假设检验 检验的p值

https://www.jianshu.com/p/4c9b49878f3d

基础知识：

t分布用于根据小样本来估计呈正态分布且方差未知的总体的均值，称为t检验。

如果总体方差已知（例如在样本数量足够多时），则应该用正态分布来估计总体均值，称为U检验。

硬币有正反两面，在概率中我们知道，出现正反面的概率各为50%（1/2），所以作为一个正常的硬币，如果我们投无限次后，结果一定会是正反各占50%。但是，如果我想知道自己手中的硬币，到底是不是正常的硬币，有没有做过手脚，在实际操作中是没办法投掷无限次的。因此，我们只能用有限的结果来判断“硬币是否为常规硬币”这个问题的答案。

显著性水平α表示错误拒绝H0假设的概率（即原假设事实上成立，但我们计算出的结果却错误判断原假设不成立的概率）。

假设置信度为95%，即错误拒绝H0的概率为0.05。展开解释就是，我们有95%的概率确信检验结果正确，有5%的概率会错误拒绝原假设。（错判）

P值

https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/p-value/

A p value is used in hypothesis testing to help you support or reject the null hypothesis. The p value is the evidence against a null hypothesis. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

When you run the hypothesis test, the test will give you a value for p. Compare that value to your chosen alpha level. For example, let’s say you chose an alpha level of 5% (0.05). If the results from the test give you:

• A small p (≤ 0.05), reject the null hypothesis. This is strong evidence that the null hypothesis is invalid.
• A large p (> 0.05) means the alternate hypothesis is weak, so you do not reject the null

https://www.statsdirect.com/help/basics/p_values.htm

The term significance level (alpha) is used to refer to a pre-chosen probability and the term "P value" is used to indicate a probability that you calculate after a given study.

If your P value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample gives reasonable evidence to support the alternative hypothesis. 

The significance level (alpha) is the probability of type I error. 

Notes about Type I error:

• is the incorrect rejection of the null hypothesis
• maximum probability is set in advance as alpha
• is not affected by sample size as it is set in advance
• increases with the number of tests or end points (i.e. do 20 rejections of H₀ and 1 is likely to be wrongly significant for alpha = 0.05)

Notes about Type II error:

• is the incorrect acceptance of the null hypothesis
• probability is beta
• beta depends upon sample size and alpha
• can't be estimated except as a function of the true population effect
• beta gets smaller as the sample size gets larger
• beta gets smaller as the number of tests or end points increases

https://www.zhihu.com/question/23680352
p-value 代表着原假设下观测到某（极端）事件的条件概率。以 D 代表极端事件，H 代表原假设，则 p-value = prob(D|H)。从它的定义出发，p-value 不代表原假设或者备择假设是否为真实的。

P-value is a statement about data in relation to a specified hypothetical explanation, and is not a statement about the explanation itself.
译：P-value 是关于数据和指定假设之间关系的陈述；而非关于假设本身的陈述。

再强调一遍：p-value 是原假设 H 成立下，D 发生的条件概率，即 prob(D|H)；它不是 prob(H|D)，即 D 发生时 H 为真的条件概率。

显著性水平是人为定的，p值是基于样本求出的。当p<α,是拒绝原假设。显著性水平α越大，拒绝的可能性越大。小于α框出范围更大，p落在该范围的可能性也更大。