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Supplement 2:
Asking Sensitive Questions in
Surveys
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-1
“Sex can wait until we are married,
say youngsters” 2007-02-12 HK Standard
 Young people say sex before marriage is not widely acceptable, although it
is perceived to be so, a survey has found.
 The Hong Kong Sex Culture Society, a Christian group, polled 943 students
from tertiary institutions and found that 51.3 percent felt that pre-marital
sexual intercourse is acceptable, but the remainder disagreed.
 Nearly 30 percent of those interviewed said they would have a problem if
their life-long partners were not virgins before marriage and another 41
percent said otherwise.
 Despite the divergence of attitudes to sex, 411 students said kissing is the
most commonly acceptable form of intimate behavior, while 27.4 percent
preferred sexual intercourse, followed by 13.6 percent who opted for
caressing.
 According to the poll, students with a religious background are sexually
more conservative and have stronger faith in life-long marriages.
 More than half the students, or 448, who were mostly polled through
Internet questionnaires and a small portion by street interviews, are
religious, with 434 of them being Christians.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-2
Examples of sensitive questions
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Have you
Have you
Have you
Have you
Have you
Have you
Have you
Have you
Ka-fu Wong © 2007
ever used illegal drugs?
ever had an abortion?
had more than one sexual partner in the past 6 months?
ever driven a motor vehicle while intoxicated?
ever shoplifted?
cheated in exam in the past six months?
ever attempted suicide?
ever invaded tax?
ECON1003: Analysis of Economic Data
Supplement2-3
Asking Sensitive Questions in
Surveys
 How to frame a question so that the respondents have no incentive
to lie?
 Only if your answer to the survey question cannot be used to infer
your true answer to the intended question.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-4
The survey question
 Spin a coin twice. Show no one the results. If the first spin resulted
in a head, answer the question marked H. If the first spin resulted
in a tail, answer the question marked T.
 H: Did you have one or more sexual partners in the past 12
months?
 T: Did the second spin of the coin result in a tail?
The respondent has no incentive to lie because only the
respondent knows which question he / she is responding to.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-5
The calculations
 The respondent will answer question H with probability q and T
with probability (1-q). If the coin is fair, q=0.5.
 Let the known probability of a YES to question T be r. If the coin is
fair, r=0.5.
 Let p be the proportion of students who have one or more sexual
partners in the past 12 months. That is, those who answer YES to
question H.
 So, the probability of answering YES to the question is
Prob(YES) =q*p + (1-q)*r
 Hence, p = [ Prob(YES) –(1-q)*r ] / q.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-6
Did you pay tax?
 According to a survey done by the National Bureau of Statistics of
China in 2002 (covering about 700 residents of Beijing, Shanghai
and Guangzhou):
Did you pay tax according to you income, in time?
I paid the full amount of my personal tax.
24.7%
I paid only part of my personal tax
33.4%
I should have paid, but I did not.
18.2%
I was not eligible to pay tax.
23.0%
Did not answer.
0.7%
Source: http://www.stats.gov.cn/was40/reldetail.jsp?docid=21970
薪酬系列调查之二：个税调节力度不够
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-7
References:
 “Randomized Response” by Donald Bentley of Pomona College
provide a good summary of the technical issues, as well as a list of
classic references on the topic.
(http://www.dartmouth.edu/~chance/teaching_aids/RResponse/RResponse.html)
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-8
Supplement 2:
Asking Sensitive Questions in Surveys
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Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement2-9