Figure 3

The QIs estimates results FE model (\({\tau }^{2}\)) by bootstrap method. This graph shows the distribution of \({\tau }^{2}\) estimates for each Quality Indicator (QI) after 500 bootstrap samples. x-axis (QI): represents the different Quality Indicators, numbered from 1 to 11. y-axis (\({\tau }^{2}\)): represents the τ2 estimates, which indicate the differences between hospitals. Red dots: represent the true \({\tau }^{2}\) value for each quality indicator. Blue dash: represents the median estimated value of \({\tau }^{2}\) for each quality indicator. The results show that the proximity of the red dots to the blue dashes confirms the robustness and consistency of the bootstrap sampling results.