Resumen

GONZALEZ HUERTA, Andrés et al. Treatments nested within a balanced complete block group arrangement. Rev. Mex. Cienc. Agríc [online]. 2024, vol.15, n.2, e3634.  Epub 21-Jun-2024. ISSN 2007-0934.  https://doi.org/10.29312/remexca.v15i2.3634.

When designing and analyzing an experiment or a series of trials in time or space, it could be of great relevance to subdivide the number of treatments by forming groups in which some important difference between them and some similarity within them are considered. This study analyzed the case presented by Gomez and Gomez (1984) regarding the grain yield recorded in 45 rice varieties, classified into three groups; their statistical model for an experimental design of randomized complete blocks was presented, complementary formulas were included to calculate the sums of squares with the methodologies of least squares and quadratic or matrix forms, and the procedure to generate an output if InfoStat were applied is proposed. In addition, other ways are mentioned to calculate degrees of freedom if the experimental area is divided into main unit and subunit, and those corresponding to the model residual or error b, which simplify manual calculations. The formulas for both methodologies were standardized based on the formal use of the symbology used in the sum and point notations; their quadratic forms are presented based on the latter. The difference between a conventional analysis of variance and the one considered in this paper, based on the sums of squares, is discussed. Finally, it is indicated how to apply Tukey’s test for the comparison of means of varieties within each group if InfoStat is used. It is also recommended to use a matrix calculator to solve calculations when using quadratic forms, which is freely available on their website.

Palabras llave : InfoStat; least squares; quadratic forms; randomized complete block design.