Lack of replicability has been of a major concern in the past two decades in various fields of science (e.g. animal behaviour, pre-clinical research and experimental psychology). In the field of animal behavioural studies, orchestrated multi-lab studies were held. Despite that, results were not replicated, proving that lack of replicability is is possibly due to lab-specific uncontrollable factors.
By modeling such a multi-lab study by a mixed 2-way ANOVA, where the lab effect is random and the studied effect is fixed, we can address the effects of the uncontrollable factors as the random interaction between the lab and the studied factor. An effect is replicable if it is significant in face of the increased variability. We therefore estimate interaction variance from multi-lab data, for the purpose of inference in a future related single-lab study. This goal puts the interaction variance estimation in the highlight. In this work, we devise estimation schemes to overcome the bias and increased MSE present in common estimation methods. The methods are extended to unbalanced sample size ANOVA, including missing combinations (cells, i.e. sample size 0).