Sample versus population SD in DEBIT

[lhdjung]

The formula difference is just whether N is used directly (as the population SD) or as N/N-1 as the sample SD. The sample SD as per the preprint is certainly more common - but not used exclusively - so that might be worth documenting as a possible reason for discrepancies?

Originally posted by @LukasWallrich in #61 (comment)

[lhdjung]

For reference, the formulas for SDs of binary data are:

• Sample SD (DEBIT preprint, p. 5): $\sqrt{ \frac{N}{N - 1} \times \frac{ab}{N^2} }$
  where $a$ and $b$ are the group sizes

• Population SD (@LukasWallrich here): $\sqrt{ \frac{M (1 - M)}{N} }$

Edit: population SD implementation:

sd_binary_population <- function(mean, n) {
  sqrt(mean * (1 - mean) / n)
}