ABSTRACT
In Chapter 7, we introduced a general framework of design and analysis for the parallel model to estimate the unknown proportion, π = Pr(Y = 1), of individuals with a sensitive characteristic in a specific population. The presented survey design is based on the introduction of two non-sensitive dichotomous variates U and W such that Y , U and W are mutually independent. The presented statistical analysis methods are based on the assumption of known proportions θ = Pr(U = 1) and p = Pr(W = 1). However, in survey practice, it is usually difficult to choose an appropriate non-sensitive dichotomous variate U with known θ = Pr(U = 1). Even if such a binary variate U can be found and a constant θ0 is assumed to be equal to the true value of the θ, testing the hypothesis H0: θ = θ0 is still not available for the parallel design. The purpose of this chapter is to present a variant of the parallel model with θ = Pr(U = 1) being unknown.
