RANDOMIZED RESPONSE METHOD FOR POTENTIALLY. EVASIVE ANSWERS. Seyda Deligonul. Graduate School of Management. St. John Fisher College.
Quality Engineering
ISSN: 0898-2112 (Print) 1532-4222 (Online) Journal homepage: http://www.tandfonline.com/loi/lqen20
RANDOMIZED RESPONSE METHOD FOR POTENTIALLY EVASIVE ANSWERS Seyda Deligonul To cite this article: Seyda Deligonul (1997) RANDOMIZED RESPONSE METHOD FOR POTENTIALLY EVASIVE ANSWERS, Quality Engineering, 10:1, 43-47, DOI: 10.1080/08982119708919107 To link to this article: http://dx.doi.org/10.1080/08982119708919107
Published online: 29 Mar 2007.
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Date: 14 December 2015, At: 08:44
Quality Engineering, 10(1), 43-47 (1997-98)
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RANDOMIZED RESPONSE METHOD FOR POTENTIALLY EVASIVE ANSWERS Seyda Deligonul Graduate School of Management St. John Fisher College Rochester, New York 14618
Key Words Bias reduction; Linear programming; Questionnaire; Randomization; Response bias; Survey techniques.
Introduction Surveys in total quality management call frequently for gathering information on sensitive topics such as employee satisfaction, conflict situations, private views, emotions, feelings, perceptions, and power struggles. These topics are all vulnerable to response distortion. The pessimistic view of management goes even further. It claims the following (1):
Professional lives are embraced by a bundle of extreme sensitivities stemming from the way management is practiced. Work camouflages coercion using the pretense of maintaining cohesion. Organizations conceal conflict under the guise of consensus and convert conformity into a semblance of creativity. Managers give unilateral decisions a codeterminist seal of approval. ,* They delay actions in the supposed interests of consultation. Management legitimizes lack of leadership and disguises expedient arguments and personal agendas.
Copyright
1997 by Marcel Dekker, Inc.
According to postmodernists, the camouflage of excessive specialization, task standardization, and repetitive tasks deskill employees subtly. Are these merely claims based on aberrations or pervasive rules of the organizational realm? Do we have resilient tools to nullify (or support) these claims? What if our instruments themselves are partial to the situation or sensitive to the intimidation? Aside from these problems, the randomized response method discussed in this article has a potential to defeat answer distortions when the topic becomes overly private, sensitive, or socially critical. So the next time your survey calls for answers concerning income, how one feels about the job or the boss, or private preferences about life, including sensitive issues such as abortion, drugs, job satisfaction, race, social loafing, sex, and so on, you might consider the techniques of this article as a potential instrument. You may also consider designing your own randomized method by following the outline presented. In a survey-based analysis of a managerial process, response distortion is a difficult problem. This is understandable; we live a socially constructed life. In there, a question, when perceived to be socially undesirable, may be coped with by an evasive answer. This belief may be natural for our desire of acceptance by the faceless but compelling crowd in which we all live. Not that we are all liars, but we feel that information we deem private is one of a personal concern. Then, the question becomes that of how one can reach and uncover the truthful answers to
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sensitive questions. Is there a way to get answers in prejudicial topics without making the interviewee uncomfortable? How is it possible to deal with the answer bias for questions which are susceptible to response distortion? This article offers an optimization methodology to improve the validity of survey answers to sensitive topics. It is an extension of the early models of the randomized response approach but differs from them in the estimation procedure. Our estimation is based on a linear programming model which builds on probabilistic arguments and randomized responses.
Randomized Response One answer to the problem of response bias is to shield the anonymity of the respondent. This is exactly what the randomized response method attempts to do. In its simplest form, this technique endows anonymity by inviting the "yes" answer to one stigmatized question out of a pack of questions directed to a group of respondents. In the pack, one question is on the sensitive topic, the other(s) is (are) innocuous. The interviewee chooses one of the questions randomly, innocuous or otherwise. Then, without revealing the choice, helshe privately records the answer as a "yes" or "no." When the responses are counted, even if the resultant answer is "yes," the interviewer will not be able to tell what the pertinent question was. This way, by not revealing the connection between answer and question, the interviewee shields his or her choice. The resulting anonymity of the process is believed to encourage truthful answers. However, in this method, despite the intraceability of individual answers, the interview structure can be arranged to estimate the proportion of stigmatized "yes" answers out of the pool of all "yes" answers. There are a number of ways to achieve this. The traditional approach relies on asking either a related or unrelated pack of questions under various forms of randomization strategies. These techniques are briefly summarized with examples in the following two sections. Then, in the following section, we propose a different technique to estimate the proportion of stigmatized "yes" answers for sensitive questions.
Related-Questions Approach Example The audience is instructed to think of the last digit of their phone numbers. If it is 6 or smaller, they are asked to answer the first question, otherwise the second.
A. I hate my boss? B. I don't hate my boss? Say that the count of the true answers turns out to be 60% of all the answers. Then, the value 0.60 must come from 70% of the "true" answers for A and 30% of the "false" answers for B. But a false answer to B implies true for A. Therefore, we can compute the unknown as 0.60 = 0.70p(TJA) + O.3O[l.O - p(TI A)]. A more formal probabilistic argument leading to this result follows.
Discussion In literature, many forms of randomization and interview constructions are proposed for this situation. In the earlier approaches (2,3), mutually exclusive questions are adopted for which a true-false response is sought. Say that we have the following pair of questions: A. I am a member of group A? B. I am not a member of group A? p(T) = P(T on question A) + P(T on question B) = P(question A is chosen) P(T answer given that question A is chosen) + P(question B is chosen) P(T answer given that question B is chosen). We can write this as
where P(True) = p(T) P(question A is chosen) = p, P(question B is chosen) = p, P(T answer given that question A is chosen) = p(T I A) P(T answer given that question B is chosen) = p(T 1 B) As can be seen from the above equation, p, cannot be 112 for our purposes. However, one can avoid this difficulty by setting the probability of choosing question A (i.e., p,) to a different value in a suitable randomization strategy. Additionally, p(T), on the left-hand side of the equation, comes from the answer count. Only unknown on the right side, p(T I A) is the desired answer. Warner (3) shows that, under the assumption of truthful answers, the procedure provides an unbiased estimate of the true population proportion. He gives the variance of p(T I A) for n number of respondents as
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Unrelated-Questions Approach Example To demonstrate the randomized response method, I tell my audience in one of my seminars to choose an arbitrary number between 1 and 100. Next, I show them the following statements: A. B.
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C.
If your number is between 1 and 49, answer the question, "Have you ever cheated on an exam?" If your number is between 50 and 84. answer the question, "Do you know your name?" If your number is between 85 and 100, answer the question, "Do you know Socrates's birthday?"
Here, B and C serve as disguises for the answers in A. A count is made of "yes" and "no" answers. Say that the "yes" answers add up to 40% of all answers. Of this, 0.35 must come from the obvious question about the name for which we assume a 100% affirmative answer, given that one looks at category B and answers the question truthfully. The remaining 0.05 is the half of the affirmative answers to the stigmatized question of cheating. Therefore, 10% of the students admit the embarrassing situation of cheating on an exam. A more formal probabilistic argument leading to this result follows. Discussion
In this approach, question and answer decoupling provides the cover for the stigmatized "yes" answer (4). Our example was designed to demonstrate the case with multiple cover questions. In this example, the following probabilities are assigned by design: P(question A is chosen) = p, = 0.50 P(question B is chosen) = p, = 0.35 P(question C is chosen) = p, = 0.15 These values are chosen arbitrarily, Further, it is assumed that P(yes answer p(Yes1 B) = P(yes answer p(Yes1C) =
given that question B is chosen) = 1 given that question C is chosen) = 0
Then, according to the following probability equation, one can compute the count of stigmatized yes answers as p(Yes I A):
Following Greenberg et al. (5). we conclude that for given p(Yes 1 B) and p(Yes I C), the equation gives us an unbiased estimate of p(Yes I A) with the variance
Variances for different methods are useful to compute confidence intervals for the estimates for the desired probability of the answer "yes" given A. Also, the above equation suggests that the variance of the unrelated question model is smaller than the variance of the related model (See Ref. 6.)
Multiple Randomization to Improve Consistency Example Let us take the following question triplets: A.
My boss increases my pessimism about the future.
B. My boss is a model for me to follow. C.
I have no faith in my boss.
(These questions, with modifications, are taken from the charisma dimension of the Bass's multifactor leadership questionnaire MLQ-1; see Ref. 7.) For the randomization, we ask our audience to choose a number between 1 and 100 again. Then, we take counts on "yes" answers in multiple consecutive rounds. In the first round, we request all those who chose numbers between 41 and 100 to answer question A, between 11 and 40 to answer B, and 1 and 10 to answer C. This is given in the first row of Table 1. This assignment scheme gives everyone a chance to take part in A, B, or C categories with the probabilities 0.60, 0.30, and 0.10, respectively. Then, we count the percentage of "yes" answers. The third row in Table 1 gives these
Table I .
Multiple-Round Example and Its Parameters
Round 1 Probability Yes answer
41-100 (A) 0.60 0.30
11-40 (B) 0.30
1-10 (C) '0.10
Round 2 Probability Yes answer
1-10 (A) 0.10 0.20
41-100 (B) 0.60
11-40 (C) 0.30
Round 3 Probability Yes answer
11-@(A) 0.30 0.50
1-10(B) 0.10
41-100 (C) 0.60
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counts. In the second round, we changed the assignments to 1-10 as A. 41-100 as B, and 11-40 as C. We take the count and record the percentage of "yesn answers. These are also given in the table. The other rows of the table have similar interpretations. Then, we plug our data into the right-hand side of the equation
Say that our prediction of the left-hand side underestimates the actual value by d+ and overestimates it by &. Because we desire a good estimate, we are required to keep the sum of deviations as small as possible. This leads to the following formulation of a linear program: Min d ;
+ d; +
+ d; '+ d; + d;;
Round 1 0.60p(Yes I A)
+ 0.30p(Yes 1 B) + 0. lOp(Yes ( C)
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Table 2. Solution of the Linear Program Using LINDO MIN DIP + D M + DZP + DZM + D3P + D3M SVBTEcl' TO 0.3 DIP D M + 0.6 PA + 0.3 PB + 0.1 PC = 2) 3) D2P D2M + 0.1 PA + 0.6 PB + 0.3 PC = 0.2 4) D3P D3M + 0.3 PA + 0.1 PB + 0.6 PC 0.5 5) PA
