Allotting treatments to units by chance is the simplest layout of data for analysis.

**RANDOMIZED AND LATIN SQUARE
DESIGNS**

Allotting
treatments to units by chance is the simplest layout of data for analysis.
Specifically, if a treatment is to be applied to four units then randomization
gives every group of four units in the experimental product an equal
probability of receiving the treatment. The units should also be processed
randomly at sub-sequent stages, where the order is likely to affect the
results. For example, time of day, or season of the year, the samples are taken
may influence processes that are susceptible to ambient conditions such as
light, temperature, and humidity if these conditions are not controlled
effectively. The advantages of this approach are complete flexibility, as any
number of treatments and replicates may be employed, and ease of statistical
analysis even if the numbers of replicates for some units or whole treatments
are missing. Relative loss of information due to missing data is smaller than
other designs. Criticism of this approach related to the loss of accuracy that
occurs as a result of the whole variation is uniformly distributed across
treatments and units and enters into the experimental error. The error can be
reduced by use of different designs. The error can be reduced by introducing
randomized blocks. The experimental product is divided into groups, each of
which constitutes a single trial or replication. Using the example above,
product could be blocked for time of day sample was taken to assign error
specifically to ambient conditions.

For
Latin square designs, treatments are grouped into replicates in two different
ways. This approach effectively gives two dimensions to the analysis and the
design assigns treatments to positions designated in a row or column of the
design. Every row and every column of the square is a complete replication.

The
effect of this double grouping is elimination from the errors all differences
among rows and columns. Thus, the Latin square design provides more opportunity
than random blocks for reduction of error by planning.

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