Minimum sample size for estimating the Net Promoter Score under a Bayesian approach.

At some moment in our lives, we are probably faced with the following question: How likely is it that you would recommend [company X] to a friend or colleague?. This question is related to the Net Promoter Score (NPS), a simple measure used by several companies as indicator of customer loyalty. Even though it is a well-known measure in the business world, studies that address the statistical properties or the sample size determination problem related to this measure are still scarce. We adopt a Bayesian approach to provide point and interval estimators for the NPS and discuss the determination of the sample size. Computational tools were implemented to use this methodology in practice. An illustrative example with data from financial services is also presented.

Sample size for estimating the mean concentration of organisms in ballast water.

We consider the computation of sample sizes for estimating the mean concentration of organisms in ballast water. Given the possible heterogeneity of their distribution in the tank, we adopt a negative binomial model to obtain confidence intervals for the mean concentration. We show that the results obtained by Chen and Chen (2012) in a different set-up hold for the proposed model and use them to develop algorithms to compute sample sizes both in cases where the mean concentration is known to lie in some bounded interval or where there is no information about its range. We also construct simple diagrams that may be easily employed to decide for compliance with the D-2 regulation of the International Maritime Organization (IMO).

Implications of heterogeneous distributions of organisms on ballast water sampling.

Ballast water sampling is one of the problems still needing investigation in order to enforce the D-2 Regulation of the International Convention for the Control and Management of Ship Ballast Water and Sediments. Although statistical "representativeness" of the sample is an issue usually discussed in the literature, neither a definition nor a clear description of its implications are presented. In this context, we relate it to the heterogeneity of the distribution of organisms in ballast water and show how to specify compliance tests under different models based on the Poisson and negative binomial distributions. We provide algorithms to obtain minimum sample volumes required to satisfy fixed limits on the probabilities of Type I and II errors. We show that when the sample consists of a large number of aliquots, the Poisson model may be employed even under moderate heterogeneity of the distribution of the organisms in the ballast water tank.