Illustrative Simulated Empirical Findings ........................................... Warner’s RR versus Unrelated Question Model-Based RR in Unequal Probability Sampling as against
Let us artificially consider N = 113 particular persons. For each of them labeled i = 1, …, N (=113), let yi denote that the ith person is “a habitual gambler” when it is valued 1 and “not so” when it is valued 0; likewise, let xi = 1 if ith person prefers cricket to football and xi = 0 in the opposite case. Let the individual (yi, xi) values be known resulting in
θ = = = =∑ ∑y
1 10 8230 0 7345. .and
Suppose a sample of size n is considered using (1) SRSWR, (2) SRSWOR, and (3) by Rao-Hartley-Cochran Scheme separately and independently from U = (1, …, N = 113). We consider (1) the CRR case when each sampled person gives an RR by a “method” specified and the (2) case when the first n1 (<n) of them gives an RR and the remaining n2 = n − n1 of them give a DR each. We illustrate the situation when n = 33, n1 = 24, and n2 = 9. The, RR schemes considered separately are (A) Warner’s and (B) Simmons’ with prescribed p and (p1, p2), respectively. To draw an RHC sample, the person’s last month pocket expenses in dollars zi are taken as the known size measures.