Statistical Significance Revisited

Abstract

Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson who brought in the concept of the alternative hypothesis with its corresponding error of the second kind. Significance tests have played a major role in various scientific and technological developments, but not without controversies. Although originally cast as frequentist approaches, Bayesian ideas have been incorporated into significance tests, widening access to them. The quantities central to computations of error probabilities are the sampling distributions, which can be computed even without thresholds or alternative hypotheses. Even though Fisher used the significance threshold of 0.05 in his calculations, he cautioned against prescribing any specific threshold. Recently, there have been calls for reformation in practice with regard to the almost standard use of the significance threshold of 0.05, prepublication confirmatory studies, the dichotomous consideration of the null and alternative hypothesis and abandoning significance tests altogether in favour of other approaches such as confidence intervals and Bayesian decision theory. In this paper, we examine these calls for reform and unearth their strengths and short comings.