Nonparametric inference for network data

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Abstract
Various theoretical concerns often require researchers to answer questions of the form does co‐membership in a group predict other ties between those individuals. Data appropriate for answering such a question often is referred to as network data. Network data exhibits row‐column dependencies that often invalidate traditional statistical methods for doing group comparisons such as analysis of variance and the Kruskal‐Wallis Procedure. Because of the positive dependence within rows/columns the significance probabilities of such traditional methods may be exaggerated. This paper uses restricted‐randomization to develop exact permutation tests for network data where co‐membership in groups can be specified a priori. This enables the nonparametric estimation of the significance of standard statistics for group‐difference tests and ordered‐alternative tests where the group orderings have been prespecified. These methods are demonstrated by examining three different data sets: Sampson's Monastery data, Carley's Tutor Selection data, and Humana's Human Rights data.