A solution is proposed for analysis of variance procedures with missing cells, such as may occur when a control group is not assigned to any of the rows or columns of the various experimental groups. Mathematical models for two-way design are presented which define several variables; as well as row effect, column effect, and row and column effects. Full rank models, also recommended for disproportional data, are also presented. Restricted models are used to test hypotheses; this is also illustrated after dropping a vector. Two examples are described in which this research design may have educational applications: (1) the experimenter has a two-way treatment classification procedure, but the true control group is administered neither of the treatment combinations; or (2) cultural bias may be accounted for when a test is more fair in particular geographic areas; distances from these areas are represented in diagrams. (Author/GDC)