Null, Not Void

• Activity Number: 581
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Pamela A. Shaw*+ and Michael A. Proschan
• Companies: National Institute of Allergy and Infectious Diseases and National Institute of Allergy and Infectious Diseases
• Keywords: Hypothesis Tests ; Nuisance Parameters ; Strong and Weak Null

Abstract

When performing a hypothesis test, the practitioner commonly focuses on one key parameter of interest, such as the mean. Choice of the null/alternative space impacts the choice of the test and what conclusions can be drawn from this statistical test. This choice is often given little attention. When a parameter is not of interest it is common to consider it a nuisance parameter and give it no consideration when defining the alternative hypothesis. We will illustrate with real data examples that even if a parameter is not of primary interest, it can still impact important properties of the chosen test. Mathematically, the issue can often be reduced to specifying what deviation from the strong null is included in the alternative. The type of deviation that is scientifically plausible and that is of scientific interest are both important to consider. We present several examples where specification of the alternative and the statistical test involved important distinctions of a seemingly nuisance parameter in the alternative space. Cases considered include ones where without careful thought, a less powerful test or one with misleading results could easily have been chosen.