P 值、显着性水平和假设 [英] P-value, significance level and hypothesis

问题描述

我对 p 值的概念感到困惑.一般而言，如果 p 值大于 alpha(通常为 0.05)，我们将无法拒绝原假设，如果 p 值小于 alpha，我们将拒绝原假设.据我了解，如果 p 值大于 alpha，则两组之间的差异只是来自抽样误差或偶然.到目前为止一切正常.但是，如果 p 值小于 alpha，则结果统计显着，我假设它统计上不显着(因为，如果 p 值小于与 alpha 相比，我们拒绝零假设).

I am confused about the concept of p-value. In general, if the p-value is greater than alpha which is generally 0.05, we are fail to reject null hypothesis and if the p-value is less than alpha, we reject null hypothesis. As I understand, if the p-value is greater than alpha, difference between two group is just coming from sampling error or by chance.So far everything is okay. However, if the p-value is less than alpha, the result is statistically significant, I was supposing it to be statistically nonsignificant ( because, in case p-value is less than alpha we reject null hypothesis).

基本上，如果结果具有统计学意义，则拒绝原假设.但是，如果一个假设在统计上是显着的，那么如何拒绝它呢?从统计显着"这个词，我理解结果是好的.

Basically, if result statistically significant, reject null hypothesis. But, how a hypothesis can be rejected, if it is statistically significant? From the word of "statistically significant", I am understanding that the result is good.

推荐答案

您误解了 p 值的重要性.

You are mistaking what the significance means in terms of the p-value.

我将尝试在下面解释:

让我们假设一个关于两个总体均值相等的检验.我们将通过从每个总体中抽取一个样本并计算 p 值来执行 t 检验来检验这一点.

Let's assume a test about the means of two populations being equal. We will perform a t-test to test that by drawing one sample from each population and calculating the p-value.

零假设和备择:

H0: m1 - m2  = 0
H1: m1 - m2 != 0 

这是一个双尾测试(虽然对此并不重要).

Which is a two-tailed test (although not important for this).

让我们假设您的 p 值为 0.01 并且您的 alpha 为 0.05.p 值是从两个总体(m1 和 m2)采样时均值相等的概率.这意味着均值有 1% 的概率相等，或者换句话说，100 个样本对中只有 1 个的均值差为 0.

Let's assume that you get a p-value of 0.01 and your alpha is 0.05. The p-value is the probability of the means being equal when sampling from the two populations (m1 and m2). This means that there is a 1% probability that the means will be equal or in other words only 1 out of 100 sample pairs will have a mean difference of 0.

两个均值相等的概率如此之低，使我们确信(使我们确定)总体的均值不相等，因此我们认为结果具有统计显着性.

Such a low probability of the two means being equal makes us confident (makes us certain) that the means of the populations are not equal and thus we consider the result to be statistically significant.

让我们认为结果重要的阈值是多少?这是由显着性水平 (a) 决定的，在这种情况下为 5%.

What is the threshold that makes us think that a result is significant? That is determined by the significance level (a) which in this case is 5%.

p 值小于显着性水平使我们认为结果是显着的，因此我们确信我们可以拒绝原假设，因为原假设为真的概率非常低.

The p-value being less than the significance level is what makes us think that the result is significant and therefore we are certain that we can reject the null hypothesis since the probability of the NULL hypothesis being true is very low.

我希望现在有意义！

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