Analyzing Hybrid Randomized Response Data with a Binomial Selection Procedure

Abstract

The operating characteristics (OCs) of an indifference-zone ranking and selection procedure are derived for randomized response binomial data. The OCs include tables and figures to facilitate tradeoffs between sample size and a stated probability of a correct selection, i.e., correctly identifying the binomial population (out of k ≥ 2) characterized by the largest probability of success. Measures of efficiency are provided to assist the analyst in selection of an appropriate randomized response design for the collection of the data. A hybrid randomized response model, which includes the Warner model and the Greenberg et al. model, is introduced to facilitate comparisons among a wider range of statistical designs than previously available. An example comparing failure rates of contraceptive methods is used to illustrate the use of these new results.

Keywords:

• Contaminated data
• Indifference-zone selection procedure
• Operating characteristics
• Probability of a correct selection
• Sample size determination

Mathematics Subject Classification:

• Primary 62F07
• Secondary 62D05