Alpha and Beta Tests for Type I and Type II Inferential Errors Determination in Hypothesis Testing

Abstract

The purpose of this paper is to introduce methods on how to determine Type I and Type II inferential errors in hypothesis testing. The current literature in the field treats this subject in the language of probability. This paper proposes two algebraic formulations call alpha and beta tests. Alpha test is used to determine Type I error. Beta test is used to determine Type II error. In every hypothesis test, the researcher must implement alpha and beta tests to verify that no inferential errors had been committed. The use of statistics test to determine whether the observed data may overcome the null hypothesis is the starting point in hypothesis testing. The next step is to engage inferential error tests. This second step is the missing link in the current research practice. This paper intends to fill that gap in the field. The introduction of alpha test is within the logic of confidence interval general practice. However, the introduction of beta test in this paper is a novelty and should be considered a contribution to the field. The new formulation is based on sample standard variance and alpha.