2024/09/22 by Matthias von Davier, von Davier, Matthias
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Mathematics and Applications #Other Statistics (stat.OT) #Statistical and numerical algorithms #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2409.14606
openalex publication_date 2024/09/22 · openalex created_date 2024/10/30 · openalex updated_date 2026/07/28
This study introduces a correction to the approximation of effective degrees of freedom as proposed by Satterthwaite (1941, 1946), specifically addressing scenarios where component degrees of freedom are small. The correction is grounded in analytical results concerning the moments of standard normal random variables. This modification is applicable to complex variance estimates that involve both small and large degrees of freedom, offering an enhanced approximation of the higher moments required by Satterthwaite's framework. Additionally, this correction extends and partially validates the empirically derived adjustment by Johnson & Rust (1992), as it is based on theoretical foundations rather than simulations used to derive empirical transformation constants.