# Reviews multiple packages for getting confidence interval of a proportion.
# Here, we'll be computing confidence interval for gender = male

#install.packages('DescTools')
#install.packages('PropCIs')
#install.packages('plyr')
library(DescTools)
library(PropCIs)
library(plyr)
library(ggplot2)

#The program first needs you to compute frequency of success and total N

count(Wk06$gender)

##   x freq
## 1 1   10
## 2 2   18

#The binom.test and BinomCI comes from DescTools. Define group 1 (male) as "success"

binom.test(10, 28, 
           0.5,
           alternative="two.sided",
           conf.level=0.95)

## 
##  Exact binomial test
## 
## data:  10 and 28
## number of successes = 10, number of trials = 28, p-value = 0.1849
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1864067 0.5593497
## sample estimates:
## probability of success 
##              0.3571429

BinomCI(10,28,
        conf.level = 0.95,
        method = "clopper-pearson")

##            est    lwr.ci    upr.ci
## [1,] 0.3571429 0.1864067 0.5593497

#You can compute confidence intervals for both success and failure in one step

observed = c(10,18)

total = sum(observed)

BinomCI(observed, total,
        conf.level = 0.95,
        method = "clopper-pearson")

##           est    lwr.ci    upr.ci
## x.1 0.3571429 0.1864067 0.5593497
## x.2 0.6428571 0.4406503 0.8135933

#Alternative approaches from the PropCIs, including "exact" and "Blaker exact"

exactci(10,28, 
        conf.level=0.95)

## 
## 
## 
## data:  
## 
## 95 percent confidence interval:
##  0.1864067 0.5593497

blakerci(10,28, 
         conf.level=0.95)

## 
## 
## 
## data:  
## 
## 95 percent confidence interval:
##  0.1924667 0.5553797