# Randomized and Latin Square Designs

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## Chapter: Pharmaceutical Engineering: Statistical Experimental Design

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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