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Treating Data Collected by the "Small World" Method as a Markov Process

John E. Hunter and R. Lance Shotland
Social Forces
Vol. 52, No. 3 (Mar., 1974), pp. 321-332
Published by: Oxford University Press
DOI: 10.2307/2576887
Stable URL: http://www.jstor.org/stable/2576887
Page Count: 12
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Treating Data Collected by the "Small World" Method as a Markov Process
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Abstract

This article uses data gathered by the "small world" technique to estimate the distance between social categories, the diffuseness of connection within a category, and the relative isolation of various categories. The critical questions for the data are the adequacy of the categories and the distribution of the chains of booklets which fail to reach the target. If the population can be divided into n categories, the natural model for the data is an n+2 state Markov process where the two additional states are "lost" and "target." The discussion centers around the use of the transition matrix as a description of social structure and the comparison of observed and predicted average chain lengths as a test for the adequacy of the categories as a descriptive system. If the categories are "good," the "lost" column of the transition matrix can be eliminated and the new matrix can then be used to "correct" the observed average chain lengths to estimates of the average chain lengths, had all chains been completed.

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