Approximate (1-alpha)100% confidence interval for proportion of a population

Approximate (1-alpha)100% confidence interval for proportion of a population

prop.ci(n, pest = 0.5, N = Inf, alpha = 0.05)

Arguments

n	Sample size
pest	Estimated positive proportion
N	Population size (default implies infinite population)
alpha	The confidence interval is (1-alpha)*100%

Details

Note that this value is generally similar to that obtained with the sampling based approach in truepos_given_sample when pest=0.5 but becomes an increasingly bad approximation as the proportion tends to 0 or 1.

References

See https://onlinecourses.science.psu.edu/stat414/node/264

See also

Other population-sampling: required.sample.size, sample_finite_population, truepos_given_sample

Examples

# 95% confidence interval for population size 43, sample size 10 and estimated
# proportion of 0.1 ...
# expressed as a proportion
prop.ci(10, pest=0.1, N=43)
#> [1] -0.06481687  0.26481687
# as a number of positives
prop.ci(10, pest=0.1, N=43)*43
#> [1] -2.787126 11.387126

## Compare with sampling based calculation
prop.ci(10, pest=0.5, N=48, alpha=.1)*48
#> [1] 12.77513 35.22487
summary(truepos_given_sample(samplepos = 5, n=10, N=48))
#>     5% Median   Mode    95% 
#>     15     25     26     35 
# more different
prop.ci(10, pest=0.2, N=48, alpha=.1)*48
#> [1]  0.620103 18.579897
summary(truepos_given_sample(samplepos = 2, n=10, N=48))
#>     5% Median   Mode    95% 
#>      5     12     10     22