Comparing Two Samples Through Stochastic Dominance: A Graphical Approach

TL;DR

This paper introduces a new graphical method to compare two samples based on their estimated cumulative distribution functions, providing visual insights into stochastic dominance that complement traditional statistical tests.

Contribution

It proposes a novel dominance measure and a graphical decomposition technique for stochastic comparison, along with a software package for practical application.

Findings

The method reveals additional insights missed by traditional tests.

Re-evaluation of existing experiments demonstrates the effectiveness of the approach.

The RVCompare software facilitates easy application of the proposed framework.

Abstract

Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which unpredictable outcomes are common. These measures can be modeled as random variables and compared among each other via their expected values or more sophisticated tools such as null hypothesis statistical tests. In this paper, we propose an alternative framework to visually compare two samples according to their estimated cumulative distribution functions. First, we introduce a dominance measure for two random variables that quantifies the proportion in which the cumulative distribution function of one of the random variables stochastically dominates the other one. Then, we present a graphical method that decomposes in quantiles i) the proposed dominance measure and ii) the probability that one of the random variables takes lower values than the other. With illustrative purposes, we re-evaluate the experimentation of an already published work with the proposed methodology and we show that additional conclusions (missed by the rest of the methods) can be inferred. Additionally, the software package RVCompare was created as a convenient way of applying and experimenting with the proposed framework.