combined_sd: Combined standard deviation

Description

Given mean, standard deviation, and N for some set of groups, calculate the combined standard deviation. Note that the groups may not overlap.

combined_sd(
  group_mean,
  group_sd,
  group_n,
  unbiased = TRUE,
  na.rm = TRUE,
  log10 = FALSE
)

Numeric: the standard deviation of the combined population (i.e. if all the groups were concatenated into one large group).

group_mean: Numeric vector: Observed sample means for summary data, or observed values for non-summary data. Censored observations should *not* be NA; they should be substituted with some value at or below the corresponding LOQ (e.g. LOQ or LOQ/2). Even if `log10 should *not* be log10-transformed.
group_sd: Numeric vector: Observed sample SDs for summary data. For non-summary data (individual-subject observations), the corresponding element of `group_sd` should be set to 0. Even if `log10 should *not* be log10-transformed.
group_n: Numeric vector: Observed sample number of subjects for summary data. For non-summary data (individual-subject observations), `group_n` should be set to 1.
unbiased: Logical. If TRUE (the default), then `group_sd` is assumed to be the unbiased estimator of population standard deviation (i.e. calculated using `n-1` in the denominator -- the way that `stats::sd()` calculates it), and the returned combined SD is also the unbiased estimator of the combined population SD. If FALSE, then `group_sd` is assumed to be the biased estimator (using `n` in the denominator), and the returned value is also the biased estimator of the combined population SD.
na.rm: Logical. If TRUE (default), then any groups where mean, SD, *or* N were NA will be dropped. If FALSE, they will be retained (and the result will be NA).
log10: Logical. If TRUE, the standard deviations are from log10-transformed values.

Caroline Ring