prec_prop returns the sample size or the precision for the provided proportion.

prec_prop(
p,
n = NULL,
conf.width = NULL,
conf.level = 0.95,
method = c("wilson", "agresti-coull", "exact", "wald"),
...
)

## Arguments

p

proportion.

n

number of observations.

conf.width

precision (the full width of the confidence interval).

conf.level

confidence level.

method

The method to use to calculate precision. Exactly one method may be provided. Methods can be abbreviated.

...

other arguments to uniroot (e.g. tol).

## Value

Object of class "presize", a list of arguments (including the computed one) augmented with method and note elements. In the wilson and agresti-coull formula, the p from which the confidence interval is calculated is adjusted by a term (i.e. $$p + term \pm ci$$). This adjusted p is returned in padj.

## Details

Exactly one of the parameters n or conf.width must be passed as NULL, and that parameter is determined from the other.

The wilson, agresti-coull, exact, and wald method are implemented. The wilson method is suggested for small n (< 40), and the agresti-coull method is suggested for larger n (see reference). The wald method is not suggested, but provided due to its widely distributed use.

uniroot is used to solve n for the agresti-coull, wilson, and exact methods. Agresti-coull can be abbreviated by ac.

## References

Brown LD, Cai TT, DasGupta A (2001) Interval Estimation for a Binomial Proportion, Statistical Science, 16:2, 101-117, doi:10.1214/ss/1009213286

binom.test, binom.confint in package binom, and binconf in package Hmisc

## Examples

# CI width for 15\% with 50 participants
prec_prop(0.15, n = 50)
#> Warning: more than one method was chosen, 'wilson' will be used
#>
#>      precision for a proportion with Wilson confidence interval.
#>
#>      p      padj  n conf.width conf.level        lwr       upr
#> 1 0.15 0.1749717 50  0.1971842       0.95 0.07637956 0.2735638
#>
#> NOTE: padj is the adjusted proportion, from which the ci is calculated.
#>
# number of participants for 15\% with a CI width of 0.2
prec_prop(0.15, conf.width = 0.2)
#> Warning: more than one method was chosen, 'wilson' will be used
#>
#>      sample size for a proportion with Wilson confidence interval.
#>
#>      p      padj        n conf.width conf.level        lwr       upr
#> 1 0.15 0.1756455 48.58521        0.2       0.95 0.07564555 0.2756455
#>
#> NOTE: padj is the adjusted proportion, from which the ci is calculated.
#>
# confidence interval width for a range of scenarios between 10 and 90\% with
#  100 participants via the wilson method
prec_prop(p = 1:9 / 10, n = 100, method = "wilson")
#>
#>      precision for a proportion with Wilson confidence interval.
#>
#>     p      padj   n conf.width conf.level        lwr       upr
#> 1 0.1 0.1147974 100  0.1191365       0.95 0.05522914 0.1743657
#> 2 0.2 0.2110980 100  0.1554622       0.95 0.13336693 0.2888292
#> 3 0.3 0.3073987 100  0.1768997       0.95 0.21894885 0.3958485
#> 4 0.4 0.4036993 100  0.1885961       0.95 0.30940129 0.4979974
#> 5 0.5 0.5000000 100  0.1923369       0.95 0.40383153 0.5961685
#> 6 0.6 0.5963007 100  0.1885961       0.95 0.50200259 0.6905987
#> 7 0.7 0.6926013 100  0.1768997       0.95 0.60415145 0.7810511
#> 8 0.8 0.7889020 100  0.1554622       0.95 0.71117083 0.8666331
#> 9 0.9 0.8852026 100  0.1191365       0.95 0.82563434 0.9447709
#>
#> NOTE: padj is the adjusted proportion, from which the ci is calculated.
#>
# number of participants for a range of scenarios between 10 and 90\% with
#  a CI of 0.192 via the wilson method
prec_prop(p = 1:9 / 10, conf.width = .192, method = "wilson")
#>
#>      sample size for a proportion with Wilson confidence interval.
#>
#>     p      padj         n conf.width conf.level       lwr       upr
#> 1 0.1 0.1353927  39.57381      0.192       0.95 0.0393927 0.2313927
#> 2 0.2 0.2167537  64.94554      0.192       0.95 0.1207537 0.3127537
#> 3 0.3 0.3087050  84.41747      0.192       0.95 0.2127050 0.4047050
#> 4 0.4 0.4038339  96.35634      0.192       0.95 0.3078339 0.4998339
#> 5 0.5 0.5000000 100.36478      0.192       0.95 0.4040000 0.5960000
#> 6 0.6 0.5961661  96.35634      0.192       0.95 0.5001661 0.6921661
#> 7 0.7 0.6912950  84.41747      0.192       0.95 0.5952950 0.7872950
#> 8 0.8 0.7832463  64.94554      0.192       0.95 0.6872463 0.8792463
#> 9 0.9 0.8646073  39.57381      0.192       0.95 0.7686073 0.9606073
#>
#> NOTE: padj is the adjusted proportion, from which the ci is calculated.
#>