STA408 Handouts by Study With BRD

DESCRIPTION

When the variation is found in two directions, it becomes necessary to remove these two sources of variation simultaneously. This is done by simultaneous blocking of experimental units in two mutually perpendicular directions called rows and columns. Since each row and each column is a complete block, the grouping for a balanced arrangement is performed by imposing the restriction that each treatment must appear “ once and only once” in each row and in each column. If there are “k” treatments then the experimental area will be divided into “k” rows and “k” columns in k x k plots or experimental units. As the experiment is laid out in a square pattern and the treatments are then assigned at random to plots or experimental units. Such a double blocking of experimental units and a corresponding double random assignment of treatments is called “Latin Square Design”. A large number of distinct Latin squares can be derived by interchanging rows and columns of a standard Latin square, where a standard Latin square is a Latin square in which the treatments in the first row and first column are arranged in alphabetical or numerical order. A standard Latin square is also called a reduced Latin square.