On Estimation of Mean and Sensitivity Level of a Stigmatizing Variable Using Two Stage Scrambling

Procuring reliable data on sensitive/stigmatizing variables is a tricky issue in many social surveys. When questioned through direct questioning respondents may report evasive answers on such sensitive variables. Consequently, a bias creeps into the estimates based on evasive answers. Different indirect questioning methods such as Item Count Technique, Three Cards Method and Randomized Response Technique (or Scrambled Response Technique) are available. The present article considers unbiased estimation of mean and sensitivity level of a sensitive variable via scrambled response modeling. The idea of dividing the sample into two subsamples has been explored further by using a separate randomization device in each subsample. Additionally, the probability of reporting the true response is distributed into two randomization stages. Relative efficiency comparisons are also made, numerically, in order to highlight the performance of proposed scrambling technique. The proposed technique resulted in relatively more precise estimation of mean but the estimator of sensitivity level is seen to be relatively less efficient. The use of proposed scrambling technique is recommended for use in the surveys where estimation of mean is of prime interest.