The Contrast Algorithm for Unbalanced Multifactor Analysis of Variance
针对非平衡多因素方差分析模型，提出一种基于Scheffé对比法的算法，通过求解更小规模的线性方程组来计算平方和，避免二次型相减带来的浮点精度损失，并支持多重比较。
Abstract We consider the problem of computing sums of squares in multifactor analysis of variance models with unequal but nonzero numbers per cell. Commonly used computing methods for obtaining main-effect and interaction hypothesis mean squares solve linear model equations X′Xβ = X′Y. We present an algorithm based on Scheffé's method of contrasts that solves a smaller set of linear equations. It avoids subtraction of quadratic forms, which degrades floating-point accuracy and facilitates Scheffé's method of multiple comparisons. Selected efficiency calculations are presented.