Arbitrary hypotheses in linear mod fi.S with unbalanced data

The Statistical Analysis System (SAS) procedure entitled General Linear Model (GLM) includes in its output four types of estimable functions that have certain arbitrariness (represented by the letter L) in their coefficients. This paper shows how such arbitrary estimable functions are derived from the known, general expressions for hypotheses tested by traditional-style F-statisties in analysis of variance calculations that are often made for unbalanced data (i.e., data having unequal numbers of observations in their subclasses).