Table 1.

Accuracy of percentiles calculated in samples with various sizes from normally and log-normally distributed population data. Results are presented as average percentile, the average of the relative differences (%) and their standard deviation (SD).

Method	Sample size	Normal distribution		Log-normal distribution

		95^th percentile		5^th percentile		95^th percentile

		Average	% Difference (SD)	Average	% Difference (SD)	Average	% Difference (SD)
A: p(n+1)	Population (n=10⁶)	1.64		0.02		44.16
	20	1.85	12.20 (31.06)	0.03	18.92 (141.23)	180.43	308.61 (1766.28)
	120	1.68	1.85 (11.88)	0.02	2.97 (46.85)	52.76	19.49 (59.86)
	500	1.65	0.47 (5.78)	0.02	0.82 (22.28)	46.01	4.20 (23.12)
	1000	1.65	0.24 (4.07)	0.02	0.42 (15.69)	45.13	2.21 (16.00)
B: pn+0.5	Population (n=10⁶)	1.64		0.02		44.16
	20	1.64	-0.56 (25.48)	0.04	83.31 (179.54)	114.69	159.73 (973.07)
	120	1.64	-0.33 (11.37)	0.03	11.74 (48.61)	48.43	9.69 (52.26)
	500	1.64	-0.07 (5.72)	0.02	2.77 (22.48)	45.16	2.27 (22.52)
	1000	1.64	-0.02 (4.05)	0.02	1.44 (15.76)	44.64	1.09 (15.70)
C: p(n-1)+1	Population (n=10⁶)	1.64		0.02		44.16
	20	1.43	-12.97 (24.17)	0.06	147.81 (244.30)	48.07	8.87 (174.14)
	120	1.60	-2.50 (11.39)	0.03	20.77 (52.38)	44.18	0.05 (47.04)
	500	1.64	-0.59 (5.71)	0.02	4.82 (22.90)	44.24	0.19 (22.16)
	1000	1.64	-0.28 (4.06)	0.02	2.46 (15.92)	44.21	0.12 (15.60)
D: p(n+1/3)+1/3	Population (n=10⁶)	1.64		0.02		44.16
	20	1.71	3.80 (27.05)	0.04	61.98 (163.85)	138.42	213.47 (1367.82)
	120	1.65	0.44 (11.52)	0.02	8.55 (47.85)	49.96	13.15 (54.94)
	500	1.65	0.12 (5.69)	0.02	2.15 (22.37)	45.44	2.91 (22.72)
	1000	1.65	0.07 (4.07)	0.02	1.07 (15.72)	44.79	1.43 (15.79)