Interpreting Statistical Confidence

The traditional interpretation of statistical confidence is mathematically descriptive. As such it provides little guidance for decision making. Three alternate interpretations of confidence are presented: the Bayesian, the pragmatic and one proposed by the author labeled herein as the neoclassical. Each alternate explanation argues that in some way a confidence interval and a numerically equivalent probability should be treated similarly. The neoclassical interpretation argues that one should be indifferent between two bets: betting on a 95% confidence interval to contain the population parameter and betting on a 95% chance that the next ball will be red in drawing from an urn containing 95% red balls. Unlike the Bayesian interpretation, the neoclassical interpretation treats the population parameter as a constant – not as a variable. The neoclassical interpretation of confidence holds that confidence measures one’s strength of belief in a particular claim and thus is psychological and subjective. Yet in some cases, one’s confidence should be the same in two apparently different situations. This neoclassical interpretation focuses on the ‘calculated risk’ or objective aspect of confidence and includes aspects from both the Bayesian and traditional viewpoints. Specific recommendations are offered.