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Margin of error (rounded)
Point Sample Absolute * Relative **
estimate size
(%)
0.1 100 0.06*** 60***
0.2 100 0.08 40
0.3 100 0.09 30
0.4 100 0.096 24
0.5 100 0.10 20
0.6 100 0.096 16
0.7 100 0.09 12
0.8 100 0.08 9.8
0.9 100 0.06 6.5
0.1 400 0.03 30
0.2 400 0.04 20
0.3 400 0.045 15
0.4 400 0.048 12
0.5 400 0.05 10
0.6 400 0.048 8.0
0.7 400 0.045 6.4
0.8 400 0.04 4.9
0.9 400 0.03 3.2
* Approximate half-width of 95% confidence interval in absolute terms
** Approximate half-width of 95% confidence interval in absolute terms, relative to the size of
the point estimate
*** Calculation: 1.96 (1/√[(0.01)(1 – 0.01) / 100]) = 1.96 (0.03) = 0.0588 ≈ 0.06 absolute
error margin
This table illustrates that:
1. quadrupling sample size halves the margin of error.
2. absolute error margin decreases as the point estimate moves away from 0.5
3. relative error margin is inversely – and very strongly – related to the size of the point
estimate
For very small point estimates, as illustrated in the following table, very large samples are required to
obtain a small relative margin of error. Even a sample size of 2,500 still produces a relative error
margin of 17% for a proportion of 0.05.
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www.sph.unc.edu/courses/EPID 168, © Victor J. Schoenbach 14. Data analysis and interpretation – 490
rev. 11/8/1998, 10/26/1999, 12/26/1999