How do you find mutually orthogonal Latin squares?
Let L1 and L2 be latin squares of the same order, say n ≥ 2. We say that L1 and L2 are mutually orthogonal if, when superimposed, each of the possible n2 ordered pairs occur exactly once. A set {L1,…,Lt} of t ≥ 2 latin squares of order n is orthogonal if any two distinct latin squares are orthogonal.
What are the conditions satisfied by Latin square?
The definition of a Latin square can be written in terms of orthogonal arrays: A Latin square is a set of n2 triples (r, c, s), where 1 ≤ r, c, s ≤ n, such that all ordered pairs (r, c) are distinct, all ordered pairs (r, s) are distinct, and all ordered pairs (c, s) are distinct.
What are the features of Latin square design?
A Latin square design is the arrangement of t treatments, each one repeated t times, in such a way that each treatment appears exactly one time in each row and each column in the design. We denote by Roman characters the treatments. Therefore the design is called a Latin square design.
What is a 4×4 Latin square?
For example, if there are 4 treatments, there must be 4 replicates, or 4 rows and 4 columns. This is a 4×4 latin square which gives a total of 16 experimental units. Because of this restriction, latin square experiments can become large and unmanageable very readily.
What is a balanced Latin square?
a type of study design in which multiple conditions or treatments are administered to the same participants over time.
What does mutually orthogonal mean?
Two vectors are said to “Mutually orthogonal” if the dot product of any pair of distinct vectors in the set is 0.
What is orthogonal Latin square design?
In combinatorics, two Latin squares of the same size (order) are said to be orthogonal if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares.
What is Latin square design?
A Latin square design is the arrangement of t treatments, each one repeated t times, in such a way that each treatment appears exactly one time in each row and each column in the design. This kind of design is used to reduce systematic error due to rows (treatments) and columns.
What are the advantages and disadvantages of Latin square design?
The disadvantages are: The number of levels of each blocking variable must equal the number of levels of the treatment factor. The Latin square model assumes that there are no interactions between the blocking variables or between the treatment variable and the blocking variable….3-Level Factors.
| A | B | C |
|---|---|---|
| B | C | A |