Confidence interval for binomial data in R?

Question

I know that I need mean and s.d to find the interval, however, what if the question is:

For a survey of 1,000 randomly chosen workers, 520 of them are female. Create a 95% confidence interval for the proportion of workers who are female based on the survey.

How do I find mean and s.d for that?

Perhaps look at the answers posted here: http://stackoverflow.com/questions/17802320/r-proportion-confidence-interval-factor — Mark Miller, Feb 12 '14 at 07:50

gd047 · Accepted Answer · 2023-05-25T14:07:47.633

34

You can also use prop.test from package stats, or binom.test

prop.test(x, n, conf.level=0.95, correct = FALSE)

        1-sample proportions test without continuity correction

data:  x out of n, null probability 0.5
X-squared = 1.6, df = 1, p-value = 0.2059
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.4890177 0.5508292
sample estimates:
   p 
0.52

You may find interesting the article TWO-SIDED CONFIDENCE INTERVALS FOR THE SINGLE PROPORTION: COMPARISON OF SEVEN METHODS, where in Table 1 on page 861 are given different confidence intervals, for a single proportion, calculated using seven methods (for selected combinations of n and r). Using prop.test you can get the results found in rows 3 and 4 of the table, while binom.test returns what you see in row 5.

edited May 25 '23 at 14:07

answered Feb 12 '14 at 07:59

gd047

29,749
18
107
146

Nice answer, and it doesn't require any external packages. – thelatemail Feb 12 '14 at 22:13
@thelatemail This is probably a dumb question, but how do you take that 95% CI and turn it into a SE and then an SD? – Alexander Jan 14 '16 at 17:12
prop.test gives very strange results. If you compare it with SAS. I would prefer to use binconf from Hmisc package (see @Zbynek answer) with known method for CI calculation. – crow16384 Jun 21 '21 at 07:44
The link is broken – Julien May 24 '23 at 07:57
@Julien I think I found it. I've updated the link. – gd047 May 25 '23 at 14:08

Zbynek · Answer 2 · 2014-02-12T07:47:10.093

22

In this case, you have binomial distribution, so you will be calculating binomial proportion confidence interval.

In R, you can use binconf() from package Hmisc

> binconf(x=520, n=1000)
 PointEst     Lower     Upper
     0.52 0.4890177 0.5508292

Or you can calculate it yourself:

> p <- 520/1000
> p + c(-qnorm(0.975),qnorm(0.975))*sqrt((1/1000)*p*(1-p))
[1] 0.4890345 0.5509655

edited Feb 12 '14 at 07:47

answered Feb 12 '14 at 06:34

Zbynek

5,673
6
30
52

What would q-norm be is you use 99% confidence interval? – DeMelkbroer Sep 12 '19 at 10:26
`qnorm(0.99)` is 2.326348 – Zbynek Sep 16 '19 at 08:49

score 21 · Answer 3 · edited Apr 28 '23 at 15:53

Alternatively, use function propCI from the prevalence package, to get the five most commonly used binomial confidence intervals:

> library(prevalence)
> propCI(x = 520, n = 1000)
    x    n    p        method level     lower     upper
1 520 1000 0.52 agresti.coull  0.95 0.4890176 0.5508293
2 520 1000 0.52         exact  0.95 0.4885149 0.5513671
3 520 1000 0.52      jeffreys  0.95 0.4890147 0.5508698
4 520 1000 0.52          wald  0.95 0.4890351 0.5509649
5 520 1000 0.52        wilson  0.95 0.4890177 0.5508292

score 6 · Answer 4 · edited Apr 28 '23 at 15:54

6

Another package: tolerance will calculate confidence / tolerance ranges for a ton of typical distribution functions.

edited Apr 28 '23 at 15:54

Rui Barradas

70,273
8
34
66

answered Feb 12 '14 at 12:42

Carl Witthoft

20,573
9
43
73

wow, that package `tolerance` is comprehensive & thorough. outstanding recommendation! – cmo Mar 20 '19 at 13:57

Confidence interval for binomial data in R?

4 Answers4

Linked