Bias Correction for Eta Squared in One-Way ANOVA

Eta squared is a popular effect size, but contains positive bias. Bootstrapping can be used to remove the bias from eta squared. Compared to epsilon squared and omega squared, bootstrap bias correction does not make distributional assumption, and it is easy to implement. A real example and computer simulations are included to illustrate its application. The bootstrap bias-corrected eta squared shows very little bias, and it serves as a good alternative to eta squared and epsilon squared, the latter of which can turn negative in some circumstances.

Automated summary

Eta squared is a commonly used effect size measure, but it tends to have positive bias. This paper introduces the use of bootstrapping to correct the bias in eta squared. Compared to other measures such as epsilon squared and omega squared, bootstrapped bias correction does not require specific distribution assumptions and is easily implemented. The application of this method is illustrated through a real example and computer simulations. The results show that the bootstrapped bias-corrected eta squared has minimal bias and can be a good alternative to eta squared and epsilon squared, especially in situations where epsilon squared can become negative.