Scrambled randomized response methods for obtaining sensitive quantitative data

We study a multiplicative randomized response method for obtaining responses to sensitive questions when the answers are quantitative. The method involves the respondent multiplying his sensitive answer by a random number from a known distribution, and giving the product to the interviewer, who does not know the value of the random number and thus receives a scrambled response. Some particular distributions for the random scrambling number are proposed and studied, and ways of generating the scrambling numbers are discussed. Some modifications for increasing the efficiency of the method are proposed, and numerical results are given that show the scrambled response method is generally superior to the previously used method of randomizing questions.