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How to find 95% confidence interval for binomial data in R?
The binomial data has two parameters, the sample size and the number of successes. To find the 95% confidence interval we just need to use prop.test function in R but we need to make sure that we put correct argument to FALSE so that the confidence interval will be calculated without continuity correction. In the below examples, we have found the 95% confidence interval for different values of sample size and number of successes.
Example
prop.test(x=25,n=100,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 25 out of 100, null probability 0.5 X-squared = 25, df = 1, p-value = 5.733e-07 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.1754521 0.3430446 sample estimates: p 0.25
Example
prop.test(x=5,n=100,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 5 out of 100, null probability 0.5 X-squared = 81, df = 1, p-value < 2.2e-16 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.02154368 0.11175047 sample estimates: p 0.05
Example
prop.test(x=5,n=1000,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 5 out of 1000, null probability 0.5 X-squared = 980.1, df = 1, p-value < 2.2e-16 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.002137536 0.011650955 sample estimates: p 0.005
Example
prop.test(x=5,n=10,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 5 out of 1000, null probability 0.5 X-squared = 980.1, df = 1, p-value < 2.2e-16 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.002137536 0.011650955 sample estimates: p 0.005
Example
prop.test(x=50,n=100,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 50 out of 100, null probability 0.5 X-squared = 0, df = 1, p-value = 1 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.4038315 0.5961685 sample estimates: p 0.5
Example
prop.test(x=500,n=1125,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 500 out of 1125, null probability 0.5 X-squared = 13.889, df = 1, p-value = 0.0001939 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.4156458 0.4736212 sample estimates: p 0.4444444
Example
prop.test(x=5000,n=9874,conf.level=0.95,correct=FALSE)
Output
1-sample proportions test without continuity correction data: 5000 out of 9874, null probability 0.5 X-squared = 1.6079, df = 1, p-value = 0.2048 alternative hypothesis: true p is not equal to 0.5 95 percent confidence interval: 0.4965185 0.5162373 sample estimates: p 0.5063804
Updated on: 10-Oct-2020
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