The Inverse Simpson Paradox (How To Win Without Overtly Cheating)

TL;DR

The paper introduces the Inverse Simpson Paradox, a method to decompose data sets to reverse statistical conclusions, highlighting its potential and limitations depending on data specifics.

Contribution

It presents a novel approach to decompose data to achieve opposite conclusions, expanding understanding of the Simpson Paradox.

Findings

Inverse Simpson decomposition is always possible

The significance of conclusions depends on data details

Method can reverse statistical inferences

Abstract

Given two sets of data which lead to a similar statistical conclusion, the Simpson Paradox describes the tactic of combining these two sets and achieving the opposite conclusion. Depending upon the given data, this may or may not succeed. Inverse Simpson is a method of decomposing a given set of comparison data into two disjoint sets and achieving the opposite conclusion for each one. This is always possible; however, the statistical significance of the conclusions does depend upon the details of the given data.