Formulas for series of experiments in a Latin square design in a split-plot arrangement - Pérez-López, Delfina de Jesús; Balbuena-Melgarejo, Artemio; Hernández-Ávila, Jesús; Franco-Martínez, J. Ramón Pascual; Rodríguez-González, José Antonio; González-Huerta, Andrés (Revista Mexicana de Ciencias Agrícolas, 2025)
Series of experiments in time, space, or combining both environments in a split-plot or split-split-plot arrangement in a Latin square design have not been frequently used. In this research, a statistical model and formulas are constructed to obtain degrees of freedom and sum of squares using quadratic or matrix forms and least squares, when the components of time and space are confused in environments, as a prerequisite to extend their analysis with balanced subsampling. In relation to the main plot, it is assumed that there is no interaction between rows, columns and levels of factor A, and rows and columns with the environments; this restriction also applies between rows and columns or both, with factors A, B and their interaction, but it is also indicated how to reach the same results by introducing the principle of crossing and nesting, particularly if a statistical package will be applied; emphasis is also placed on the formulas to directly calculate degrees of freedom and sum of squares for errors a and b, as well as for those corresponding to main plots and subplots.
Keywords: matrices; statistical models; years and localities confused in environments