lect9 - THE RANDOMIZED RESPONSE SCHEME VARIANCE AND...

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THE RANDOMIZED RESPONSE SCHEME I S Outline THE RANDOMIZED RESPONSE SCHEME Point Estimate Interval Estimate VARIANCE AND STANDARD DEVIATION Variance of Sums of Independent Random Variables Mean and Variance of Binomials RANDOMIZED RESPONSE SCHEME REVISITED Statistical Inference 1 / 16 Xinghua Zheng Lect 9: Randomized response scheme, standard deviation
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THE RANDOMIZED RESPONSE SCHEME I S Point Estimate Interval Estimate THE RANDOMIZED RESPONSE SCHEME If you directly ask others a sensitive question, you’re likely to get a dishonest answer E.g., Have you fallen in love with another boy/girl when you are not available? Q: How to find the percentage of people who have the property specified by a sensitive question? The randomized response scheme : ask the interviewees to do the following 1. flip a (fair) coin twice (and keep the results secret) 2. If a head comes up on the 1st toss, then he/she answers the sensitive question 3. Otherwise he/she answers an innocuous question like “Did you get a head on the 2nd toss?” 2 / 16 Xinghua Zheng Lect 9: Randomized response scheme, standard deviation
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THE RANDOMIZED RESPONSE SCHEME I S Point Estimate Interval Estimate THE RANDOMIZED RESPONSE SCHEME, ctd Since the question an interviewee is answering is chosen at random by his/her private coin tosses, no one will know how to interpret a “Yes” answer: It could be a “Yes” answer to the sensitive question. But it could also be a “Yes” answer to the innocuous question. Similarly, for a “No” answer. Given the ambiguity in a “Yes” and “No” answer, hopefully the interviewee will feel free to answer the sensitive question honestly, if he/she is supposed to answer that question. 3 / 16 Xinghua Zheng Lect 9: Randomized response scheme, standard deviation
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THE RANDOMIZED RESPONSE SCHEME I S Point Estimate Interval Estimate RELATING PERCENT “YES” TO PERCENT “HAVES” Let p be the fraction among the interviewees who have the property specified by the sensitive question.
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This note was uploaded on 11/27/2011 for the course ISOM 3540 taught by Professor Zheu during the Spring '11 term at HKUST.

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lect9 - THE RANDOMIZED RESPONSE SCHEME VARIANCE AND...

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