How to Calculate a Binomial Confidence Interval in R?

In this article, we will discuss how to calculate a Binomial Confidence interval in R Programming Language. We can calculate Binomial Confidence Interval by using the below formulae:

p  +/-  z*(√p(1-p) / n)

where,

• p is for the  proportion of successes
• z is  the chosen value
• n is the  sample size

We can calculate by using the below methods

Method 1: Use the prop.test() function

This function is used to calculate the 95% binomial confidence interval.

Syntax: prop.test(x, n, conf.level=.95, correct=FALSE)

where,

• x is the input variable
• n is the sample size
• conf.level is the confidence level which is used to calculate the 95% binomial confidence interval.

# calculate for 34
print(prop.test(x = 34, n = 100, 
                conf.level = .95, 
                correct = FALSE))

Output:

    1-sample proportions test without continuity correction

data:  34 out of 100, null probability 0.5
X-squared = 10.24, df = 1, p-value = 0.001374
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.2546152 0.4372227
sample estimates:
   p 
0.34 

Method 2: Use the binconf() function

binconf() function is available in the Hmisc package. To install this package run the following commands:

install.packages("Hmisc")

Syntax of binconf(): 

Syntax: binconf(x, n, alpha)

where

• x is the input variable
• n is the sample size
• alpha is the binomial confidence level

# load the library
library(Hmisc)

# calculate for 34 with 95%confidence level
print(binconf(x=34, n=100,
              alpha=.05))

Output:

 PointEst     Lower     Upper
     0.34 0.2546152 0.4372227

Method 3: Calculate the Confidence Interval with Formulae

In this method, we will use binomial confidence interval in R using this formula:

Syntax: p + c(-qnorm(1-a/2), qnorm(1-a/2))*sqrt((1/100)*p*(1-p))

where,

• p is the proportional value
• a is the significance level

# p value
p = 52/56

# alpha  value
a = 0.05

# calculate binomial  interval
print(p + c(-qnorm(1-a/2),
            qnorm(1-a/2))*sqrt((1/100)*p*(1-p)))

Output:

[1] 0.8780946 0.9790482

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Article Tags :

• R Language
• R-Statistics