I discussed recently with one of my colleagues about the Greenhouse-Geisser correction for non-sphericity. I told him first that this correction is very conservative and that it would be more efficient to perform an alternative analysis not relying on the sphericity assumption. He answered that, in his case, the effects were statistically significant after applying the G-G correction and that consequently he did not have to care about the conservative nature of his analysis. As a reply, I said that since G-G correction influences the statistical significance, this correction might maybe influence the bias and efficiency of the effect size estimations. However, this first reply was intuitive and after having thought about that later, I think now that I was probably wrong. Indeed, the correction might affect only the statistical significance treshold as if we worked with a higher alpha than the conventional .05. However, while writing my question I just remember of formula allowing to compute effect size estimation using the F statistic and its df. So maybe I was also wrong in the way I re-thought to the question. The G-G correction might affect both the statistical significance treshold and the effect size estimation. What is your opinion about that? Thanks in advance for your answers.