Beta Risk (ß=beta)

Purpose

Beta Risk (ß=beta) is the probability of accepting the null hypothesis H₀ when it is actually false. It is the risk of not discovering a difference in the sample characteristic of interest (e.g. the mean), when in reality such a difference does exist. It is also known as the risk of making a Type 2 Error. Sometime , it is referred as Produce Error. In practical a Beta Risk means overkill of a good product judge as bad product. Where else Alpha Risk is also called as Type I or Customer Error.

Anatomy

Reference: Juran’ Quality Control Handbook – Ch. 23, P. 60-63, The Vision of Six Sigma: Tools and Methods for Breakthrough
by M. J. Harry – Ch. 13, P. 9-11

Terminology

A. The null hypothesis will either be true or false for the population under investigation. Beta risk is the probability of making a wrong decision when the null hypothesis is in fact false.

If the null hypothesis H_o is false, then accepting H₀ will be the wrong decision and a type 2 error is made. The risk of committing a type 2 error is known as the beta risk ß, which is important because it is an insurance against saying there is no difference when in actual fact there is.

If the null hypothesis H_o is false, then rejecting H₀ will be the correct decision.

Note: That a type 1 and type 2 error cannot be committed simultaneously, since the null hypothesis cannot be true and false at the same time.