Testing Rankings with Cross-Validation

TL;DR

This paper evaluates hybrid statistical tests with cross-validation for comparing rankings, finding that Wilcoxon's test with eight folds generally performs best across various data scenarios.

Contribution

It introduces a comprehensive framework for testing ranking similarity using cross-validation combined with multiple statistical tests, and systematically compares their effectiveness.

Findings

Wilcoxon's test with eight folds is most reliable across scenarios.

Dietterich and Alpaydin tests excel in type I error but perform poorly in type II.

The methodology is applicable in diverse fields like machine learning and social sciences.

Abstract

This research investigates how to determine whether two rankings come from the same distribution. We evaluate three hybrid tests: Wilcoxon's, Dietterich's, and Alpaydin's statistical tests combined with cross-validation (CV), each operating with folds ranging from 5 to 10, thus altogether 18 variants. We have applied these tests in the framework of a popular comparative statistical test, the Sum of Ranking Differences that builds upon the Manhattan distance between the rankings. The introduced methodology is widely applicable from machine learning through social sciences. To compare these methods, we have followed an innovative approach borrowed from Economics. We designed nine scenarios for testing type I and II errors. These represent typical situations (that is, different data structures) that CV tests face routinely. The optimal CV method depends on the preferences regarding the minimization of type I/II errors, size of the input, and expected patterns in the data. The Wilcoxon method with eight folds proved to be the best for all three investigated input sizes. Although the Dietterich and Alpaydin methods are the best in type I situations, they fail badly in type II cases. We demonstrate our results on real-world data, borrowed from chess and chemistry. Overall we cannot recommend either Alpaydin or Dietterich as an alternative to Wilcoxon cross-validation.