Carkeet A, Goh YT. Trust and coverage for Bland Altman compliance limits and their approximate confidence intervals. Stat Methods Med Res. 2018;27:1559-74. Given the stochastic nature of statistical inference, it is more instructive to construct confidence intervals for target parameters than a single estimate of their values. General exposures and general principles for estimating intervals are available in Hahn [10, 11], Hahn and Meeker  and Vardeman . As a result, different normal percentrile interval methods have been described from different angles. The exact interval method of the normal percentile is documented in the literature, cf. z.B.
Hahn and Meeker , Johnson, Kotz and Balakrishnan  and Owen . In addition, the unilateral intervals of the normal percentre are closely related to the unilateral tolerance limits of a normal distribution, as established in David and Nagaraja , Krishnamoorthy and Mathew , as well as Odeh and Owen . Vardeman SB. What about the other intervals? In Stat. 1992; 46:193-7. with τ BAL = z p N1/2 – t1 − α/2 (ν) b1/2 and τ BAU = p n1/2 + t1 – α / 2 (ν) b1/ 2. In the specific case of α = 0.05, the general expressions are reduced to the confidence intervals for both ends of the 95% correspondence limits taken into account in Bland and Altman : Chakraborti S, Li J. Estimation of the confidence interval of a normal percentile. In Stat. 2007;61:331–6. The probability of simulated coverage was the proportion of the 10,000 replicates whose confidence interval contained the normal perzentile of the population.
Then, the adequacy of the one- and two-sided interval procedures is determined by the error = simulated coverage probability – nominal hedging probability. The results are summarized in Tables 1, 2, 3 and 4 for the exact and approximate confidence intervals with the bilateral confidence coefficient 1 – α = 0.90 and 0.95 respectively. The errors resulting from the three types of confidence intervals show that the exact approach of the 96 cases presented in Tables 1, 2, 3 and 4 is extremely good. For the two approximate methods Chakraborti and Li  and Bland and Altman , the probabilities of coverage of their bilateral interval remain quite close to the nominal confidence levels. However, the corresponding unilateral interval procedures do not retain the same desired accuracy, unless the sample size is large. Due to differences in the degree of presumed simplification, the interval procedure of Bland and Altman  is inferior to that of Chakraborti and Li , especially for small sample sizes. . . .