R 如何根据比例计算置信区间

Question

I'm new to R and trying to learn stats.. Here is one practice question that I'm trying to figure out How should I use R code to create a function based on this math equation?

I have a dataframe like this the "exposed" column from the df contains two groups, one is called"Test Group (Exposed)" the other one is called "Control Group". So the math function is referring to these two groups.

In another practice I have these codes here to calculate the confidence interval

# sample size
# OK for non normal data if n > 30
n <- 150

# calculate the mean & standard deviation
will_mean <- mean(will_sample)
will_s <- sd(will_sample)

# normal quantile function, assuming mean has a normal distribution:
qnorm(p=0.975, mean=0, sd=1) # 97.5th percentile for a N(0,1) distribution
# a.k.a. Z = 1.96 from the standard normal distribution

# calculate standard error of the mean
# standard error of the mean = mean +/- critical value x (s/sqrt(n))
# "q" functions in r give the value of the statistic at a given quantile
critical_value <- qt(p=0.975, df=n-1)
error <- critical_value * will_s/sqrt(n)

# confidence inverval 
will_mean - error
will_mean + error

but I'm not sure how to do the exposed 2 groups

Answer 1

Don't worry it's quite easy if you have experience in at least one programming language, R is quite trivial. The only remarkable difference between R and most of other programming languanges is that R was developed for statistical purposes. You can compute what is the quantile for a certain significance level α (reminds to divide it by 2 for your formula) by using the function qnorm() . By default it is set up for standardized normal distribution, like in your case, but you can get more details using the documentation, reachable by the command ?qnorm() . Actually in the exercise you are not required to compute it, since you have to pass it as argument, but in reality you need to. The code should be something like:

conf <- function(p1,p2,n1,n2,z){
      part = z*(p1*(1-p1)/n1+p2*(1-p2)/n2)**(1/2)
      return(c(p1-p2-part,
               p1-p2+part))
}