A percentile is a numerical measure that represents the reference point below which a certain percentage of the target population values decreases. Because of the conceptual simplicity and the uns contextal characteristic, percentiles are often used to determine the relative size and essential importance of quantitative measurements in all scientific fields. For example, children`s health conditions are often assessed on the basis of weight and height relative to national averages and national percentiles in growth charts. In addition, reference limits in medicine and related fields are widely applied to identify an informative amount of measurement from a reference population. The most typical reference limits are the central 95% of the interest population. As an important application, Bland and Altman`s compliance limits [1, 2] are composed of 95% of the 2.5th percentile and the 97.5th percentile for the distribution of the difference between the melted measurements. Although the practical implementation of the exact Method of the Carkeet Interval [19] is well illustrated, the explanation of the differences between the exact and approximate methods has mainly focused on the relative sizes and symmetrical/asymmetrical limits of the resulting confidence limits. On the other hand, Bland-Altman`s 95% agreement limits are generally considered to be related to the measurement of compliance in comparing methods. Carkeet [19] and Carkeet and Goh [20] therefore focused on comparing approximate confidence intervals for the upper and lower limits of torque chords and tolerance intervals on both sides for normal distribution. Therefore, the particular benefit of precise interval procedures and the ability to limit approximate confidence intervals for each upper and lower limit of the Carkeet [19] and De Carkeet and Goh [20] agreement were not fully discussed. It is practical to conduct a detailed assessment of the accuracy and discrepancy between exact and approximate interval methods for an individual match limit in a multitude of model configurations.

The problem of achieving a uniform confidence interval to cover both limitations of the agreement at the same time is more involved and an in-depth discussion on this subject goes beyond the scope of this study. Carkeet A, Goh YT. Confidence and coverage for Bland-Altman limits the agreement and their approximate confidence intervals. Med Res Stat Methods. 2018;27:1559-74. Errors in the three types of confidence intervals resulting showed that the exact approach works very well in the 96 cases presented in Tables 1, 2, 3 and 4. For the two approximate methods of Chakraborti and Li [24] and Bland and Altman [2], the odds of coverage of their bilateral interval remain fairly close to the nominal confidence level.