## What is the 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 meant by Latin square?

Definition of Latin square

: a square array which contains n different elements with each element occurring n times but with no element occurring twice in the same column or row and which is used especially in the statistical design of experiments (as in agriculture)

Why is it called Latin square?

The name “Latin square” was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3. Euler began the general theory of Latin squares.

### Why would you use a Latin square design?

Latin square designs allow for two blocking factors. In other words, these designs are used to simultaneously control (or eliminate) two sources of nuisance variability.

When was Latin square design used?

Latin squares design is an extension of the randomized complete block design and is employed when a researcher has two sources of extraneous variation in a research study that he or she wishes to control or eliminate.

How do you make a Latin square design?

Make a balanced square design for six participants A B C D E F with six testing conditions. Step 1: Make the first row using the formula: row1 = 1,2,n,3,n-1,n-2. Step 2: Fill in the first column sequentially. Step 2: Continue filling in the columns sequentially until the square is completed.

## Who invented Latin square design?

A Latin square of order n is an n × n array of cells in which n symbols are placed, one per cell, in such a way that each symbol occurs once in each row and once in each column. R. A. Fisher promoted the use of Latin squares in experiments while at Rothamsted (1919– 1933) and his 1935 book The Design of Experi- ments.

How do you analyze a Latin square?

Latin Square Design – How to analyse data – YouTube

How many Latin squares are there?

This example illustrates one of the 576 possible Latin squares for a 4-by-4 layout; larger squares have many orders of magnitude more combinations (e.g., 161,280 for a 5-by-5 layout).

### What is Latin square problem?

The minimum number of transversals of a Latin square is also an open problem. H. J. Ryser conjectured (Oberwolfach, 1967) that every Latin square of odd order has one. Closely related is the conjecture, attributed to Richard Brualdi, that every Latin square of order n has a partial transversal of order at least n − 1.

How do you draw a Latin square?

Step 1: Make the first row using the formula: row1 = 1,2,n,3,n-1,n-2. Step 2: Fill in the first column sequentially. Step 2: Continue filling in the columns sequentially until the square is completed. A completed balanced square design with an even number of conditions.

How do you balance a Latin square?

It is a form of Latin square that must fulfill three criteria: Each treatment must occur once with each participant, each treatment must occur the same number of times for each time period or trial, and each treatment must precede and follow every other treatment an equal number of times.

## How do you use Latin squares?

A latin square is a design in which each treatment is assigned to each time period the same number of times and to each subject the same number of times (see Dean and Voss 1999, chap. 12). If there are t treatments, t time periods, and mt subjects then m latin squares (each with t treatment sequences) would be used.

How do you make a Latin square?

What are the conditions for Latin square design?

12.3.
The Latin square design requires that the number of experimental conditions equals the number of different labels. The same number of experimental runs as the number of treatment conditions is also used. The treatment conditions are labeled once using each label and sampled once under each experimental run.