From one environment to many: The problem of replicability of statistical inferences

Abstract: Among plausible causes for replicability failure, one that has not received sufficient attention is the environment in which the research is conducted. Consisting of the population, equipment, personnel, and various conditions such as location, time, and weather, the research environment can affect treatments and outcomes, and changes in the research environment that occur when an experiment is redone can affect replicability. We examine the extent to which such changes contribute to replicability failure. Our framework is that of an initial experiment that generates the data and a follow-up experiment that is done the same way except for a change in the research environment. We assume that the initial experiment satisfies the assumptions of the two-sample t-statistic and that the follow-up experiment is described by a mixed model which includes environmental parameters. We derive expressions for the effect that the research environment has on power, sample size selection, p-values, and confidence levels. We measure the size of the environmental effect with the environmental effect ratio EER which is the ratio of the standard deviations of environment by treatment interaction and error. By varying EER, it is possible to determine conditions that favor replicability and those that do not.