Survey Methodology Barbara Kowalczyk SGH Warsw School of Economics

Transcription

1 Survey Methodology Barbara Kowalczyk SGH Warsw School of Economics Uwaga: materiały objęte są prawami autorskimi i udostępnione są studentom SGH z przedmiotu Teoria i projektowanie badań reprezentacyjnych tylko na potrzeby wykładu bez prawa do dalszego rozpowszechniania

2 Sensitive questions Private Stigmatizing Socially unaccepted Illegal e.g. drug uses, beating children, politically incorrect views, voting (only in some countries), atypical sexual behaviors, abortion, bribery of officials (corruption), tax frauds, illegal work (black market)

3 Sensitive questions Direct methods of questioning ensuring anonymity creating an atmosphere of trust redirecting focus: e.g. not Have you ever hit your wife? but rather How many times have you hit your wife? using authority: e.g. Many people from the school authorities used to smoke marihuana in their youth. Have you ever tried marihuana? Indirect methods of questioning

4 Sensitive questions Indirect methods of questioning It is not possible to prove to the respondent that he or she possesses the sensitive attribute Researcher does not know if particular respondent possesses the sensitive attribute or not It is still possible to inference about population proportion of people who have the sensitive attribute Full privacy is assure usually at the expense of the efficiency of the estimation (larger samples sizes are needed)

5 Randomized response technique RRT Non-related question design Please take out any banknote you have. If the last number of the serial number on your banknote (do not show it to me) is 0,1,2,3,4 or 5 please answer the question: Have you ever bribed an official? If the last number of the serial number on your banknote (do not show it to me) is 6, 7, 8 or 9 please answer the question: Where you born in an even month of the year?

6 Non-related question design Greenberg at al. (1969) n sample size q probability of answering the sensitive question (1-q) probability of answering the non-related question r probability of answering YES to the non-related question p - unknown probability of answering YES to the sensitive question

7 Non-related question desisgn n nq n(1-q) YES NO YES NO nqp nq(1-p) n(1-q)r n(1-q)(1-r) All YESes nqp+n(1-q)r p All YESes n(1 q)r nq

8 Item Count Technique Survey respondents are randomly assigned to either the control or treatment group, n = n C + n T Respondents in the control group are given a list of J neutral questions (or statements) with binary outcomes Respondents in the treatment group are given a list of J+1 questions, J the same neutral questions as in the control group plus 1 sensitive Respondents are asked to report only the total of their Yes (or True) answers. In the control group it can be a number from 0 to J, in the treatment group it can be a number from 0 to J+1.

9 Item Count Technique (Conrol group) Now I m going to read you three things that sometimes make people angry or upset. After I read all three, just tell me HOW MANY of them upset you. (I don t want to know which ones, just how many) the federal government increasing the tax on gasoline; professional athletes getting million-dollar-plus salaries; large corporations polluting the environment. How many, if any, of these things upset you? Source: Imai K., (2011), Multivariate regression analysis for the item count technique, Journal of American Statistical Associasion, 206, p

10 Item Count Technique (Treatment group) Now I m going to read you three things that sometimes make people angry or upset. After I read all three, just tell me HOW MANY of them upset you. (I don t want to know which ones, just how many) the federal government increasing the tax on gasoline; professional athletes getting million-dollar-plus salaries; large corporations polluting the environment; a black family moving next door to you. How many, if any, of these things upset you? Source: Imai K., (2011), Multivariate regression analysis for the item count technique, Journal of American Statistical Associasion, 206, p

11 Item Count Technique Difference in means (method of moments) estimator of the unknown population proportion of people declaring a black family moving next door is upsetting them is: p Ƹ = തY T തY C തY T - sample mean in the control group തY C - sample mean in the control group

12 Randomized response technique RRT Mirrored question design Please take out any banknote you have. If the last number of the serial number on your banknote (do not show it to me) is 0,1,2,3,4 or 5 please answer the question: Is it true that you have bribed an official? If the last number of the serial number on your banknote (do not show it to me) is 6, 7, 8 or 9 please answer the question: Is it true that you have never bribed an official?

13 Randomized response technique RRT YES NO YES NO 1200p 1200(1-p) 800(1-p) 800p All YESes 1200p+800(1-p) p All YESes

14 Randomized response technique RRT Mirror question design Warner (1965) q known probability of choosing the positive question (in previous example 0.6) 1-q known probability of choosing the negative question (in previous example 0.4) p unknown population proportion of people having the sensitive attribute (parameter under study) Maximum likelihood ML estimator of p: p Ƹ = all YESes n(1 q) (2q 1)n

15 Forced question design Fox and Tracy (1986) With probability p, respondents are asked (forced) to write NO, with probability q, respondents are asked (forced) to write YES, with probability 1 p q they are asked to answer the sensitive question.