what is the effect on alpha if beta is increased decreased A

what is the effect on alpha if beta is increased, decreased? Also if power is increased, decreased?

Solution

alpha is the probability of type 1 error

beta is the probability of type 2 error.

now by neyman pearson\'s theory we can\'t reduce both type of errors simultaneously. so as one decreases other must increase.

so if beta is increased alpha is decreased

if deta is decreased alpha is increased.

now power=1-probability of type 2 error=1-beta

so as power increases beta decreases hence alpha increases.

similarly as power decreases beta increases hence alpha decreases.