Frequentist statistics answers the wrong question: the case for Bayesian inference in anaesthesia research

Statistical inference is based on the laws of probability. However, frequentists and Bayesians interpret probability differently. Frequentists interpret probability as a long-run frequency over repeated sampling. Consequently, frequentist probability statements are sampling probabilities from a sampling distribution. A sampling distribution is the hypothetical long-run distribution of a statistic we would expect to observe, assuming the population value is fixed. The frequentist interpretation is confusing and leads to the widespread misinterpretation of P-values and confidence intervals. Bayesians interpret probability as a strength of belief. Consequently, Bayesian probability statements are inferential probabilities. An inferential probability is a direct statement about the quantity of interest, that is, the truth of the hypothesis and the size of the treatment effect, given the data observed. As clinicians and researchers, we seek inferential probabilities ('What is the probability the treatment works given the study data?') not sampling probabilities ('If the treatment does not work, how surprising are the study data?'). I explore the frequentist and Bayesian perspectives on probability, address the barriers to adopting Bayesian methods, and make the case for Bayesian inference in anaesthesia research.