The 90 per cent confidence intervals presented in this report were calculated using the Finite Population Correction Appendix 4 (FPC) to account for the relatively large size of the sample relative to the in-scope population. The FPC is generally used Construction when the sampling fraction exceeds 5 per cent. Because percentage agreement scores are reported for the 2021 GOS, the formula for the confidence interval of a of confidence proportion is used. The Agresti-Coull method is used as it performs well with both small and large counts, consistently producing intervals that are more likely to contain the true value of the proportion in comparison to the previous Wald intervals method. Where is the adjusted estimated proportion of satisfied responses, N is the size of the population in the relevant subgroup, n is the number of valid responses in the relevant subgroup, n1 is the number of positive responses in the relevant subgroup, 1.645 is the standard normal value for 90 per cent confidence and FPC is the Finite Population Correction term. The 90 per cent confidence interval of each estimated proportion is then calculated as the adjusted proportion plus or minus its 90 per confidence interval bound. Figure 6 Formula for a 90 per cent confidence interval using the Agresti-Coull method with FPC 2021 GOS International Report 57

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