Inference in “One-Way” Random Designs - Discussing Sub-D and ANOVA based Estimators

Recently it was shown through simulations studies that Sub-D produces estimates with unbiased and lower variance-covariance estimates than the ANOVA-based estimator, ex- cept in case of random “one-way” balanced designs. In this designs the simulations studies suggested they have the same variance-covariance estimates. This paper aims to compare the common ANOVA-based estimator to Sub-D in random “one-way” designs with two groups of treatment and in random “one-way” balanced designs. The comparison will be conducted through theoretical results and corroborated with simulation studies. It will be proved that the ANOVA-base estimator and Sub-D have exactly the same variance- covariance estimates in both above referred designs. The proof will be given firstly for random “one-way” designs with two groups of treatment and then for random “one-way” balanced designs.