Game-Theoretic Decision-Making to Optimize Type-I and Type-II Errors in Statistical Hypothesis Testing

• Activity Number: 141
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Mehmet Sahinoglu* and Rasika Kelum Balasurya and David Tyson
• Companies: Auburn University and Auburn University at Montgomery and Auburn University at Montgomery
• Keywords: Game-theoretic ; type-I and type-II errors ; hypothesis testing ; producer's and consumer's risks ; cost ; utility

Abstract

What should constitute suitably small values of alpha and beta in tests of hypotheses? This is not a question to answer unequivocally for all situations. When establishing a test procedure to investigate statistically the credibility of a stated hypothesis, several factors must be considered one of which is the size of the sample. However, the most significant of all these factors is unquestionably to optimize Type I and II errors. Statisticians have by rule of thumb selected, such as a=0.05, none for ß depending on the alternative hypothesis at hand. Although, common logic usually played a major role such as in the case of testing null hypothesis of the patient being sick needs a fairly significant size of type I error lest we lose the patient if we reject that she is sick while she truly is sick and probably dying. But all these previous up-to-date arguments are not somewhat connected with cost or utility of producer's and consumer's risks in the sense of quality control or life sciences or in the cyber-risk domain or other manufacturing industries while testing a hypothesis of a good product vs. bad. This research innovatively outlines Game-theoretic approaches, such as that of von Neumann to this archaic problem to justify some optimal choices for a and ß when cost, utility and associated market factors are incorporated.