Peter D. Killworth, Christopher McCarty, Eugene C. Johnsen, H. Russell Bernard, and Gene A. Shelley, Investigating the Variation of Personal Network Size Under Unknown Error Conditions, Sociological Methods & Research 2006 35: 84-112.

This article estimates the variation in personal network size,^{ }using respondent data containing two systematic sources of error.^{ }The data are the proportion of respondents who, on average,^{ }claim to know zero, one, and two people in various subpopulations,^{ }such as “people who are widows under the age of 65” or “people^{ }who are diabetics.” The two kinds of error—transmission^{ }error (respondents are unaware that someone in their network^{ }is in a subpopulation) and barrier error (something causes a^{ }respondent to know more or less than would be expected, in a^{ }subpopulation)—are hard to quantify. The authors show^{ }how to estimate the shape of the probability density function^{ }(pdf) of the number of people known to a random individual by^{ }assuming that respondents give what they assume to be accurate^{ }responses based on incorrect knowledge. It is then possibleto estimate the relative effective sizes of subpopulations and^{ }produce an internally consistent theory. These effective sizes^{ }permit an evaluation of the shape of the pdf, which, remarkably,agrees with earlier estimates.

Key Words: social networks • errors • probability density function

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