A rational approach to statistical thinking: What if there were no thresholds?

Objectives: Statistics is an integral part of scientific innovations. Conventionally, findings are dichotomized as "significant" or "non-significant" based on specified thresholds. In medical research statistical power is set at 80% and significance level of 5%. Threshold requirement and the methods for meeting them have severe flaws. Variability of biological phenomena influences the projected scientific or practical value. This precludes any meaningful blanket cut-offs and neglects meaningful results. The aim is to review and critique evidence of classical statistics and to raise awareness of alternatives.
Methods: A theoretical discussion of the philosophy of statistical thinking and a comparison of inferential approaches.
Results: Contrary to common dogma, p-values bear minimal information. Reporting isolated p-values neglects important results. The more intuitive alternative, Bayesian inference, is infrequent. Contrasting p-values, Bayesian results are reported as probability of a hypothesis being true and are considerably more comprehensible.
Conclusions: P-values are uninformative and may hinder the scientific process. Current conventions harm the research process in many ways: promoting misinterpretation of completed studies, eroding scientific integrity, promoting publication bias, inhibiting innovation, perverting ethical standards, wasting effort, and wasting money. If we routinely specified plausible null hypotheses, studied random samples, checked distribution assumptions, estimate power for every test and understood the correct meaning of p-values, there would be no problem with our inferences. Some suggestions in this paper include assigning p-values smaller role, computation of effect size and CI for all parameters of interest and evaluation of the substantive significance results.

To promote more rational research activities, extreme cautions is needed before dichotomizing results as "significant" or "insignificant" and statistical reports should bear meaningful results. Further a proposal to have Bayesian inference take a more central role is given. Bayesian inference avoids many of the fundamental limitations.