Examples of Intra-Block Analysis for Factorials in Group Divisible, Partially Balanced, Incomplete Block Designs

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Abstract
Methods of incorporating factorial treatment combinations in group divisible, partially balanced, incomplete block designs are given. The factorial treatment combinations are so matched with the basic treatments in the association matrices of the designs that the sums of squares for factorial effects can be obtained as functions of the original treatment estimators. It is shown how a two-factor factorial may be incorporated into group divisible designs. Single-degree-of-freedom contrasts are obtained for the effects in much the usual way as for factorials in complete block designs. Multi-factor factorials and fractional replications of factorials are also discussed. Two numerical examples are given showing the calculations required in detail for a group divisible design and the simplifications that occur when the group divisible design is also a near balance lattice.

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