Sample size determination for estimating prevalence and a difference between two prevalences of sensitive attributes using the non-randomized triangular design

A non-randomized triangular design has been shown to be more efficient than the conventional random response model in estimating the prevalence of sensitive attributes in surveys. Since most surveys focus on estimation, herein we derive sample size formulas for estimation of prevalence and a difference between two prevalences in this design. In contrast to the conventional approach to sample size estimation, we explicitly incorporate into the formulas an assurance probability of achieving the pre-specified precision. Exact evaluation results demonstrate that these formulas perform well. The methods are illustrated using data from a real study.