Fig. 4

The true value of average power is covered by the credible interval in simulation experiments. The EB based average power estimator \(\bar {\eta }^{(2)}_{\textit {EB}}\) estimates more accurately than other plug-in based average power estimators \(\bar {\beta }^{(2)}\left (\widehat {\mu }^{(1)}\right)\), \(\bar {\beta }^{(2)}\left (\widehat {\mu }_{\textit {CMLE}}^{(1)}\right)\), \(\bar {\beta }^{(2)}\left (\hat {\mu }^{(1)}_{BR2}\right)\) and \(\bar {\beta }^{(2)}\left (\widehat {\mu }_{\textit {EB}}^{(1)}\right)\). Average power \(\bar {\beta }^{(2)}(\mu)\) is defined in the main text. A method combining Monte Carlo method and bootstrap is proposed to create the credible intervals of the replication study’s average power. In the 5 runs of the simulation experiments, the underlying true values of the average power is covered by created intervals. Compared to other plug-in based average power estimators, \(\bar {\eta }^{(2)}_{\textit {EB}}\) is the closest to \(\bar {\beta }^{(2)}(\mu)\)