LATIN SQUARE DESIGN - RESEARCH DESIGN

LATIN SQUARE DESIGN RESEARCH DESIGN: DESCRIPTION OF LATIN SQUARE DESIGN, PROCEDURE, TABLES, LINEAR MODEL, ANALYSIS, ADVANTAGES AND DISADVANTAGES OF LATIN SQUARE DESIGN

1. LATIN SQUARE DESIGN PRESENTED BY: MANISHA THAKUR

2. DEFINITION A Latin square is a square array of objects (letters A, B, C, …) such that each object appears once and only once in each row and each column. Example - 4 x 4 Latin Square. A B C D B C D A C D A B D A B C LATIN SQUARE DESIGN

3. Latin Square Designs Selected Latin Squares can be in these forms: 3 x 3 4 x 4 A B C A B C D A B C D A B C D A B C D B C A B A D C B C D A B D A C B A D C C A B C D B A C D A B C A D B C D A B D C A B D A B C D C B A D C B A

4. In a Latin square we have three factors: Treatments ( t ) ( letters A, B, C, …) Rows ( t ) Columns ( t ) The number of treatments = the number of rows = the number of columns = t . The row-column treatments are represented by cells in a t x t array. The treatments are assigned to row-column combinations using a Latin-square arrangement.

5. Procedure for a Latin Experiment   An appropriate randomization strategy is as follows: Write down any Latin square of the required size (it could be a standard Latin square) Randomize the order of the rows. Randomize the order of the columns. Randomize the allocation of treatments to the letters of the square.

6. EXAMPLE In this Experiment the we are interested in how weight gain ( Y) in rats is affected by Source of protein (Beef, Cereal, and Pork) and by Level of Protein (High or Low). There are a total of t = 3 X 2 = 6 treatment combinations of the two factors. Beef -High Protein Cereal-High Protein Pork-High Protein Beef -Low Protein Cereal-Low Protein Pork-Low Protein

7. IN THIS EXAMPLE WE WILL CONSIDER USING A LATIN SQUARE DESIGN Six Initial Weight categories are identified for the test animals in addition to Six Appetite categories. A test animal is then selected from each of the 6 X 6 = 36 combinations of Initial Weight and Appetite categories. A Latin square is then used to assign the 6 diets to the 36 test animals in the study.

8. In the latin square the letter A represents the high protein-cereal diet B represents the high protein-pork diet C represents the low protein-beef Diet D represents the low protein-cereal diet E represents the low protein-pork diet and F represents the high protein-beef diet.

9. ADVANTAGES Allows the experimenter to control two sources of variation 

10. DISADVANTAGES The experiment becomes very large if the number of treatments is large. The statistical analysis is complicated by missing plots and misassigned treatments. Error df is small if there are only a few treatments • This limitation can be overcome by repeating a small Latin Square and then combining the experiments - 3x3 Latin Square repeated 4 times, a 4x4 Latin Square repeated 2 times