Latin Square Design

1. Prepared By: Group 3
*

2. *
*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 t2
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. *
*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. *
•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:
•Allows for control of two extraneous sources of variation.
•Analysis is quite simple.
*Disadvantages:
•Requires t2 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. *
*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. *
*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 Latin square design.

24. *