Least Squares Means

When there are no missing cells in ANOVA designs with categorical predictor variables, the subpopulation (or marginal) means are least square means, which are the best linear-unbiased estimates of the marginal means for the design (see, Milliken and Johnson, 1986). Tests of differences in least square means have the important property that they are invariant to the choice of the coding of effects for categorical predictor variables (e.g., the use of the sigma-restricted or the overparameterized model) and to the choice of the particular generalized inverse of the design matrix used to solve the normal equations. Thus, tests of linear combinations of least square means in general are said to not depend on the parameterization of the design.

See also the General Linear Model (GLM) or General Regression Models (GRM) methods of analysis.