C.2 Confidence intervals

For statistics whose sampling distribution has an approximate normal distribution, confidence intervals (CIs) have the form $\text{statistic} \pm \big( \text{multiplier} \times \text{s.e.}(\text{statistic})\big).$

Notes:

The multiplier is approximately $2$ to create an approximate $95$ % CI (based on the $68$ -- $95$ -- $99.7$ rule).
The quantity ' $\text{multiplier} \times \text{s.e.}(\text{statistic})$ ' is called the margin of error.
Software uses exact multipliers to form exact confidence intervals.
When the sampling distribution for the statistic does not have an approximate normal distribution (e.g., for ORs and correlation coefficients), this formula does not apply and the CIs are taken directly from software output when available.