Wednesday, 28 November 2018

How many zombies are there in New Zealand?

Let's say there is some rare group of people and that you want to know how many people there are in the group. Say, people who own fifteen or more cats, or avid fans of curling. Conducting a population survey isn't going to help much, because if you survey 10,000 people and three belong to the group that doesn't tell you very much. Now, let's say that not only is the group rare, but people don't want to admit (even in a survey) that they belong to the group. Say, people who enjoyed the movie Green Lantern, or secret agents, or aliens, or vampires, or zombies. How do you get a measure of the size of those populations?

One way that you might be able to achieve this is an indirect method. If you survey a random sample of people, and you know how many people they know (that is, how many people are in their social network), you could simply ask each person in your survey how many Green Lantern lovers, or how many zombies, they know. You could then extrapolate from that how many there are in the population as a whole, if you make some assumptions about the overlaps between the networks of the people you surveyed.

It's not a totally crazy idea, but is sufficiently lampooned by Andrew Gelman (Columbia University) in this article published on ArXiv:
Zombies are believed to have very low rates of telephone usage and in any case may be reluctant to identify themselves as such to a researcher. Face-to-face surveying involves too much risk to the interviewers, and internet surveys, although they originally were believed to have much promise, have recently had to be abandoned in this area because of the potential for zombie infection via computer virus...
Zheng, Salganik, and Gelman (2006) discuss how to learn about groups that are not directly sampled in a survey. The basic idea is to ask respondents questions such as, "How many people do you know named Stephen/Margaret/etc." to learn the sizes of their social networks, questions such as "How many lawyers/teachers/police officers/etc. do you know," to learn about the properties of these networks, and questions such as "How many prisoners do you know" to learn about groups that are hard to reach in a sample survey. Zheng et al. report that, on average, each respondent knows 750 people; thus, a survey of 1500 Americans can give us indirect information on about a million people.
If you're interested, the Zheng et al. paper is open access and available here. So, how many zombies are there in New Zealand? To find out, someone first needs to do a random survey asking people how many zombies they know.

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