Intra- and Inter-Block Analysis for Factorials in Incomplete Block Designs

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Abstract
The main objective of this paper is to extend the work of Kramer and Bradley to the use of factorials in the several suitable classes of two-associated class, partially balanced incomplete block (p. b. i. b.) designs not previously considered. A second objective is to complete the earlier work through utilization of inter-block information in combined intra- and inter-block estimators. We consider specifically recovery of inter-block information in Group Divisible designs, both intra- and combined intra- and inter-block analyses for Latin-Square, Sub-type L2 designs and Latin Square, Sub-type L3 designs and discuss other p. b. i. b. designs with two associate classes. In each situation tests of significance and estimators of factorial effects are obtained along with efficiencies of contrasts.