Sample Sizes for the Crosswise and Triangular Models

Sample size calculation is an essential component in survey designs on sensitive topics. In this chapter, we will discuss sample size calculation for the crosswise and triangular models based on the power analysis method for both one-sample and two-sample problems. In Section 4.1, we briefly introduce two methods (i.e., the precision analysis method and the power analysis method) for sample size calculations. In Section 4.2, we consider one-sample problem and derive sample size formulae for the triangular model for both one-and two-sided tests based on the large-sample normal approximation. Evaluation of the performance is conducted by comparing exact power with asymptotic power and by calculating n

T and the ratio n

D . In Section

4.3, we obtain sample sizes for the crosswise model for a one-sample problem. In Section 4.4, we numerically compare sample sizes required for the crosswise design with those needed for the triangular design. A theoretical justification is also provided. In Section 4.5, we obtain a sample size formula for the triangular model for a two-sample problem. An example about an induced abortion study in Taiwan is presented to illustrate these methods in Section 4.6 (see Tian et al., 2011).