NAP (nonoverlap of all pairs)

NAP compares every measurement of the baseline (A) with every measurement of the intervention phase (B). It counts in how many of these pairs the B value is better than the A value; a tie counts half. The result lies between 0 and 1: 0.5 means no difference, 1 means every B value is better than every A value. According to Parker and Vannest (2009), up to .65 is weak, up to .92 medium, from .93 strong. NAP is the probability that a randomly drawn B value is better than a randomly drawn A value (equal to the AUC). The Newcombe confidence interval shows how uncertain the value is with few measurements.

Example: NAP = .97, 95% CI [.70, 1.00], p = .003: in 97% of all A-B pairs the value in B is better.

Caution: NAP does not take a trend already during baseline into account and reaches 1 as soon as every B value is better - it does not show by how much. The p value (Mann-Whitney) assumes independent measurements, which time series often do not provide. The grouping into weak, medium and strong is a rule of thumb.