Intraclass Correlation Coefficient
Kelley's Epsilon Squared
These are all biased estimators. Omega squared applies to the fixed effects model, and the intraclass correlation coefficient applies to the random effects model.
Thus omega squared should be used if you want to make inferences only about the specific categories of the nominal variable which appear in the data, whereas the intraclass correlation coefficient should be used if you view the particular categories that appear in the data as a random sample from a larger set of potential categories and you want to make inferences about the total set of potential categories.
Kelley's epsilon squared is used for exactly the same purpose as omega squared, but it differs very slightly in computation. Omega squared was apparently developed independently of Kelley's earlier statistic. Kelley's epsilon squared is precisely equivalent to eta squared after the latter is adjusted for degrees of freedom. The MicrOsiris commands ANOVA and MCA to compute eta squared and ANOVA computes omega squared and the omega squared effective size value.
For hypothesis testing, the F test should be used. ANOVA and MCA
Certain assumptions for interval scaled data may apply.