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# 统计代写| 假设检验作业代写Hypothesis testing代考|The Good Side of High P-values

##### 空白假设的早期选择

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

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

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

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

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## 统计代写| 假设检验作业代写Hypothesis testing代考|The Good Side of High P-values

Can high p-values be helpful? What do high p-values mean?
Typically, when you perform a hypothesis test, you want to obtain low p-values that are statistically significant. Small p-values are sexy. They represent exciting findings and can help you get articles published.
However, you might be surprised to learn that higher p-values, which are not statistically significant, are also valuable. In this section, I’ll show you the potential value of a p-value greater than $0.05$, or whatever significance level you’re using.

Hypothesis testing is a form of inferential statistics. You want to use your sample data to draw conclusions about the entire population. When you collect a random sample, you might observe an effect within the sample, such as a difference between group means. But, does that effect exist in the population? Or is it just random error in the sample?

For example, suppose you’re comparing two teaching methods and determining whether one produces higher mean test scores. In your sample data, you see that the mean for Method A is greater than Method B. However, random samples contain random error, which makes your sample means very unlikely to equal the population means precisely. Unfortunately, the difference between the sample means of two teaching methods can represent either an effect in the population or random error in your sample.

This point is where p-values and significance levels come in. Typically, you want p-values that are less than your significance levels (e.g., $0.05$ ) because it indicates your sample evidence is strong enough to conclude that Method A is better than Method B for the entire population. The teaching method appears to have a real effect. Exciting stuff!

However, I’ll go in the opposite direction for this section and try to help you appreciate higher, insignificant p-values! These are cases where you cannot conclude that an effect exists in the population. For the teaching method example above, a higher p-value indicates that we have insufficient evidence to find that one teaching method is better than the other.

Let’s graphically illustrate three different hypothetical studies about teaching methods in the plots below. Which of the following three studies have statistically significant results? The difference between the two groups is the effect size for each experiment. Here’s the CSV data file: $\text { studies }$.

All three studies appear to have differences between their sample means. However, even if the population means are equal, the sample means are unlikely to be equal. We need to filter out the signal (real differences) from the noise (random error). That’s where hypothesis tests play a role.

## 统计代写|假设检验作业代写HYPOTHESIS TESTING代考|Practical vs. Statistical Significance

In the previous section, we looked at how a relatively large effect in your sample might really be random error. We saw how high p-values can protect you from jumping to conclusions based on the error. In this section, I help you avoid the opposite condition.

Imagine you’ve just performed a hypothesis test and your results are statistically significant. Hurray! These results are important, right? Not so fast. Statistical significance does not necessarily mean that the results are practically meaningful in the real world. You can have significant results for a small effect. Remember how the previous section showed how effect size was only one factor out of three?

In this section, I’ll talk about the differences between practical significance and statistical significance, and how to determine if your results are meaningful in the real world.
Statistical Significance
The hypothesis testing procedure determines whether the sample results that you obtain are likely if you assume the null hypothesis is correct for the population. If the results are sufficiently improbable under that assumption, you can reject the null hypothesis and conclude that an effect exists. In other words, the strength of the evidence in your sample has passed your defined threshold of the significance level (alpha). Your results are statistically significant.

Consequently, it might seem logical that p-values and statistical significance relate to importance. However, that is false because conditions other than large effect sizes can produce tiny p-values.

Hypothesis tests with small effect sizes can produce very low p-values when you have a large sample size and/or the data have low variability. Consequently, effect sizes that are trivial in the practical sense can be statistically significant.
Here’s how small effect sizes can still produce tiny p-values:
You have a very large sample size. As the sample size increases, the hypothesis test gains greater statistical power to detect small effects. With a large enough sample size, the hypothesis test can detect an effect that is so miniscule that it is meaningless in a practical sense.
The sample variability is very low. When your sample data have low variability, hypothesis tests can produce more precise estimates of the population’s effect. This precision allows the test to detect tiny effects.

Statistical significance indicates only that you have sufficient evidence to conclude that an effect exists. It is a mathematical definition that does not know anything about the subject area and what constitutes an important effect.
Practical Significance
Size matters!
While statistical significance relates to whether an effect exists, practical significance refers to its magnitude. However, no statistical test can tell you whether the effect is large enough to be important in your field of study. Instead, you need to apply your subject area knowledge and expertise to determine whether the effect is big enough to be meaningful in the real world. In other words, is it large enough to care about?

How do you do this? I find that it is helpful to identify the smallest effect size that still has some practical significance. Again, this process determine whether all, some, or none of that range represents practically significant effects.

## 统计代写|假设检验作业代写HYPOTHESIS TESTING代考|Practical Tips to Avoid Being Fooled

After reading the chapter to this point, you should have no doubts that understanding your hypothesis test result is not as simple as only whether your p-value is less than your significance level. Now, I’ll build on the information we covered throughout this chapter and present practical advice that helps you assess and minimize the possibility of being fooled by false positives and other misleading results.

Previously, I showed how a common misconception about interpreting p-values produces the illusion of substantially more evidence against the null hypothesis than is justified. For example, a p-value near $0.05$ often has a false positive error rate of between $23-50 \%$. These greater than expected false positive rates create doubts about trusting statistically significant results. Relatedly, we saw how the reproducibility rate for psychology studies is surprisingly low.

When a hypothesis test produces significant results, there is always that chance that it is a false positive. In this context, a false positive occurs when you obtain a statistically significant p-value, and you unknowingly reject a null hypothesis that is actually true. You conclude that an effect exists in the population when it does not exist.

From a scientific point of view, the high false-positive rates are problematic because of the misleading results. From a practical standpoint, if you are using a hypothesis test to improve a product or process, you won’t obtain the benefits that you expect if the test results are a false positive. That can cost you a lot of money!

Let’s delve into the tips. These tips will help you develop a deeper understanding of your test results. I’ll use a real AIDS vaccine study conducted in Thailand to work through these considerations. The study obtained a p-value of $0.039$, which sounds great. Hurray, the vaccine works! However, after reading this book, you might think differently.

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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。