Asking sensitive questions: A statistical power analysis of randomized response models.

Abstract

This article derives the power curves for a Wald test that can be applied to randomized response models when small prevalence rates must be assessed (e.g., detecting doping behavior among elite athletes). These curves enable the assessment of the statistical power that is associated with each model (e.g., Warner's model, crosswise model, unrelated question model, forced-choice models, item count model, cheater detection model). This power analysis can help in choosing the optimal model and sample size and in setting model parameters in survey studies. The general framework can be applied to all existing randomized response model versions. The Appendix of this article contains worked-out numerical examples to demonstrate the power analysis for each specific model.

Randomized Response Estimates for the 12‐Month Prevalence of Cognitive‐Enhancing Drug Use in University Students

“…The null hypothesis of this power analysis assumes that = 0. Under this assumption, a sample size of 2500 provides a power of approximately 0.85 for rejecting the null hypothesis …”

“…Under this assumption, a sample size of 2500 provides a power of approximately 0.85 for rejecting the null hypothesis. 20…”

RRreg: An R Package for Correlation and Regression Analyses of Randomized Response Data

“…Package RRreg provides functions to assess two major practical issues that have to be considered in any RR application: statistical power and robustness. The RR technique necessarily reduces statistical power, because it adds random noise to the responses by design (Ulrich, Schröter, Striegel, and Simon 2012). Therefore, compared to standard correlation and regression analyses, larger sample sizes are required to obtain the same level of precision.…”

Multiple sensitive estimation and optimal sample size allocation in the item sum technique

“…Useful and detailed studies on recent methodological advances, more complex estimation problems and new challenges may be found, among others, in Arcos, Rueda, and Singh (), Barabesi, Diana, and Perri (, ), Diana and Perri (), Fox, Entink, and Avetisyan (), Glynn (), Groenitz (), Hoffmann and Musch (), Hoffmann, Diedenhofen, Verschuere, and Musch (), Hussain, Shabbir, and Shabbir (), Ibrahim (), Imai (), Imai, Park, and Greene (), Liu and Tian (), Moshagen, Hilbig, Erdfelder, and Moritz (), Nepusz, Petróczi, Naughton, Epton, and Norman (), Perri and van der Heijden (), Petróczi et al. (), Rueda, Cobo, and Arcos (), Tsuchiya (), Ulrich, Schörter, Striegel, and Simon (), Wu and Tang ().…”

“…For a comprehensive review of the topic, interested readers are referred to Fox and Tracy (1986), Chaudhuri and Mukerjee (1988), Chaudhuri (2011), Chaudhuri and Christofides (2013), Tian and Tang (2014). Useful and detailed studies on recent methodological advances, more complex estimation problems and new challenges may be found, among others, in Arcos, Rueda, and Singh (2015), Perri (2013, 2015), Perri (2011), Fox, Entink, andAvetisyan (2014), Glynn (2013), Groenitz (2014), , Hoffmann, Diedenhofen, Verschuere, and Musch (2016), Hussain, Shabbir, and Shabbir (2015), Ibrahim (2016), Imai (2011), Imai, Park, and Greene (2015), Liu and Tian (2013), Moshagen, Hilbig, Erdfelder, and Moritz (2014), Nepusz, Petróczi, Naughton, Epton, and Norman (2014), Perri and van der Heijden (2012), Petróczi et al (2011), Rueda, Cobo, and Arcos (2016), Tsuchiya (2005), Ulrich, Schörter, Striegel, and Simon (2012), Wu and Tang (2016).…”