RAO'S SCORE TEST FOR THE OVERLAPPING COEFFICIENT IN A CENTRAL COMPOSITE DESIGN

An application of the score test of Rao is developed and presented for the overlap coefficient in the Draper and Guttman's model using the response surface generated by the central composite design. The score test of Rao for overlap makes use of the theory associated with the perpendicular projection operators and can be applied with different patterns of neighborhood of a seeding whenever the closest neighbor can be considered as the experimental unit directly affected by the treatments. The illustration for the application of the test was,developed in the culture of lettuce sowed to the usual plant density, which was used to define the patterns neighborhood and the associated weight matrix, for which no effect of overlap was found from the statistical point of view. The method is simple to implement and can be applied in the field of agronomy or in similar studies in other areas such as pasture and forage management for animal and veterinary production, as well as in the area of education when different teaching modalities linked to the technologies information and communication are evaluated.