B0444
Title: Counternull sets in randomized experiments
Authors: Donald Rubin - Harvard University (United States)
Marie-Abele Bind - Massachusetts General Hospital (United States) [presenting]
Abstract: In statistical parlance, the null value of an estimand is a value that is distinguished in some way from other possible values. Often it is a particular value that indicates no difference. In contrast, a counternull value is a value of that estimand that is supported by the same amount of evidence that supports the null value. Of course, such a definition depends critically on how evidence is defined, which depends on the context for the collection of data. The context of a randomized experiment is considered where evidence is summarized by the significance value (i.e., p-value) according to Fishers randomization test. Consequently, a counternull value has the same p-value from the randomization test as does the null value. There are two advantages to using the counternull in addition to using the null value. The first is pedagogical, in that reporting avoids the mistake of implicitly accepting the null hypothesis when it is not rejected; this use is similar to the use of confidence intervals, except the counternull has fewer extraneous assumptions, which are rarely made explicit in practice. The second use is that reporting counternull values can be scientifically helpful in revealing values of estimands that were not considered as important as the null value prior to seeing the current data.
