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What is a Latin square and why would you use it?
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. So, both rows and columns can be used as blocking factors.
What is a Latin square in maths?
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3×3 Latin square is. A. B. C.
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. This kind of design is used to reduce systematic error due to rows (treatments) and columns.
How does a Latin square work?
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.
What are the disadvantages of Latin square design?
Disadvantages of latin square designs 1. Number of treatments is limited to the number of replicates which seldom exceeds 10. 2. If have less than 5 treatments, the df for controlling random variation is relatively large and the df for error is small.
Is Sudoku a Latin square?
Every Sudoku square is a special kind of a Latin square2 (where numbers 1 through n are arranged in an n × n array such that every row and every column has each number exactly once). In fact, Sudoku squares form a tiny proportion of Latin squares of the same order.
What is a latin square in psychology?
a type of within-subjects design in which treatments, denoted by Latin letters, are administered in sequences that are systematically varied such that each treatment occurs equally often in each position of the sequence (first, second, third, etc.).
Is Sudoku a latin square?
Where is latin square design used?
The Latin square design applies when there are repeated exposures/treatments and two other factors. This design avoids the excessive numbers required for full three way ANOVA.
What is an example of a factorial design?
For example, if she has two levels for time of day, morning and afternoon, she needs to different 2×3 boxes: one for morning and one for afternoon. Likewise, the naming of the design changes with a third variable: now Jessie has a 2x3x2 factorial design.
Which is the best definition of a balanced Latin square?
BALANCED LATIN SQUARE. refers to a single Latin square with an even number of treatments, or a pair of Latin squares with an odd number of treatments. Each treatment occurs equally often in each position of the sequence (e.g., first, second, third, etc.) and in addition, each sequence of treatments (reading both forward and backward)…
How did the Latin square design get its name?
The Latin Square Design gets its name from the fact that we can write it as a square with Latin letters to correspond to the treatments. The treatment factor levels are the Latin letters in the Latin square design. The number of rows and columns has to correspond to the number of treatment levels.
When to use an intensive Latin square design?
If the full Latin square design is not feasible because multiple periods are not practical, you may use incomplete Latin square designs (i.e., the number of rows does not equal the number of columns) ( Figures 6.13a-c ). Conversely, if the availability of the patients is an issue (e.g., with orphan indications), intensive design may be used.
When to use the Latin square dye swapping design?
The Latin square design is a general version of the dye-swapping design for samples from more than two biological conditions. 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.