Quality & Quantity 38: 675–680, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
On Estimating the Proportion of a Qualitative
Sensitive Character Using Randomized Response
, CHIH-LI WANG
and KUO-CHUNG HUANG
Department of Management Sciences, Tamkang University, Tamsui, Taipei, Taiwan 251, R.O.C.
Department of Applied Statistics and Information Sciences, Mingchuan University, Taoyuan,
Taiwan 333, R.O.C.
Department of Business Administration, Chung-Yu Junior Institute of Technology, Keelung, Taiwan
Abstract. In this paper, we present results pertaining to investigations concerning randomized re-
sponse sampling. We consider a simple generalization for some existing investigations, and then
provide the suitable choices for design parameters. It is also demonstrated the superiority of the
proposed procedure over Warner (1965) procedure.
To procure reliable sample data for estimating π, the proportion of respondents
possessing a sensitive attribute A, Warner (1965) proposed an ingenious procedure,
called randomized response technique. In this procedure, a simple random sample
of size n is drawn from the population with replacement. Each sampled-respondent
is provided with a suitable randomization device that comprises of two statements
viz. “I am a member of A”, and “I am not a member of A”, represented with
and 1 − p
, respectively. The respondent randomly chooses one
statement and report “yes” or “no” with respect to his/her actual status, without
revealing to the interviewer which of the two statements he/she has chosen. Thus,
in this whole procedure, privacy of the respondent is maintained.
Assuming truthful reporting, the probability of “yes” answer, λ
π + (1 − p
)(1 − π). (1.1)
− (1 − p