Dichotomizing Continuous Data Which Retains Statistical Precision Using a Bayesian Distributional Approach That Reflects the True Uncertainty

In order to address the issue of dichotomization, a previous literature developed an asymptotic distributional approach from a frequentist perspective assuming that the data are normally distributed and the variances in two groups are equivalent. This approach was further extended to the case of unequal variances.

The previous works improve the dichotomization in many ways but assumes that the variance of data is known which does not reflect the realistic situation where both mean and variance are unknown. In this paper, we develop a Bayesian distributional methodology that inherits the advantages of previous attempts but considers all levels of uncertainty. For comparison purposes, we also reframe the original asymptotic approach from a Bayesian perspective.