What is the confidence interval formula that RMISC package in R uses? [closed]

Question

I tried figuring out the formula that the RMISC package uses but I wasn't sure, I couldn't find the documentation on it? I tried using the t, and Z statistic but it wasn't giving me the same answer as this package. Any recommendations?

Answer 1

The CI function uses the following formula:

$$ \bar{x} \pm t_{\alpha/2, n-1}\times \frac{s}{\sqrt{n}} $$ where $t_{\alpha/2, n-1}$ is the upper $\alpha/2$ critical point of a $t$ distribution with $n-1$ degrees of freedom.

Example

In the following example, I'm drawing 50 random variables from a normal distribution with mean 100 and standard deviation 15 (the values don't matter).

library(Rmisc)

set.seed(142857)
x <- rnorm(50, 100, 15) # draw 50 rvs from a normal distribution

xbar <- mean(x)
s <- sd(x)
n <- length(x)

# Calculate the confidence interval by hand
xbar + c(-1, 1)*qt(0.975, n -1)*(s/sqrt(n))
[1]  96.18685 105.28056

# Use the "CI" function from the package
CI(x, 0.95)
    upper      mean     lower 
105.28056 100.73370  96.18685

The two confidence limits are exactly the same.

To see what formula the function CI uses, you can look at the source code by typing CI in to the R console without the parentheses. Like that:

CI

function (x, ci = 0.95) 
{
    a <- mean(x)
    s <- sd(x)
    n <- length(x)
    error <- qt(ci + (1 - ci)/2, df = n - 1) * s/sqrt(n)
    return(c(upper = a + error, mean = a, lower = a - error))
}