Bootstrap (percentile interval)

The bootstrap estimates the uncertainty of a statistic for which there is no simple formula (for example the indirect effect a·b). Statable draws 5000 new samples of the same size with replacement from the people, recalculates the statistic each time and takes the limits at 2.5% and 97.5% of the ordered results as the 95% confidence interval (percentile interval). With a fixed seed, the same data always give the same interval.

Example: ab = 0.42, 95% bootstrap CI [0.27, 0.58]: in 95% of the 5000 new samples, a·b lay between 0.27 and 0.58. If the interval does not include 0, this is statistical evidence for an effect.

Caution: With few people (below about 50) the interval is imprecise and often too narrow. A different seed shifts the limits only slightly; if a limit is very close to 0, the conclusion can change.