Alpha and Beta in statistics

First-and second-type errors can be combined

1. Level of significance alpha is the maximum value for rejecting the correct 0 hypothesis

That is, the probability of falling into a reject domain under H0.

H0 if the simple hypothesis, only a probability distribution, such as P=P0, then directly seek

H0 If a compound hypothesis is desirable, multiple probability distributions, such as P<=P0, are the maximum probability of rejecting H0.

Here is the compound hypothesis, p can take more than one value, but because with the P increment, so p takes the maximum value is the alpha value

Therefore, the maximum probability of rejecting H0 is alpha, the minimum probability of accepting H0 is 1-alpha

2. Test efficacy (power of the test)

The effect is to reject the error 0 hypothesis probability, recorded as 1-beta: that is, H1 the probability of rejecting H0

Alpha is generally unique, but the effect is not always unique.

H1 is a simple hypothesis when the only

H1 is a composite hypothesis, each probability function will have a different 1-beta value, at which time the effect depends on a number of different possible probability functions

Alpha is a type of error probability

Beta is type two error probability

Alpha and 1-beta say reject 0 hypothesis

Alpha and Beta in statistics