No. of correct answers | No. of samples | |||||
10 | 10 | 14 | 20 | 30 | 30 | |
No. of correct answers | 90% CI | 90% CI | No. of correct answers | |||
n/n | 10/10 | 76.2 to 99.5 | 81.9 to 99.7 | 86.7 to 99.8 | 90.8 to 99.8 | 30/30 |
n–1/n | 9/10 | 63.6 to 96.7 | 72.1 to 97.6 | 79.3 to 98.3 | 85.6 to 98.8 | 29/30 |
n–2/n | 8/10 | 53.0 to 92.1 | 63.7 to 94.3 | 72.9 to 96.0 | 81.1 to 97.3 | 28/30 |
n–3/n | 7/10 | 43.6 to 86.5 | 56.0 to 90.3 | 67.1 to 93.2 | 76.8 to 95.5 | 27/30 |
n–4/n | 6/10 | 35.0 to 80.0 | 48.9 to 85.8 | 61.6 to 90.1 | 72.9 to 93.4 | 26/30 |
n–5/n | 5/10 | 27.1 to 72.9 | 42.3 to 80.9 | 56.3 to 86.8 | 69.0 to 91.2 | 25/30 |
n–6/n | 4/10 | 20.0 to 65.0 | 36.0 to 75.6 | 51.3 to 83.2 | 65.3 to 88.9 | 24/30 |
n–7/n | 3/10 | 13.5 to 56.4 | 30.0 to 70.0 | 46.4 to 79.4 | 61.7 to 86.5 | 23/30 |
n–8/n | 2/10 | 7.9 to 47.0 | 24.4 to 64.0 | 41.7 to 75.5 | 58.2 to 83.9 | 22/30 |
n–9/n | 1/10 | 3.3 to 36.4 | 19.1 to 57.7 | 37.2 to 71.4 | 54.8 to 81.3 | 21/30 |
n–10/n | 0/10 | 0.5 to 23.8 | 14.2 to 51.1 | 32.8 to 67.2 | 51.5 to 78.7 | 20/30 |
For a specific set of samples in proficiency testing (n=10, 14, 20 and 30), the 90% confidence interval (CI), which is the region between the 5th percentile and 95th percentile of the posterior probability distribution) is shown for the success rate (fraction of correct answers×100%). The 90% CI is constructed with Bayesian statistics21 assuming uniform prior probability for the success rate on the interval between 0 and 1.