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Lattice Designs for Unreplicated Yield Trials of Maize Varieties at Several Plant Densities¹

The analysis of lattice designs with varieties showing a linear response to levels of some factor confounded with replications is described and illustrated with a hypothetical example. The theory is applied to a 7x7 quadruple lattice maize (Zea mays L.) variety trial with replications of the lattice planted at different plant densities. A linear regression model is used which assumes that the yield of each variety expressed as log (yield/plant) responds linearly to plant density. In a manner analogous to ordinary lattice designs, corrections for block differences to be applied Jo variety means and regression coefficients are obtained. Two methods of adjusting for variable stands, viz., covariance analysis with deviation from average stand at) a given plant density level as the covariable (Method I) and adjustment of the raw data using preliminary estimates of the variety regression coefficients (Method II), are suggested and compared with a generalized least squares solution (Method III). Method III is the theoretically correct procedure but we consider it impractical for large experiments. Both Methods I and II gave good approximations to the results for Metlfod III.

The experiment showed significant differences among variety means and among variety regression coefficients. Information on varietal response to plant density is obtained at the cost of very little loss of precision on variety means. It is suggested that for equivalent varietal replication more comprehensive yield trial data could be obtained by evaluation at more plant density levels with less (or possibly no) replication ot each density.

Key Words: Zea mays L. • Experimental design • Split plots • Corn plant population • Crop variety testing

² Assistant professor of agronomy and statistics and research analyst, Univ. of Kentucky, Lexington, KY 40506, respectively.

Received for publication April 23, 1975.