Sample size estimation for power and accuracy in the experimental comparison of algorithms

TL;DR

This paper introduces a methodology for determining the necessary sample sizes in algorithm comparison experiments to ensure desired accuracy and statistical power, improving the reliability of performance evaluations.

Contribution

It provides a systematic approach for defining sample sizes that control accuracy and power in algorithm performance comparisons on specific problem classes.

Findings

Method accurately estimates required sample sizes for desired statistical properties.

Application examples demonstrate the method's effectiveness.

Ensures experiments meet predefined accuracy and power levels.

Abstract

Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical properties for the comparison of two methods on a given problem class. The proposed approach allows the experimenter to define desired levels of accuracy for estimates of mean performance differences on individual problem instances, as well as the desired statistical power for comparing mean performances over a problem class of interest. The method calculates the required number of problem instances, and runs the algorithms on each test instance so that the accuracy of the estimated differences in performance is controlled at the predefined level. Two examples illustrate the application of the proposed method, and its ability to achieve the desired statistical properties with a methodologically sound definition of the relevant sample sizes.