Whats the tradeoff between Alpha PowerSolutionlet we have a

Whats the tradeoff between Alpha & Power?

Solution

let we have a null hypothesis H0 and an alternative hypothesis H1.

then we have type I error=rejecting H0 given that H0 is true.

and type II error=accepting H0 given that H1 is true

there is alpha=level of significance.

now level of significance means Probabaility of type I error

so alpha=P[type I error]=P[rejecting H0|H0 is true]

and we have power=P[rejecting H0|H1 is true]

                           =1-P[accepting H0|H1 is true]

                           =1-P[type II error]

but the fact is the probability of two errors can not be simultaneously reduced.

if P[type I error] is reduced then P[type II error] gets increased automatically for a fixed sample size.

so when alpha=P[type I error] is reduced P[type II error] gets increased.

which means 1-P[type II error] gets reduced or power gets reduced.

hence as ALPHA decreases POWER also decreases or as ALPHA increase POWER also increases.

the objective is to decrease alpha and increase power as possible. but due to the above relation between alpha and power it is not possible to decrease alpha and increase power simultaneously.

now according NEYMAN-PEARSON theory alpha is more sensitive than power.

so what is done is that alpha is fixed at a certain level and then power is increased as much as possible keeping in mind that alpha can not exceed the given level.