Evaluating federated voluntary associations’ membership data: An application of Benford's Law

Abstract

Objective: Large, federated voluntary associations of the late 19th and early 20th centuries produced detailed reports of national meetings that included comprehensive data on statelevel membership. Though used in previous scholarship, the veracity of these data has never been evaluated. Methods: We test 16 associations' state-level membership data, generally between 1880 and 1920, using Benford's Law, a mathematical principle used to discern whether data are potentially problematic-through error, fraud, or other reasons-and require further investigation. Results: Our initial analyses reveal that these data deviate statistically from Benford's predictions. Further investigation, however, finds that these differences are not substantively significant; an aggregate measure of all associations shows close conformity to the Newcomb-Benford distribution. Conclusion:The data presented in voluntary associations' annual reports are likely trustworthy. These findings have important implications for future use of these data, other association data, and the role of associations in promoting civil society. Federated voluntary membership associations have been credited as the organizing force behind the American "nation of joiners" (Schlesinger, 1944). Scholars have devoted substantial attention to understanding these groups' development, operations, membership, and prominence in civic and political life. These analyses have chronicled associations' reach in American cities (Gamm and Putnam, 1999), detailed groups' influence on public policy (