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Analysis of Diallel-Type Competition Studies¹

The basic linear model for diallelic competition studies corresponds to the model for the diallel cross mating design with parents included. It is demonstrated that this model does not allow for unbiased estimation or testing of the average competitive effects unless certain restrictions are imposed on the parameters. Both the "adjusted" and "unadjusted" results of Hanson et al. (1961) are biased with respect to the basic unrestricted model but both are shown to provide unbiased results if alternative sets of restrictions on the [S₁(jk)] are imposed. Thus, the two "adjusted" and "unadjusted" analyses may be more appropriately referred to as two alternative models. Two methods of competitor assignment which are consistent with the two sets of restrictions are described and it is left to the experimenter to decide which model more nearly represents his experimental situation. High correlation of results between the two models makes it unnecessary to perform both analyses. Estimators and variances of competitive effects and competition biases are presented for both models.

Key Words: Estimability • Model restrictions

² Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27607.

Received for publication August 29, 1973.