Introduction: Recently a survey was taken of Americans, asking, among other things, ``How many males do you know incarcerated in state or federal prison?'' The mean of the responses to this question was 1.0. To readers of this journal that number may seem shockingly high. We would guess that you probably don't know anyone in prison. In fact, we would guess that most of your friends don't know anyone in prison either. This number may seem totally incompatible with your social world.
So how was the mean of the responses 1? According to the data, 70% of the respondents reported knowing zero people in prison. However, the responses show a wide range of variation, with almost 3% reporting that they know at least 10 prisoners. Responses to some other questions of the same format, for example “How many people do you know named Nicole?” show much less variation.
This difference in the variability of responses to these "how many people do you know" questions is the manifestation of fundamental social processes at work. Through careful examination of this pattern, as well as others in the data, we can learn about important characteristics of the social network connecting Americans, as well as the processes that create this network. This analysis also furthers our understanding of statistical models from two-way data.