Beyond Size: The Fragmentation of the Library Index and the Rise of Institutional Complexity in Academic Library Statistics

Abstract

For over four decades, academic libraries were quantitatively evaluated under the assumption that a single "Library Size" index could accurately summarize their operational capacity. This thesis mathematically tests that historical assumption by deploying longitudinal Principal Component Analysis and K-Means clustering on an eleven-year panel (2014-2015 to 2024-2025 Academic Year) of the federal IPEDS database. The analysis first uncovered the "IPEDS Imputation Trap" demonstrated that complex administrative reporting variables have artificially hijacked the primary variance of the national dataset due to federal imputation practices. After filtering this noise, the study proves that the historical library size monolith has permanently fractured. Projecting the national cohort onto these new axes establishes a modern taxonomy consisting of four distinct operational postures. Ultimately, this research proves that an academic library is no longer defined by a universal standard of size, but by the highly specialized economic survival strategies it executes within a decentralized landscape.