Randomized Response Polling | Stats + Short Stories Episode 341 / by Stats Stories

Dr. James Hanley is a professor of biostatistics in the Faculty of Medicine at McGill University. His work has received several awards including the Statistical Society of Canada Award for Impact of Applied and Collaborative Work and the Canadian Society of Epidemiology and Biostatistics: Lifetime Achievement Award.

+Full Transcript

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John Bailer
Did you ever think that you could know something about a population based on measurements that you didn't know were correct for any individual, or what it even meant for an individual in the population? That's something that's available through a method called randomized response. Well, not only could you ask questions about health care or health considerations and sensitive health questions, which was the motivation for it when it was developed many decades ago. There's a recent paper in the Journal of Statistics and Data Science Education on investigating sensitive issues in class through randomized response polling. And we're delighted to have James Hanley joining us to talk a little bit about this project. James, welcome back.

James Hanely
Thank you very, very much.

John Bailer
Yeah, so, so randomized response in classroom settings. Can you just give a quick summary of what the randomized response method is for our audience?

James Hanely
Yes, the idea is that I'm facing you. You're answering a survey, and I would like to know whether you've cheated on exams or not? Well, not you, but the class.

John Bailer
Me? Never James. Me, never, no, no.

James Hanely
But what about your taxes? Or, you know, what about something else, or I didn't give a book back to the library or whatever? But for a group, you can work out what proportion of them have or not with a certain plus and minus on it by giving you one of two questions to answer, and they could be the flip of each other as well, or they could be an irrelevant question, like, When was your mother born? Was your mother born in April? That's another version of it. Or did you cheat on your taxes? Those are two versions. So when I hear the answer yes from you, I don't know whether it's today. Are you lying about your mother? Are they cheating? And so the receiver can't interpret it. But when you put them all together, all the answers from all the classes should be a certain aggregate, and the aggregate is a mixture now of the two types of answers. So it's a mix. And if we know the mixing, which is what the probability of answering one way or the other does, we can then deconstruct it and separate out at an average level, what's going on. So that's the basic idea of it. Yeah, it's very clever. It hasn't worked very well, though, in sociology and in surveys. And I remember doing a seminar on this, and they gave you a talk about it when I graduated in 1973. The problem is that the general public doesn't understand it. They think you're cheating some or recording it, or doing some things, or have a camera. There's some way to do it. So I think it only works for a fairly sophisticated public, but the university students should be able to get it, but it's tricky. It's tricky. We were motivated by it because I was so annoyed that McGill wouldn't let us ask the question of our students whether they had been vaccinated against covid or not. So it was a huge political war at our university. I was talking to my co author, and I said, I am really esteemed, and I've actually written up this way of doing it again and adapting it. And Christian Jenna, my first co author, they said, oh my goodness, he had written a popular article for a journal doing it, but without any example, a real example that No, we've got to do this in class for real. Yeah. But the younger teachers at McGill didn't want to do it. They were afraid that the university had come down on them for breaking privacy laws, because in Quebec, your medical record is private and vaccination is part of your medical record. And in your country, you had no problem. Most of the American universities had no problem asking and insisting on vaccination. We were not allowed to, and it caused major trouble. And I sent the article to the provost the other day. I said, Look, you know, out of necessity comes methods, yeah, so we adapted it.

Rosemary Pennington
You stole my question from me because I was about to ask you what spurred this particular–

James Hanely
Don't get me started. We're still upset at the university in Quebec. It's private. Your vaccination status in Ontario and every other province with a different kind of law, or way of human you know, civil liberties, they had it the opposite way you had, yeah, if you weren't vaccinated and they let you into class, that's it. And you American reviewers of our paper had a tough time understanding why? Why? Why can't you ask? So we had a lot of trouble, and then we didn't get it accepted right away. So it was all about covid In the first version, and then we didn't get accepted right away. We need revisions, and we're all so busy, we didn't get to it. Revised the article two years later, and by that time, the whole story was stale. So that's when we had to broaden it so that it could go to cheating or whatever. But the original impetus was and in the article, I say in the little time. My own art class of 10 or 12, we repeated it. The one new twist we have is you can repeat the survey with people and ask them several times, and you can average the answers, and that's what gets you a narrower margin of error. And in fact, one of the reviewers said to her, if I asked you often enough, I should be able to figure out, even for you, whether you were ever not cheating, because the two mixes, rather than will, kind of diverge, you know, whichever you'll see one or the other eventually. But that was going too far.

John Bailer
Well, I'm afraid that's all the time we have for this rather short but very interesting episode of Stats and Short Stories. James, thank you so much for joining us.

James Hanley It was a pleasure.

John Bailer Stats and Stories is a partnership between Miami University's departments of statistics and media, journalism and film and the American Statistical Association. You can follow us on Twitter, Apple podcasts or other places where you can find podcasts. If you'd like to share your thoughts on our program, Send your email to stats and stories@miamioh.edu or check us out@statsandstories.net and be sure to listen for future editions of stats and stories where we discuss the statistics Behind the stories and the stories behind the statistics.

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