Coverage and Precision of Net Promoter Score Confidence Intervals Across Sampling Distributions

The Net Promoter Score (NPS) is a widely used metric for customer loyalty in business. However, the current theoretical gaps in the literature suggest practical refinements for real-world applications. In this simulation study, we use an unbiased estimator of the variance for the sample NPS to examine coverage and width for three different confidence interval methods: Wald, bootstrap t, and adjusted Wald with weights corresponding to four underlying population distribution shapes: extreme (E), left-skewed (LS), triangular (T), and uniform (U). As the sample size increased, all methods approached the nominal 95% coverage rate with an exception for the extreme population; the adjusted Wald method with triangular and uniform weights is particularly robust among the representative population shapes examined. All adjusted Wald methods performed comparably in width, especially at a larger n. The confidence interval width depended on the population shape. Overall, the Wald and bootstrap t methods should be avoided at small sample sizes and are not recommended. Our methods raise awareness of the sampling distribution of the NPS statistic, provide a theoretical basis for an unbiased estimator of the variance, and assess reliable confidence interval construction. These results provide an informed application of NPS and lay the foundation for future methodological development.