A Revisit to Satterthwaite Approximation to the Distribution of a Linear Combination of Sample Mean Squares - V.T. Prabhakaran (Journal of the Indian Society of Agricultural Statistics, 2025)
Linear combinations of mean squares occur in many areas of research like statistical hypothesis testing, design of experiments, and statistical genetics. The present paper demonstrates how the Satterthwaite approximation dating back to early nineteenth century is still a potential tool to reduce complicated problems to a solvable format. Significantly, a new derivation of the distribution of a linear combination of ‘Between sires’ and ‘Between dams within sires’ mean squares under certain restrictions is proposed which is quite simple compared the Graybill (1956) approach to the problem.