A new randomized response technique for estimating the population total, or the population mean of a quantitative variable is proposed. It provides a high degree of protection to the respondents because they never report their data. Therefore, it may be favorably perceived by them and increase their willingness to cooperate. Instead of revealing the true value of the characteristic under investigation, the respondent only states whether the value is greater (or smaller) than a number which is selected by him/her at random and is unknown to the interviewer. For each respondent, this number, a sort of individual threshold, is generated as a pseudorandom number. Furthermore, two modifications of the proposed technique are presented. The first modification assumes that the interviewer also knows the generated random number. The second modification deals with the issue that, for certain variables, such as income, it may be embarrassing for the respondents to report either high or low values. Thus, depending on the value of the fixed threshold (unknown to the respondent), the respondent is asked different questions to avoid being embarrassed. The suggested approach is applied in detail to the simple random sampling without replacement, but it can be, after a straightforward modification, applied to many sampling schemes, including cluster sampling, two-stage sampling, or stratified sampling. The results of the simulations illustrate the behavior of the proposed technique.

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