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  [SNA & Statistics] Why Standard Statistics Fail on Network Data

Networks Are Interdependent

Social Network Analysis (SNA) has moved beyond visualizing complex structures of nodes and edges or reporting descriptive measures. It now enters the stage of causal inference using network variables. This shift brings a core statistical challenge: the inherent interdependency of network data.

Traditional statistical models based on the General Linear Model assume independence of error terms. Methods such as t tests, ANOVA, and OLS regression compute p values under the assumption that observations are randomly sampled and mutually independent.

Network data violate this assumption by definition. One person’s friendships are not independent of another’s, and communication frequency within an organization is constrained by its structure. Applying conventional tests to such data underestimates standard errors and inflates test statistics, increasing the risk of false positives.

How have researchers addressed this issue across fields?

Permutation tests offer a solution. Without assuming a specific probability distribution, they randomly rearrange the data to generate the null distribution of a statistic. Statistical significance is then assessed by the probability of observing a value more extreme than the one observed under random permutations.

(1) Relational correlation analysis using QAP correlation
(2) Linear and logistic regression for matrix level prediction using MRQAP
(3) Regression analysis for node level association and prediction

These cases may help inform how such methods can be incorporated into ongoing or planned research designs.

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