Nomological validity is the extent to which the measurement instrument correlates in theoretically predictable ways with measures of different but related constructs.
The authors conducted a survey of 159 respondents at a Midwest university for attitudes toward banking services, cell phone services, and hairdresser/barber services. The authors asked the 11-point LTR, a three-item WOM in seven-point scales, three purchase intent scales, and three satisfaction scales. The authors found strong correlations between customer satisfaction and repurchase intention and the NPS. The correlation between NPS and mean repurchase intentions is r = .88 compared to the mean of the three-item WOM measure and purchase intentions (r = .95).
Note that the authors in this paper used a relatively small sample size of students and did not correlate the attitudinal data to actual purchases. Instead they used only stated purchase intent collected from the same respondents in the same survey, likely inflating the correlations. They found that the three-item measure of WOM was a better predictor of purchase intentions, but not by much.
Takeaway: The authors show the NPS correlates (r = .88) with stated repurchase intentions (not actual purchases) but isn’t as strong a predictor as a three-item measure of word of mouth (r = .95).