of data. For example, calculating an average requires interval or ratio data; but classifying sample members is possible for all four levels of data. Social scientists who ignore the level of their data risk producing meaningless results (like the mean gender in a sample) or distorted statistics. Using the wrong statistical methods for a level of data is considered an elementary error and a sign of flawed research.

Some researchers also classify their data as being continuous or discrete. Continuous data are data that have many possible values that span the entire length of a scale with no large gaps in possible scores. Discrete data can only have a limited number of possible values.

## 统计代写|Generalized linear model代考广义线性模型代写|Reflection Questions: Application

1. Classify the following variables into the correct level of data (nominal, ordinal, interval, or ratio):
b. Height, measured in centimeters
c. Reaction time
d. Kelvin temperature scale
e. Race/ethnicity
f. Native language
g. Military rank
h. Celsius temperature scale
i. College major
j. Movie content ratings (e.g., $\mathrm{G}, \mathrm{PG}, \mathrm{PG}-13, \mathrm{R}, \mathrm{NC}-17$ )
k. Personality type
2. Hours spent watching TV per week
$\mathrm{m}$. Percentage of games an athlete plays without receiving a penalty
n. Marital status (i.e., single, married, divorced, widowed)
o. Fahrenheit temperature scale.
3. Label each of the examples in question $6(a-o)$ as continuous or discrete data.
4. Kevin has collected data about the weight of people in his study. He couldn’t obtain their exact weight, and so he merely asked people to indicate whether they were “skinny” (labeled group 1) “average” (group 2), or “heavy” (group 3).
a. What level of data has Kevin collected?
b. Could Kevin convert his data to nominal level? Why or why not? If he can, how would he make this conversion?
c. Could Kevin convert his data to ratio level? Why or why not? If he can, how would he make this conversion?
5. At most universities the faculty are – in ascending seniority – adjunct (i.e., part-time) faculty, lecturers, assistant professors, associate professors, and full professors.
a. What level of data would this information be?
b. If a researcher instead collected the number of years that a faculty member has been teaching at the college level, what level of data would that be instead?
c. Of the answers to the two previous questions ( $9 \mathrm{a}$ and $9 \mathrm{~b})$, which level of data is more detailed?
6. What is the minimal level of data students must collect if they want to
a. classify subjects?

## 统计代写|Generalized linear model代考广义线性模型代写|SPSS

SPSS permits users to specify the level of data in the variable view. (See the Software Guide for Chapter 1 for information about variable view.) Figure $2.1$ shows five variables that have been entered into SPSS. Entering the name merely requires clicking a cell in the column labeled “Name” and typing in the variable name. In the column labeled “Type,” the default option is “Numeric,” which is used for data that are numbers. (Other options include “String” for text; dates; and time measurements.) The next two columns, “Width” and “Decimals” refer to the length of a variable (in terms of the number of digits). “Width” must be at least 1 digit, and “Decimals” must be a smaller number than the number entered into “Width.” In this example, the “Grade” variable has 5 digits, of which 3 are decimals and 1 (automatically) is the decimal point in the number. The “Label” column is a more detailed name that you can give a label. This is helpful if the variable name itself is too short or if the limits of SPSS’s “Name” column (e.g., no variables beginning with numbers, no spaces) are too constraining.

The “Values” column is very convenient for nominal and ordinal data. By clicking the cell, the user can tell SPSS what numbers correspond to the different category labels. An example of this appears in Figure 2.2. This window allows users to specify which numbers refer to the various groups within a variable. In Figure 2.2, Group 1 is for female subjects, and Group 2 is for male subjects. Clicking on “Missing” is similar, but it permits users to specify which numbers correspond to missing data. This tells SPSS to not include those numbers when performing statistical analyses so that the results are not distorted. The next two columns (labeled “Columns” and “Align”) are cosmetic; changing values in these columns will make the numbers in the data view appear differently, but will not change the data or how the computer uses them.

To change the level of data for a variable, you should use the column labeled “Measure.” Clicking a cell in this column generates a small drop-down menu with three options, “Nominal” (for nominal data), “Ordinal” (for ordinal data), and “Scale” (for interval and ratio data). Assigning a variable to the proper level of data requires selecting the appropriate option from the menu.

## 统计代写|Generalized linear model代考广义线性模型代写|Reflection Questions: Application

1. 将以下变量分类为正确的数据级别（名义、有序、区间或比率）
B. 高度，以厘米为单位
C. 反应时间
D. 开尔文温标
e. 种族/民族
f. 母语
g. 军衔
h. 摄氏温度标度
i。大学专业
j。电影内容分级（例如，G,磷G,磷G−13,R,ñC−17)
k. 性格类型
2. 每周看电视的时间
米. 运动员未受罚的比赛的百分比
n。婚姻状况（即单身、已婚、离婚、丧偶
）华氏温标。
3. 标记每个有问题的示例6(一种−这)作为连续或离散数据。
4. 凯文在他的研究中收集了有关人们体重的数据。他无法获得他们的确切体重，所以他只要求人们指出他们是“瘦”（标记为第 1 组）“平均”（第 2 组）还是“重”（第 3 组）。
一种。凯文收集了什么级别的数据？
湾。凯文能否将他的数据转换为名义水平？为什么或者为什么不？如果可以，他将如何进行这种转换？
C。凯文能否将他的数据转换为比率水平？为什么或者为什么不？如果可以，他将如何进行这种转换？
5. 在大多数大学中，教师是——按资历递增的——兼职（即兼职）教师、讲师、助理教授、副教授和正教授。
一种。这些信息将是什么级别的数据？
湾。如果研究人员收集的是一名教员在大学任教的年数，那将是什么级别的数据？
C。前两个问题的答案（9一种和9 b)，哪个级别的数据更详细？
6. 如果学生愿意，他们必须收集的最低数据水平是多少
？分类科目？
湾。把分数加起来？

## 统计代写|Generalized linear model代考广义线性模型代写|SPSS

SPSS 允许用户在变量视图中指定数据级别。（有关变量视图的信息，请参阅第 1 章的软件指南。） 图2.1显示已输入 SPSS 的五个变量。输入名称只需要单击标有“名称”的列中的单元格并输入变量名称。在标有“类型”的列中，默认选项是“数字”，用于数字数据。（其他选项包括文本的“字符串”；日期；和时间测量。）接下来的两列，“宽度”和“小数”是指变量的长度（以位数表示）。“宽度”必须至少为 1 位，“小数”必须小于“宽度”中输入的数字。在本例中，“Grade”变量有 5 位数字，其中 3 位是小数，1（自动）是数字中的小数点。“标签”列是一个更详细的名称，您可以给它一个标签。

“值”列对于名义和有序数据非常方便。通过单击单元格，用户可以告诉 SPSS 哪些数字对应于不同的类别标签。图 2.2 中显示了一个示例。此窗口允许用户指定哪些数字引用变量中的各个组。在图 2.2 中，第 1 组针对女性受试者，第 2 组针对男性受试者。单击“丢失”是类似的，但它允许用户指定哪些数字对应于丢失的数据。这告诉 SPSS 在执行统计分析时不要包含这些数字，以免结果失真。接下来的两列（标记为“列”和“对齐”）是装饰性的；更改这些列中的值将使数据视图中的数字显示不同，但不会更改数据或计算机使用它们的方式。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Levels of Data

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Defining What to Measure

The first step in measuring quantitative variables is to create an operationalization for them. In Chapter 1, an operationalization was defined as a description of a variable that permits a researcher to collect quantitative data on that variable. For example, an operationalization of “affection” may be the percentage of time that a couple holds hands while sitting next to each other. Strictly speaking, “time holding hands” is not the same as “affection.” But “time holding hands” can be objectively observed and measured; two people measuring “time holding hands” for the same couple would likely produce similar data. However, “affection” is abstract, ambiguous, and unlikely to produce consistent results. Likewise, a researcher could define “attentiveness” as the number of times a parent makes eye contact with a child or the number of times he or she says the child’s name. Again, these operationalizations are not the same thing as “attentiveness,” but they are less ambiguous. More important, they produce numbers that we can then use in statistical analysis.

You may have a problem with operationalizations because using operationalizations means that researchers are not really studying what interests them, such as “affection” or “attentiveness.” Rather, they are studying the operationalizations, which are shallow approximations for the ideas that really interest them. It is understandable why operationalizations are dissatisfying to some: no student declares a major in the social sciences by saying, “lam so excited to learn about the percentage of time that parents hold handsl”
Critics of operationalizations say that – as a result – quantitative research is reductionist, meaning that it reduces phenomena to a shadow of themselves, and that researchers are not really studying the phenomena that interest them. These critics have a point. In a literal sense, one could say that no social scientist has ever studied “affection,” “racism,” “personality, ” “marital satisfaction, ” or many other important phenomena. This shortcoming is not unique to the social sciences. Students and researchers in the physical and biological sciences operationalize concepts like “gravity, ” “animal packs, “and “physical health” in order to find quantifiable ways of measuring them.

There are two responses to these criticisms. First, it is important to keep in mind that quantitative research is all about creating models, which are simplified versions of reality – not reality itself (see Chapter 1). Part of that simplification is creating an operationalization that makes model building possible in the first place. As long as we remember the difference between the model and reality, the simplified, shallow version of reality is not concerning.

My second response is pragmatic (i.e., practical) in nature: operationalizations (and, in turn, models) are simply necessary for quantitative research to happen. In other words, quantitative research “gets the job done,” and operationalizations and models are just necessary parts of the quantitative research process. Scientists in many fields break down the phenomena they study into manageable, measurable parts – which requires operationalization. A philosopher of science may not think that the “because it works” response is satisfactory, but in the day-to-day world of scientific research, it is good enough.

If you are still dissatisfied with my two responses and you see reductionism as an unacceptable aspect of quantitative science, then you should check out qualitative methods, which are much less reductionist than quantitative methods because they focus on the experiences of subjects and the meaning of social science phenomena. Indeed, some social scientists combine qualitative and quantitative research methods in the same study, a methodology called “mixed methods” (see Dellinger \& Leech, 2007). For a deeper discussion of reductionism and other philosophical issues that underlie the social sciences, I suggest the excellent book by Slife and Williams (1995).

## 统计代写|Generalized linear model代考广义线性模型代写|Levels of Data

Operationalizations are essential for quantitative research, but it is necessary to understand the characteristics of the numerical data that operationalizations produce. To organize these data, most social scientists use a system of organizing data created by Stevens (1946). As a psychophysicist, Stevens was uniquely qualified to create a system that organizes the different types of numerical data

that scientists gather. This is because a psychophysicist studies the way people perceive physical stimuli, such as light, sound, and pressure. In his work Stevens often was in contact with people who worked in the physical sciences – where measurement and data collection are uncomplicated – and the social sciences – where data collection and operationalizations are often confusing and haphazard (Miller, 1975). Stevens and other psychophysicists had noticed that the differences in perceptions that people had of physical stimuli often did not match the physical differences in those stimuli as measured through objective instruments. For example, Stevens (1936) knew that when a person had to judge how much louder one sound was than another, their subjective reports often did not agree with the actual differences in the volume of the two sounds, as measured physically in decibels. As a result, some researchers in the physical sciences claimed that the data that psychologists gathered about their subjects’ perceptions or experiences were invalid. Stevens had difficulty accepting this position because psychologists had a record of success in collecting useful data, especially in studies of sensation, memory, and intelligence.

The argument between researchers in the physical sciences and the social sciences was at an impasse for years. Stevens’s breakthrough insight was in realizing that psychologists and physicists were both collecting data, but that these were different levels of data (also called levels of measurement). In Stevens’s (1946) system, measurement – or data collection – is merely “the assignment of numerals to objects or events according to rules” (p. 677$)$. Stevens also realized that using different “rules” of measurement resulted in different types (or levels) of data. He explained that there were four levels of data, which, when arranged from simplest to most complex, are nominal, ordinal, interval, and ratio data (Stevens, 1946). We will explore definitions and examples of each of these levels of data.

Nominal Data. To create nominal data, it is necessary to classify objects into categories that are mutually exclusive and exhaustive. “Mutually exclusive” means that the categories do not overlap and that each object being measured can belong to only one category. “Exhaustive” means that every object belongs to a category – and there are no leftover objects. Once mutually exclusive and exhaustive categories are created, the researcher assigns a number to each category. Every object in the category receives the same number.

There is no minimum number of the objects that a category must have for nominal data, although it is needlessly complicated to create categories that don’t have any objects in them. On the other hand, sometimes to avoid having a large number of categories containing only one or two objects, some researchers create an “other” or “miscellaneous” category and assign a number to it. This is acceptable as long as the “miscellaneous” category does not overlap with any other category, and all categories together are exhaustive.

## 统计代写|Generalized linear model代考广义线性模型代写|Other Ways to Classify Data

The Stevens (1946) system is – by far – the most common way to organize quantitative data, but it is not the only possible scheme. Some social scientists also attempt to ascertain whether their data are continuous or discrete. Continuous data are data that permit a wide range of scores that form a constant scale with no gaps at any point along the scale and also have many possible values. Many types of data in the social sciences are continuous, such as intelligence test scores, which in a normal human population range from about 55 to 145 on most tests, with every whole number in between being a possible value for a person.

Continuous data often permit scores that are expressed as fractions or decimals. All three temperature scales that I have discussed in this chapter (i.e., Fahrenheit, Celsius, and Kelvin) are continuous data, and with a sensitive enough thermometer it would be easy to gather temperature data measured at the half-degree or tenth-degree.

The opposite of continuous data are discrete data, which are scores that have a limited range of possible values and do not form a constant, uninterrupted scale of scores. All nominal data are discrete, as are ordinal data that have a limited number of categories or large gaps between groups. A movie rating system where a critic gives every film a $1-, 2-, 3-$, or 4 -star rating would be discrete data because it only has four possible values. Most interval or ratio data, however, are continuous – not discrete – data. The point at which a variable has “too many” values to be discrete and is therefore continuous is often not entirely clear, and whether a particular variable consists of discrete or continuous data is sometimes a subjective judgment. To continue with the movie rating system example, the website Internet Movie Database (IMDb) asks users to rate films on a scale from 1 to 10 . Whether ten categories are enough for the data to be continuous is a matter of argument, and opinions may vary from researcher to researcher.

## 统计代写|Generalized linear model代考广义线性模型代写|Other Ways to Classify Data

Stevens (1946) 系统是迄今为止最常见的定量数据组织方式，但它并不是唯一可能的方案。一些社会科学家还试图确定他们的数据是连续的还是离散的。连续数据是允许范围广泛的分数的数据，这些分数形成一个恒定的尺度，在尺度上的任何一点都没有间隙，并且还具有许多可能的值。社会科学中的许多类型的数据是连续的，例如智力测试分数，在大多数测试中，在正常人群中的范围从大约 55 到 145，其中每个整数都是一个人的可能值。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Reflection Questions

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Comprehension

1. Why do researchers in the social sciences rarely have data from the entire population of subjects that they are interested in?
2. Why is it important to have the ability to independently evaluate researchers’ interpretation of their data?
3. What trait do theoretical models, statistical models, and visual models all have in common?
4. Most undergraduate students in the social sciences will not become professional researchers in their careers. So why is it necessary that they take a statistics course?
5. What is a model? How does the scientific usage of the word “model” differ from the everyday definition of a model? How is it similar?
6. Explain:
a. Why every model is wrong in some way.
b. Why practitioners and researchers in the social sciences should use models if they are all wrong.
c. How researchers and practitioners judge whether they should use a particular model.
7. What are the four main ways that social science practitioners use statistics in their work?

## 统计代写|Generalized linear model代考广义线性模型代写|Reflection Questions: Application

1. Carl believes in the power of magnets in relieving physical pain, and he wears magnets on his body for this purpose. However, his magnetic bracelet doesn’t help with his arthritis pain. He consulted a website about healing magnets, and found that he needs to periodically change the location of the magnet on his body until his pain is relieved. Why is Carl’s hypothesis about the healing properties of magnets unscientific?
2. What would be an example of a theory in your major? Can you give an example of how that theory has given rise to a theoretical model? What would be a possible situation that would disprove the theory?
3. A researcher wishes to study stress, and so she records the heart rate of each of her subjects as they are exposed to a distressful situation. Is “heart rate” an independent or dependent variable? Justify your response.
4. A social worker wants to study the impact of the instability of a child’s home life on the child’s academic performance. She defines “instability” as the number of homes that the child lives in during a year and “academic performance” as the child’s grades that the teacher assigns on a scale from 0 to 100 . Which step of the quantitative research process is this?
5. Teresa wants to know if people who post more messages about themselves on social media are more selfish than people who do not.

a. She decides to count the number of Facebook status updates that her subjects post in a week that include the word “I.” She also administers a psychological test that her professor told her measures selfishness. By using these methods of measuring her variables, what step of the research is she engaging in?
b. Teresa believes that selfishness also causes people to post more self-centered messages on social media. Which variable is the independent variable in her study? Which variable is the dependent variable? Why?
c. Is this a correlational design or an experimental design?

1. Some cultural anthropologists study “rites of passage,” which are certain rituals where people transition from one stage of their life to another. The idea of “rites of passage” is very broad and can be applied to rituals in many cultures and in all stages of life from birth to death. An anthropologist decides to use the rite of passage framework to understand how adolescents in a specific tribal culture become recognized as adults.
a. In this context, is the idea of “rites of passage” a theory, a theoretical model, a statistical model, or a visual model?
b. When the anthropologist applies this idea to a specific culture and explains the stages of that culture’s rites of passage, is this a theory, a theoretical model, a statistical model, or a visual model?
2. A political science student is interested in the votes that legislators in different countries cast when considering different bills. The student decides that it is impractical to study every vote by every politician in every country. So, he decides to study only a selection of votes.
a. What is the population in this example?
b. What is the sample in this example?
3. A family science professor wants to study the impact of frequent quizzes on her students’ study habits. In one of her classes she does not offer quizzes. In another class, she offers a quiz once per week. In her last class she offers a quiz in every class session. In each class she asks her students how many hours per week they studied.
a. What is the independent variable in this example?
b. What is the dependent variable in this example?
c. How did the professor operationalize “study habits”?
d. Is this an experimental design or a correlation design?

## 统计代写|Generalized linear model代考广义线性模型代写|Excel

After opening Excel, you should see a screen similar to the one below, which shows a blank grid. Each of the boxes in the grid is called a cell. Selecting a cell permits you to enter a datum into it. In Excel it doesn’t matter whether each row represents a variable or whether each column represents a variable, though many users find it easier to treat columns as variables. (This also makes it easier to import a file from Excel into another data analysis program, like SPSS.) Most people use the first row or column to label their variables so that they can easily remember what the data mean.

There are a few features that you can see in Figure 1.3. First, the bottom left has three tabs labeled “Sheet1,” “Sheet2,” and “Sheet3.” A sheet is the grid that you see taking up the majority of the screen. Each Excel file can store multiple sheets, which is convenient for storing multiple datasets in the same file. The top bar displays several tools useful for formatting, permitting the user to make cosmetic changes to the data, such as select a font, color-code cells, and select the number of decimal places in a cell. If your instructor or an employer requires you to use software for data analysis, I suggest that you invest some time into exploring these and other features in the program.

The opening screen for SPSS looks similar to Excel’s opening screen, as is apparent when comparing Figures $1.3$ and 1.4. Both programs feature a grid made of cells that permit users to enter data directly into the program. In SPSS this is called the “data view.” In the data window the columns are variables and the rows are called “cases” (which are usually individual sample members, though not always).

On the bottom left of the screen in SPSS are two tabs. One highlighted in Figure $1.4$ is the data view; the other is the variable view. Clicking “Variable View” will change the screen to resemble Figure 1.5. Variable view allows users to enter information about variables, including the name, the type of variable, the number of decimal places, and more. We will discuss variable view more in Chapter 2. Until then, I recommend that you experiment with entering data into SPSS and naming variables.

## 统计代写|Generalized linear model代考广义线性模型代写|Comprehension

1. 为什么社会科学研究人员很少有来自他们感兴趣的全部学科的数据？
2. 为什么能够独立评估研究人员对其数据的解释很重要？
3. 理论模型、统计模型和视觉模型有什么共同点？
4. 大多数社会科学专业的本科生在他们的职业生涯中不会成为专业的研究人员。那么为什么他们有必要参加统计课程呢？
5. 什么是模型？“模型”一词的科学用法与模型的日常定义有何不同？有什么相似之处？
6. 解释：
A. 为什么每个模型在某些方面都是错误的。
湾。如果他们都错了，为什么社会科学的从业者和研究人员应该使用模型。
C。研究人员和从业者如何判断他们是否应该使用特定模型。
7. 社会科学从业者在工作中使用统计数据的四种主要方式是什么？

## 统计代写|Generalized linear model代考广义线性模型代写|Reflection Questions: Application

1. 卡尔相信磁铁可以减轻身体疼痛，为此他在身上佩戴了磁铁。然而，他的磁性手镯对他的关节炎疼痛没有帮助。他查阅了一个关于治愈磁铁的网站，发现自己需要定期更换磁铁在身上的位置，直到疼痛缓解。为什么卡尔关于磁铁治疗特性的假设不科学？
2. 你的专业的理论例子是什么？您能否举例说明该理论是如何产生理论模型的？什么情况可能会反驳这个理论？
3. 一位研究人员希望研究压力，因此她记录了每个受试者在面临痛苦情况时的心率。“心率”是自变量还是因变量？证明你的回应。
4. 一名社工想要研究孩子家庭生活的不稳定性对孩子学习成绩的影响。她将“不稳定”定义为孩子在一年中居住的家庭数量，将“学业表现”定义为老师以从 0 到 100 的等级分配的孩子成绩。这是定量研究过程的哪一步？
5. 特蕾莎想知道在社交媒体上发布更多关于自己的信息的人是否比不这样做的人更自私。

C。这是相关设计还是实验设计？

1. 一些文化人类学家研究“通过仪式”，这是人们从生命的一个阶段过渡到另一个阶段的某些仪式。“通过仪式”的概念非常广泛，可以应用于许多文化中的仪式，以及从出生到死亡的所有生命阶段。一位人类学家决定使用成人仪式框架来了解特定部落文化中的青少年如何被视为成年人。
一种。在这种情况下，“通过仪式”的概念是理论、理论模型、统计模型还是视觉模型？
湾。当人类学家将这一想法应用于特定文化并解释该文化的成年仪式的各个阶段时，这是一种理论、理论模型、统计模型还是视觉模型？
2. 政治学专业的学生对不同国家的立法者在考虑不同法案时所投的票感兴趣。学生认为研究每个国家/地区每个政治家的每张选票是不切实际的。所以，他决定只研究选票。
一种。这个例子中的人口是多少？
湾。此示例中的示例是什么？
3. 一位家庭科学教授想要研究频繁测验对学生学习习惯的影响。在她的一堂课中，她不提供测验。在另一堂课中，她每周提供一次测验。在她的最后一堂课中，她在每节课中都提供了一个测验。在每节课上，她都会问她的学生他们每周学习了多少小时。
一种。这个例子中的自变量是什么？
湾。这个例子中的因变量是什么？
C。教授是如何操作“学习习惯”的？
d。这是实验设计还是相关设计？

## 统计代写|Generalized linear model代考广义线性模型代写|Excel

SPSS 的打开屏幕看起来类似于 Excel 的打开屏幕，这在比较图时很明显1.3和 1.4。这两个程序都有一个由单元格组成的网格，允许用户将数据直接输入程序。在 SPSS 中，这称为“数据视图”。在数据窗口中，列是变量，行称为“案例”（通常是单个样本成员，但并非总是如此）。

SPSS 屏幕的左下角有两个选项卡。图中突出显示的一个1.4是数据视图；另一个是变量视图。单击“Variable View”将改变屏幕，类似于图 1.5。变量视图允许用户输入有关变量的信息，包括名称、变量类型、小数位数等。我们将在第 2 章中详细讨论变量视图。在此之前，我建议您尝试将数据输入 SPSS 并命名变量。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|Generalized linear model代考广义线性模型代写|Statistics and Models

statistics-lab™ 为您的留学生涯保驾护航 在代写Generalized linear model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Generalized linear model代写方面经验极为丰富，各种代写Generalized linear model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|Generalized linear model代考广义线性模型代写|Why Statistics Matters

Although many students would not choose to take a statistics course, nearly every social science department requires its students to take a statistics course (e.g., Norcross et al., 2016; Stoloff et al., 2010). Why? Apparently, the professors in these departments think that statistics is essential to their students’ education, despite what their students may think.

The main reason that many students must take statistics is that research in the social sciences is dominated by methodologies that are statistics-based; this family of methods is called quantitative research. Researchers who use quantitative research convert their data into numbers for the purpose of analysis, and the numbers are then analyzed by statistical methods. Numerical

data are so important that one social scientist even argued that “progress in science is impossible without numbers and measurement as words and rhetoric are not enough” (Bouchard, 2014, p. 569).
Quantitative methods – and therefore statistics – dominate most of the behavioral sciences: psychology, sociology, education, criminal justice, economics, political science, and more. Most researchers working in these fields use statistics to test new theories, evaluate the effectiveness of therapies, and learn about the concepts they study. Even workers who do not conduct research must understand statistics in order to understand how (and whether) to apply scientific knowledge in their daily work. Without statistics a practitioner risks wasting time and money by using ineffective products, therapies, or procedures. In some cases this could lead to violations of ethics codes, accusations of malpractice, lawsuits, and harm to clients or customers. Even students who do not become scientists may need statistics to verify whether an anecdotal observation (e.g., that their company sells more products after a local sports team wins a game than after a losing one) is true. Thus, a mastery of statistics is important to many people, not just researchers and social scientists.
There are four main ways that practitioners use statistics in their work in the social sciences:

1. Separating good research from bad
2. Evaluating the conclusions of researchers
3. Communicating findings to others
4. Interpreting research to create practical, real-world results.
There is some overlap among these four points, so some job tasks will fall into more than one category. Nevertheless, this is still a useful list of ways that professionals use statistics.

Separating good research from bad is important for any practitioner. The quality of the research published in scientific journals varies greatly. Some articles become classics and spark new avenues of research; others report shoddy research. Thus, the fact that a study was published in a scientific journal is not, by itself, evidence of good-quality scientific work. A knowledge of statistics is one of the most important tools that a person can have in distinguishing good research from bad. Having the ability to independently judge research prevents practitioners from being susceptible to fads in their field or from wasting resources on practices that provide few benefits.

The benefits of separating good research from bad research are important for the general public, too (not just practitioners). Most people rely on reports from the news media and the Internet to learn about scientific findings. However, most journalists are not trained scientists and do not have the skills needed to distinguish between a high-quality study and a low-quality one (Yettick, 2015). Readers with statistical training will be able to make these judgments themselves, instead of relying on the judgment of a journalist or social media contacts.

Statistical savviness can also help people in evaluating researchers’ conclusions. Ideally, the conclusions in a scientific article are supported by the data that the researchers collected. However, this is not always the case. Sometimes researchers misinterpret their data because they either used the wrong statistical procedures or did not understand their results. Having statistical competence can prevent research consumers from being at the mercy of the authors and serve as an independent check on researchers.

## 统计代写|Generalized linear model代考广义线性模型代写|Two Branches of Statistics

As the science of quantitative data analysis, statistics is a broad field, and it would be impossible for any textbook to cover every branch of statistics while still being of manageable length. In this book we will discuss two branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is concerned with merely describing the data that a researcher has on hand. Table $1.1$ shows an excerpt from a real collection of data from a study (Waite, Cardon, \& Warne, 2015) about the sibling relationships in families where a child has an autism spectrum disorder. (We will discuss this study and its data in much more detail in Chapters 3 and 10.) Each row in the dataset represents a person and each column in the dataset represents a variable. Therefore, Table $1.1$ has 13 people and 6 variables in it. Each piece of information is a datum (plural: data), and because every person in the table has a value for every variable, there are 84 data in the table (13 people multiplied by 6 variables $=78$ data). A compilation of data is called a dataset.

Even though the dataset in Table $1.1$ is small, it is still difficult to interpret. It takes a moment to ascertain, for example, that there are more females than males in the dataset, or that most people are satisfied with their relationship with their sibling with autism. Table $1.1$ shows just an excerpt of the data. In the study as a whole, there were 45 variables for 13 subjects, which totals to 585 data. No person – no matter how persistent and motivated they are – could understand the entire dataset without some simplification. This is actually a rather small dataset. Most studies in the social sciences have much larger sample sizes. The purpose of descriptive statistics is to describe the

dataset so that it is easier to understand. For example, we could use descriptive statistics to say that in the range of scores on the variable that measures people’s satisfaction with their sibling relationship, the average score is $4.1$, while the average score on the variable measuring whether the sibling with autism understands the respondent’s interests is $2.9$. Chapters 2 – 5 are concerned with descriptive statistics.

On the other hand, if a researcher only has sample data on hand, descriptive statistics tell the researcher little about the population. A separate branch of statistics, termed inferential statistics, was created to help researchers use their sample data to draw conclusions (i.e., inferences) about the population. Inferential statistics is a more complicated field than descriptive statistics, but it is also far more useful. Few social scientists are interested just in the members of their sample. Instead, most are interested in their entire population, and so many social scientists use inferential statistics to learn more about their population – even though they don’t have data from every population member. In fact, they usually only have data from a tiny portion of population members. Inferential statistics spans Chapters $6-15$ of this book.

An example of a use of inferential statistics can be found in a study by Kornrich (2016). This researcher used survey data to examine the amount of money that parents spend on their children. He divided his sample into five groups, ranked from the highest income to the lowest income. He then found the average amount of money that the parents in each group spent on their children and used inferential statistics to estimate the amount of money each group in the population would spend on their children. Unsurprisingly, richer parents spent more money on their children, but Kornrich $(2016)$ also found that the gap in spending on children between the richest $20 \%$ and poorest $20 \%$ of families had widened between 1972 and 2010 . Because Kornrich used inferential statistics, he could draw conclusions about the general population of parents – not just the parents in his sample.

## 统计代写|Generalized linear model代考广义线性模型代写|Models

This book is not organized like most other textbooks. As the title states, it is built around a general linear model (GLM) approach. The GLM is a family of statistical procedures that help researchers ascertain the relationships between variables. Chapter 7 explains the GLM in depth. Until then, it is important to understand the concept of a model.

When you hear the word “model,” what do you think of? Some people imagine a fashion model. Others think of a miniature airplane model. Still others think of a prototype or a blueprint. These are all things that are called “models” in the English language. In science, models are “simplifications of a complex reality” (Rodgers, 2010, p. 1). Reality is messy and complicated. It is hard to understand. In fact, reality is so complex-especially in the social sciences – that in order for people to comprehend it, researchers create models.

An example from criminology can illustrate the complexity of reality and the need for models. One of the most pressing questions in criminology is understanding who will commit crimes and why. In reality, it is impossible to comprehend every influence that leads to a person’s decision to commit a crime (or not). This would mean understanding the person’s entire personal history, culture, thoughts, neighborhood, genetic makeup, and more. Andrews and Bonta (2010) have developed the risk-need-responsivity (RNR) model of criminal conduct. Although not its only purpose, the RNR model can help users establish the risk that someone will commit a crime. Andrews and Bonta do not do this by attempting to understand every aspect of a person. Rather, they have chosen a limited number of variables to measure and use those to predict criminal activity. Some of these variables include a history of drug abuse, previous criminal behavior, whether the person is employed, the behavior of their friends, and the presence of certain psychological diagnoses (all of which affect the probability that someone will commit a crime). By limiting the number of variables they measure and use, Andrews and Bonta have created a model of criminal behavior that has been successful in identifying risk of criminal behavior and reducing offenders’ risk of future reoffending after treatment (Andrews, Bonta, \& Wormith, 2011). This model because it does not contain every possible influence on a person’s criminal behavior – is simplified compared to reality.

This example illustrates an important consequence of creating a model. Because models are simplified, every model is – in some way – wrong. Andrews and Bonta (2010) recognize that

their model does not make perfect predictions of criminal behavior every time. Moreover, there are likely some influences not included in the RNR model that may affect the risk of criminal behavior, such as a cultural influence to prevent family shame or the dying request of a beloved relative. Therefore, one can think of a trade-off between model simplicity and model accuracy: simpler models are easier to understand than reality, but this simplification comes at a cost because simplicity makes the model wrong. In a sense, this is true of the types of models most people usually think about. A miniature airplane model is “wrong” because it often does not include many of the parts that a real airplane has. In fact, many model airplanes don’t have any engines – a characteristic that definitely is not true of real airplanes!

Because every model is wrong, it is not realistic to expect models to be perfectly accurate. Instead, models are judged on the basis of how useful they are. A miniature model airplane may be useless in understanding how a full-sized airplane works, but it may be very helpful in understanding the aerodynamic properties of the plane’s body. However, a different model – a blueprint of the engine – may be helpful in understanding how the airplane obtains enough thrust and lift to leave the ground. As this example shows, the usefulness of the model may depend on the goals of the researcher. The engineer interested in aerodynamics may have little use for the engine blueprint, even though a different engineer would argue that the engine blueprint is a vital aspect of understanding the airplane’s function.

This example also shows one last important characteristic of models: often multiple models can fit reality equally well. In other words, it is possible for different models to fit the same reality, such as the miniature airplane model and the plane engine blueprint (Meehl, 1990). As a result, even if a model explains a phenomenon under investigation very well, it may not be the only model that could fit reality well. In fact, there is no guarantee that the model is even the best possible model. Indeed, many researchers in the social sciences are interested in improving their models because that would lead to an improved understanding of the things they investigate. This improvement can happen by combining two models together, finding improved operationalizations of variables, or eliminating unnecessary parts from a model.

## 统计代写|Generalized linear model代考广义线性模型代写|Why Statistics Matters

1. 区分好的研究和坏的研究
2. 评估研究人员的结论
3. 与他人交流调查结果
4. 解释研究以创造实用的、真实的结果。
这四点之间有一些重叠，因此一些工作任务将属于不止一个类别。尽管如此，这仍然是专业人士使用统计数据的有用列表。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。