How to find confidence interval for binomial distribution in R?

To find confidence interval for binomial distribution in R, we can use binom.confint function of binom package. This will result in confidence intervals based on many different methods. Check out the below examples to understand how it can be done.

Example 1

Loading Binom package and finding 95% confidence interval for a binomial distribution with sample of size 20 in which 5 outcomes are favourable −

library(binom)
binom.confint(5,20,conf.level=0.95)

Output

      method    x n    mean       lower     upper
1 agresti-coull 5 20 0.2500000 0.10808718 0.4724754
2 asymptotic    5 20 0.2500000 0.06022730 0.4397727
3 bayes         5 20 0.2619048 0.08992554 0.4465447
4 cloglog       5 20 0.2500000 0.09099388 0.4485345
5 exact         5 20 0.2500000 0.08657147 0.4910459
6 logit         5 20 0.2500000 0.10805797 0.4783907
7 probit        5 20 0.2500000 0.10174363 0.4691922
8 profile       5 20 0.2500000 0.09790183 0.4624698
9 lrt           5 20 0.2500000 0.09784246 0.4624509
10 prop.test    5 20 0.2500000 0.09593259 0.4941155
11 wilson       5 20 0.2500000 0.11186170 0.4687009

Example2

Loading Binom package and finding 95% confidence interval for a binomial distribution with three samples of sizes 20 in which 1, 5, and 10 outcomes are favourable −

library(binom)
binom.confint(c(1,5,10),rep(20,3),conf.level=0.95)

Output

      method     x n     mean          lower    upper
1  agresti-coull 1 20 0.05000000 -0.0091018717 0.2541145
2  agresti-coull 5 20 0.25000000 0.1080871818 0.4724754
3  agresti-coull 10 20 0.50000000 0.2992980082 0.7007020
4  asymptotic    1 20 0.05000000 -0.0455168294 0.1455168
5  asymptotic    5 20 0.25000000 0.0602273032 0.4397727
6  asymptotic   10 20 0.50000000 0.2808693649 0.7191306
7  bayes         1 20 0.07142857 0.0001187325 0.1796346
8  bayes         5 20 0.26190476 0.0899255405 0.4465447
9  bayes        10 20 0.50000000 0.2933764847 0.7066235
10 cloglog       1 20 0.05000000 0.0034540161 0.2052993
11 cloglog       5 20 0.25000000 0.0909938830 0.4485345
12 cloglog      10 20 0.50000000 0.2713277573 0.6918925
13 exact         1 20 0.05000000 0.0012650895 0.2487328
14 exact         5 20 0.25000000 0.0865714691 0.4910459
15 exact         10 20 0.50000000 0.2719578496 0.7280422
16 logit          1 20 0.05000000 0.0069965317 0.2822034
17 logit          5 20 0.25000000 0.1080579663 0.4783907
18 logit         10 20 0.50000000 0.2938989119 0.7061011
19 probit         1 20 0.05000000 0.0050705318 0.2361551
20 probit         5 20 0.25000000 0.1017436289 0.4691922
21 probit        10 20 0.50000000 0.2914069826 0.7085930
22 profile        1 20 0.05000000 0.0048919016 0.2022422
23 profile        5 20 0.25000000 0.0979018304 0.4624698
24 profile       10 20 0.50000000 0.2910140565 0.7089859
25 lrt            1 20 0.05000000 0.0029056199 0.2022295
26 lrt            5 20 0.25000000 0.0978424584 0.4624509
27 lrt           10 20 0.50000000 0.2909826477 0.7090174
28 prop.test      1 20 0.05000000 0.0026155551 0.2694437
29 prop.test      5 20 0.25000000 0.0959325919 0.4941155
30 prop.test     10 20 0.50000000 0.2992980082 0.7007020
31 wilson         1 20 0.05000000 0.0088814488 0.2361312
32 wilson         5 20 0.25000000 0.1118617014 0.4687009
33 wilson        10 20 0.50000000 0.2992980082 0.7007020

Example3

Loading Binom package and finding 95% confidence interval for a binomial distribution with three samples of sizes 10 in which 1, 2, and 3 outcomes are favourable −

library(binom)
binom.confint(1:3,rep(10,3),conf.level=0.95)

Output

     method      x n       mean    lower       upper
1  agresti-coull 1 10 0.1000000 -0.0039414975 0.4259677
2  agresti-coull 2 10 0.2000000 0.0458872705 0.5206324
3  agresti-coull 3 10 0.3000000 0.1033384179 0.6076747
4  asymptotic    1 10 0.1000000 -0.0859385097 0.2859385
5  asymptotic    2 10 0.2000000 -0.0479180129 0.4479180
6  asymptotic    3 10 0.3000000 0.0159742349 0.5840258
7  bayes         1 10 0.1363636 0.0003602864 0.3308030
8  bayes         2 10 0.2272727 0.0234655042 0.4618984
9  bayes         3 10 0.3181818 0.0745442290 0.5794516
10 cloglog       1 10 0.1000000 0.0057234564 0.3581275
11 cloglog       2 10 0.2000000 0.0309090243 0.4747147
12 cloglog       3 10 0.3000000 0.0711344923 0.5778673
13 exact         1 10 0.1000000 0.0025285785 0.4450161
14 exact         2 10 0.2000000 0.0252107263 0.5560955
15 exact         3 10 0.3000000 0.0667395112 0.6524529
16 logit         1 10 0.1000000 0.0138816573 0.4672367
17 logit         2 10 0.2000000 0.0504128149 0.5407080
18 logit         3 10 0.3000000 0.0997683156 0.6236819
19 probit        1 10 0.1000000 0.0096150450 0.4121325
20 probit        2 10 0.2000000 0.0420691842 0.5175162
21 probit        3 10 0.3000000 0.0899134733 0.6150429
22 profile       1 10 0.1000000 0.0096116957 0.3716898
23 profile       2 10 0.2000000 0.0371119907 0.4994288
24 profile       3 10 0.3000000 0.0847027179 0.6065091
25 lrt           1 10 0.1000000 0.0059948560 0.3716367
26 lrt           2 10 0.2000000 0.0363654430 0.4994445
27 lrt           3 10 0.3000000 0.0845854470 0.6065389
28 prop.test     1 10 0.1000000 0.0052423016 0.4588460
29 prop.test     2 10 0.2000000 0.0354269437 0.5578186
30 prop.test     3 10 0.3000000 0.0809478242 0.6463293
31 wilson        1 10 0.1000000 0.0178762131 0.4041500
32 wilson        2 10 0.2000000 0.0566821515 0.5098375
33 wilson       3 10 0.3000000 0 .1077912674 0.6032219