For example, the data in Table 4.4 are measurements of Forced Expiratory Volume in one second (FEV1) for 57 male medical students:
2.85 | 3.19 | 3.50 | 3.69 | 3.90 | 4.14 | 4.32 | 4.50 | 4.80 | 5.20 |
2.85 | 3.20 | 3.54 | 3.70 | 3.96 | 4.16 | 4.44 | 4.56 | 4.80 | 5.30 |
2.98 | 3.30 | 3.54 | 3.70 | 4.05 | 4.20 | 4.47 | 4.68 | 4.90 | 5.43 |
3.04 | 3.39 | 3.57 | 3.75 | 4.08 | 4.20 | 4.47 | 4.70 | 5.00 | |
3.10 | 3.42 | 3.60 | 3.78 | 4.10 | 4.30 | 4.47 | 4.71 | 5.10 | |
3.10 | 3.48 | 3.60 | 3.83 | 4.14 | 4.30 | 4.50 | 4.78 | 5.10 |
For these FEV1 data the median is 4.1, the 29th value in the Table. For
the 95% confidence interval for the median, n = 57 and q
= 0.5, and
j = 57 × 0.5 − 1.96 × √(57 × 0.5 × (1−0.5)) = 21.10
k = 57 × 0.5 + 1.96 × √(57 × 0.5 × (1−0.5)) = 35.90
The 95% confidence interval is thus from the 22nd to the 36th observation,
3.75 to 4.30 litres from the Table. Compare this to the 95% confidence
interval for the mean, 3.9 to 4.2 litres, which is completely included
in the interval for the median. This method of estimating percentiles is
relatively imprecise. Another example is given in
Section 15.5.
Adapted from page 110 of An Introduction to Medical Statistics by Martin Bland, 2015, reproduced by permission of Oxford University Press.
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Last updated: 7 August, 2015.