Point and interval estimators of a changepoint in stochastical dominance between two distributions

TL;DR

This paper introduces point and interval estimators for a changepoint in stochastic dominance between two distributions, addressing limitations of traditional effect measures when variances differ.

Contribution

It develops a new approach based on stochastic ordering, providing estimators and confidence intervals for the changepoint in distributional dominance.

Findings

Simulation shows estimators have low bias

Bootstrap confidence intervals achieve good coverage

Method effectively detects distributional changes

Abstract

For differences between means of continuous data from independent groups, the customary scale-free measure of effect is the standardized mean difference (SMD). To justify use of SMD, one should be reasonably confident that the group-level variances are equal. Empirical evidence often contradicts this assumption. Thus, we have investigated an alternate approach, based on stochastic ordering of the treatment and control distributions, that takes into account means and variances. For applying stochastic ordering, our development yields a key quantity, $\mathsf{A}$, the outcome value at which the direction of the ordering of the treatment and control distributions changes. Using an extensive simulation, we studied relative bias of point estimators of $\mathsf{A}$ and coverage and relative width of bootstrap confidence intervals.