# Why reject Null Hypothesis when p value< alpha? [duplicate]

As per statistical literature, there seems to be this understanding that given a p value less than alpha, we are to reject the null hypothesis.

The way I am interpreting this is that is the critical region, as defined by the alpha is the 'False Rejection' (TYPE 1 error) zone and constitutes the error threshold, why then p-value for a sample that is less than the alpha and within the error zone results in rejection of the null hypothesis?

Another line of thought - if the p-value is a way of saying how extreme a test statistic is for our sample data and seems to have a low probability, then how does it constitute evidence against the null hypothesis? Where am I going wrong?

## marked as duplicate by whuber♦Dec 6 '18 at 19:11

The "alpha" ($$\alpha$$) is set a priori to be the probability of rejecting the null hypothesis when the null hypothesis is true (the Type I error as you stated). If, after conducting your statistical test, the $$p$$-value is found to be less than $$\alpha$$, this shows that, under the assumed null hypothesis, the probability you'd observe a test statistic as large (or larger) as the one you did, is very small. Something with such a small small probability of occuring should be considered suspicious. How could something be observed when it's so unlikely? Two things could have happened:
2) You got a very unlucky result. This is simply the risk you are willing to take and you should set your $$\alpha$$/critical region accordingly when you set up your test. If you can tolerate more risk, set $$\alpha$$ to be larger. If you can't, set $$\alpha$$ to be smaller.