Formula to calculate standard error using 95% confidence interval

Question

I have a column containing 95% confidence intervals as shown below. I would like to calculate standard error using the formula SE = (upper limit – lower limit)/3.92 in R studio.

I would like to know how to calculate SE when the upper limit and lower limit are in the same as shown below:

Answer 1

You want to first separate lower bound and upper bound into two columns.

interval <- c("(0.023, 0.031)", "(-0.031, -0.022)")
lim <- do.call("rbind", stringr::str_extract_all(interval, "[+-]?[0-9\\.]+"))
mode(lim) <- "numeric"
lim
#       [,1]   [,2]
#[1,]  0.023  0.031
#[2,] -0.031 -0.022

Then you can use your formula:

(lim[, 2] - lim[, 1]) / 3.92
#[1] 0.002040816 0.002295918

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Note for others: 3.96 = 1.96 * 2, and 1.96 is -qnorm(0.025) .