SAS/IML program required to calculate sample size to ensure sufficient reliability to reach the desired width for the percentile confidence interval. (DOCX 67 kb) In particular, 10,000 iteration simulation studies were conducted to calculate the probability of simulated coverage of accurate and approximate confidence intervals for percentiles in a standard distribution N (0, 1). The sample size is six different sizes: No. 10, 20, 30, 50, 100 and 200. In addition, eight probabilities of percentiles are studied: p – 0.025, 0.05, 0.10, 0.20, 0.80, 0.90, 0.95 and 0.975. For each replication, the lower and upper confidence limits () (“widehat” (Uptheta) L , “”uptheta” U, DIE A/ (“widehat” (“breithat” – “uptheta”) AL, “widehat” and “uptheta” and “breithat”) were calculated to establish unilateral confidence intervals of 95 and 97.5%, as well as reciprocal confidence intervals of 90 and 95%. The probability of simulated coverage was the proportion of 10,000 replications whose confidence interval contained the normal percentile of the population. Second, the adequacy of one- and two-side interval procedures is determined by error – simulated coverage probability – nominal probability of coverage. The results are summarized in Tables 1, 2, 3 and 4 for precise and approximate confidence intervals with two-sided confidence coefficient 1 – α – 0.90 and 0.95. Additional SAS/IML and R computer programs are made available to use embedded statistical functions to calculate precise confidence intervals. We see in section V6:Y8 of Figure 3 of Bland-Altman Plot that the 95% confidence interval is for the average [-366, 3,396] while the 95% confidence interval for compliance levels is [-9.606, 12,636]. To illustrate the characteristics and differences of the two proposed sample size methods for an accurate estimate of the interval of normal percentiles, numerical calculations are used to p – 0.025, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 0.95 and 0.975 depending on the expected width and reliability criteria.

Settings configurations are defined as μ 0, 2 – 1, 1 – α – 0.95 during empirical evaluation. In addition, the two thresholds of the expected width are δ 0.5 and 1.0. For the background assessment, the four parameters indicated are 1 – γ – 0.80 and 0.9 combined with s – 0.5 and 1.0. These configurations are selected to reflect the common sampling sizes used in typical search settings. For a simple representation, the calculated sample sizes are presented in Figure 2. Hahn GJ, Meeker WQ. Statistical intervals: a guide for practitioners. New York: Wiley; 1991 where δ (> 0) is a constant. On the other hand, the minimum sample size required to ensure, with some probability of guarantee, that the width of a bilateral confidence interval of 100 (1 – α) does not exceed the expected value: from the point of view of the study project, it is important to determine the optimal sample sizes so that the resulting confidence interval meets the expected precision requirement. Two particularly useful criteria relate to the control of expected width and the reliability of width within a given limit (Beal [26]; Kupper and Hafner [27]). The values obtained for the average and the limits of the match are based on a single sample and may therefore reflect or not the values for the population as a whole. It is therefore useful to consider the confiscated intervals for these values.

To calculate these confidence intervals, we first note that the standard errors for averages and agreement limits are Barnhart HX, Haber MJ, Lin LI.