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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
Updated on: 11-Aug-2021
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