the same philosophy: Under the null hypothesis, the test statistics would distribute like normal/t/chi-sq/F/whatever distribution. Then the probability that the (otherwise fitting the H0) test statistics (which is a RV) farther in the tail than the calculated test statistics is x--which is the same as the probability of getting wrong if you reject H0. Then you reject H0 understanding you might get it wrong with probability x, or not reject understanding you might get it wrong with another probability, which usually not known, but decreases as x increases. Then you make your own decision. Then the role for the test is over.

How to interpret your decision (reject as desire or not reject as "appropriate") is not the test's business. If I have to concern whether a test is "粗放", I would first worry whether/how close the test statistics under H0 is really the normal/t/chi-sq/F/whatever distribution I am using.