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AP Stats: DAT‑2 (EU), DAT‑2.E (LO), DAT‑2.E.1 (EK), DAT‑2.E.2 (EK), DAT‑2.E.6 (EK), VAR‑1 (EU), VAR‑1.E (LO), VAR‑1.E.1 (EK)

Video transcript

- [Instructor] We're told that David hosts a podcast and he is curious how much his listeners like his show. He decides to start with an online poll. He asks his listeners to visit his website and participate in the poll. The poll shows that 89% of about 200 respondents "love" his show. What is the most concerning source of bias in this scenario? And well, like always, pause this video and see if you can figure it out on your own and then we'll work through it together. Let's think about what's going on. He has this population of listeners, right? I'll assume that the number of listeners is more than 200. And he says, "Hey I want to find a sample, "and I can't ask all of my listeners." Who knows, maybe he has 10,000 listeners, they don't tell us that, but let's say there's 10,000 listeners here. And he says, "Well I want to get an indication "of what percentage like my show. "So I need a sample." But instead of taking a truly random sample, he asks them to volunteer. He asks his listeners to visit his website. So that's classic volunteer response sampling. This is not random because who decides to go to his website and listen to what he just said, and maybe even has access to a computer. That's not random. In fact, the people more likely to do that, so these are the people out of the 10,000, these are the 200 responders here who decided to do it. These are more likely to be the people who already like David or like to listen to what he tells them to do. The people, the listeners who are not into David or don't want to do what he tells them to do, they're unlikely to say, "Oh, I'm not really into David "and I don't like him telling me what to do, "but hey, I'm gonna go to his website anyway, "I'm gonna fill out that poll." That's less likely. Or you might get extremes, people who really don't like him, might say, "I'm gonna definitely go there." But in this case, I would say that it's more likely your fans are gonna do what you ask them to do and go to your website and spend time on your website. And because of that, that 89% is probably an overestimate. 89% is probably an overestimate of the number of listeners who really love his show. Cause you're more likely to get the ones who love him to show up and fill out that actual survey. Now these other forms of bias. Response bias, this is when you're asking something that people don't necessarily want to answer truthfully, or the way that it's phrased, it might make someone respond, you see, in a biased way. Classic examples of this are like, "Have you lied to your parents in the past week?" Or "have you ever cheated on your spouse." Something, "do you smoke?" Any of these things that people might not want to answer completely truthfully or they might be hiding from the world, they might not just want to answer that truthfully on a survey. And so you're going to have response bias. But that's not the case right over here. And undercoverage is when the way that you're sampling, you're definitely missing out on an important constituency. Voluntary response we're likely missing out on some important constituencies, on some people who might not be into going to your website, but undercoverage is where it's a little bit more clear that that is happening. Let's do another case, let's do another case, maybe an alternate reality where David's trying to figure this out again, he's still hosting a podcast, he's still curious how much his listeners like his show, but he tries to take a different sample. He decides in this case, to poll the next 100 listeners who send him fan emails. They don't all respond, but 94 out of the 97 listeners polled said they "loved his show." What is the most concerning source of bias in this scenario? Well this is a classic, "Hey I have a group, "I have a sample sitting in front of me, "it's in my inbox in my email, let me just go to them." Isn't that convenient? So this is classic convenience sample. And this isn't just like, hey, these are the first 100 people to walk through the door and there's, a lot of times you can argue why that might be not so random, but these're the next 100 listeners who sent him fan emails. (laughing) So this is convenience sampling and the sample that you happen to use out of convenience is one that's going to be very skewed to liking you. So once again, this is overestimating, overestimating the percent, the percent that love his show. Now nonresponse is when you ask a certain number of people to fill out a survey or to answer a questionnaire, and for some reason, some percent do not fill it out. And you're like, "Wow, who are those people? "Maybe they would have said something important "and maybe their viewpoint "is not properly represented in the overall number "that actually did fill it out." And there is some nonresponse going on here. He asks 100 people who sent fan emails to fill out the survey to say whether they love it or not, 97 fill it out. So there are three people who did not fill out the survey. So there is some nonresponse going on that would be a source of bias, but it's not the most concerning. Right over here they're asking us, fill out the most concerning source of bias, and the convenience sampling is definitely the biggest deal here. There were three people who didn't respond, but that's not as big of a deal. Voluntary response sampling. Well, he didn't ask people, like in the last example, "Hey, if you can go here and fill it out?" I guess, I take that back, there is a little bit of voluntary response here, where he goes to these 100 people and he asks them to respond. And so you have the 97 people who chose to respond. But once again, that could be a source of bias, but most of the 97 of the 100 are responding, and once again, the most concerning thing is the convenience sampling, which will once again, based on this sample that he's happening to use out of convenience, is going to be a very, a significant overestimate in terms of representing the entire population of his listeners.