统计代写|假设检验代写hypothesis testing代考|STA2023

统计代写|假设检验代写hypothesis testing代考|P-values Are NOT an Error Rate

Unfortunately, p-values are frequently misinterpreted. A common mistake is that they represent the likelihood of rejecting a null hypothesis that is actually true (Type I error). The idea that p-values are the probability of making a mistake is WRONG!

You can’t use p-values to calculate the error rate directly for several reasons.

First, p-value calculations assume that the null hypothesis is correct. Thus, from the p-value’s point of view, the null hypothesis is $100 \%$ true. Remember, p-values assume that the null is true, and sampling error caused the observed sample effect.

Second, p-values tell you how consistent your sample data are with a true null hypothesis. However, when your data are very inconsistent with the null hypothesis, p-values can’t determine which of the following two possibilities is more probable:

• The null hypothesis is true, but your sample is unusual due to random sampling error.
• The null hypothesis is false.
To figure out which option is right, you must apply expert knowledge of the study area and, very importantly, assess the results of similar studies.

Going back to our medication study, let’s highlight the correct and incorrect way to interpret the p-value of $0.03$ :

• $\quad$ Correct: Assuming the medication has zero effect in the population, you’d obtain the sample effect, or larger, in $3 \%$ of studies because of random sample error.
• Incorrect: There’s a 3\% chance of making a mistake by rejecting the null hypothesis.

Yes, I realize that the incorrect definition seems more straightforward, and that’s why it is so common. Unfortunately, using this definition gives you a false sense of security, as I’ll show you next.

统计代写|假设检验代写hypothesis testing代考|What Is the True Error Rate?

The difference between the correct and incorrect interpretation is not just a matter of wording. There is a fundamental difference in the amount of evidence against the null hypothesis that each definition implies.

The $\mathrm{p}$-value for our medication study is $0.03$. If you interpret that $\mathrm{p}$ value as a $3 \%$ chance of making a mistake by rejecting the null hypothesis, you’d feel like you’re on pretty safe ground. However, after reading this section, you should realize that p-values are not an error rate, and you can’t interpret them this way.

If the p-value is not the error rate for our study, what is the error rate? Hint: It’s higher!

As I explained earlier, you can’t directly calculate an error rate based on a p-value, at least not using the frequentist approach that produces p-values. However, you can estimate error rates associated with p-values by using Bayesian methodologies and simulation studies.

These higher error rates probably surprise you! Regrettably, the common misconception that $\mathrm{p}$-values are the error rate produces the false impression of considerably more evidence against the null hypothesis than is warranted. A single study with a p-value around $0.05$ does not provide substantial evidence that the sample effect exists in the population.

These estimated error rates emphasize the need to have lower p-values and replicate studies that confirm the initial results before you can safely conclude that an effect exists at the population level. Additionally, studies with smaller p-values have higher reproducibility rates in follow-up studies.

In a nutshell, p-value calculations assume that the null hypothesis is correct and use that assumption to determine the likelihood of obtaining your observed sample data. P-values answer the question, “Are your sample data unusual if the null hypothesis is true?”

假设检验代考

统计代写|假设检验代写hypothesis testing代考|P-values Are NOT an Error Rate

• 原假设为真，但由于随机抽样误差，您的样本不寻常。
• 零假设是错误的。
要找出哪个选项是正确的，您必须应用研究领域的专业知识，并且非常重要的是，评估类似研究的结果。

• 正确：假设药物对人群的影响为零，您将获得样本效应或更大的效应3%由于随机样本误差的研究。
• 不正确：拒绝零假设有 3% 的几率出错。

统计代写|假设检验代写hypothesis testing代考|What Is the True Error Rate?

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