Latin square design

Latin Square Design

1. Prepared B y: Group 3 Latin Square Design

2. Latin Square Design A class of experimental designs that allow for two sources of blocking. Can be constructed for any number of treatments, but there is a cost. If there are t treatments, then t 2 experimental units will be required. If one of the blocking factors is left out of the design, we are left with a design that could have been obtained as a randomized block design. Analysis of a Latin square is very similar to that of a RBD, only one more source of variation in the model. Two restrictions on randomization.

3. The major feature of this design is its capacity to simultaneously handle two known sources among experimental units. The two directional blocking in a LS Design, commonly referred to as row-blocking and column-blocking. It is accomplished by ensuring that every treatment occurs only once in each row-block and once in each column block. This procedure makes it possible to estimate the variation among row-blocks as well as column blocks and to remove them from experimental error.

4. Functions Field trials in which the experimental area has two fertility gradients running perpendicular to each other, or has a unidirectional fertility gradient but also has residual effects from previous trials. Insecticide field trials where the insect migration has a predictable direction that is perpendicular to the dominant fertility gradients of the experimental field Greenhouse trials in which the experimental pots are arranged in straight line perpendicular to the glass or screen walls, such that the difference among rows and the distance from the glass wall are expected to be the two major sources of variability among the experimental pots. Laboratory trials with replication over time, such that the difference among experimental units conducted at the same time and among those conducted over time constitute the two known sources of variability.

5. Examples A researcher wishes to perform a yield experiment under field conditions, but she/he knows or suspects that there are two fertility trends running perpendicular to each other across the study plots. An animal scientists wishes to study weight gain in piglets but knows that both litter membership and initial weights significantly affect the response. In a greenhouse, researchers know that there is variation in response due to both light differences across the building and temperature differences along the building. An agricultural engineer wishing to test the wear of different makes of tractor tire, knows that the trial and the location of the tire on the (four wheel drive, equal tire size) tractor will significantly affect wear.

6. Advantages and Disadvantages Advantages: Allows for control of two extraneous sources of variation. Analysis is quite simple. Disadvantages: Requires t 2 experimental units to study t treatments. Best suited for t in range: 5  t  10 . The effect of each treatment on the response must be approximately the same across rows and columns. Implementation problems. Missing data causes major analysis problems.

7. Randomization and Lay-out Step 1: Select a sample LS plan with five treatments from Appendix K. Example: A B C D E B A E C D C D A E B D E B A C E C D B A

8. Step 2: Randomized the row arrangement of the plan selected in step 1, following one of the randomization schemes. For this experiment, the table-of-random-numbers method is applied. Select five three-digit random numbers; for example: 628, 846, 475, 902 and 452. Rank the selected random numbers from lowest to highest: Random No. Sequence Rank 628 1 3 846 2 4 475 3 2 902 4 5 452 5 1

9. Step 3: Randomize the column arrangement, using the same procedure used for row arrangement in step 2. For example, the five random numbers selected and their ranks are: Random No. Sequence Rank 792 1 4 032 2 1 947 3 5 293 4 3 196 5 2

10. Computing Formulas and Illustrative Examples There are four sources of variation in a LS design, two more than that for the CRD and one more than that for the RCB design. The sources of variation are row column, treatment and experimental error. To illustrate the computation procedure for the analysis of variance of a LS design, we use data on grain field of three promising maize hybrids (A,B and D) and of a check (C) from an advanced yield trial 4x4 L atin square design.

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