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In the aquaculture experiment, the ordered triple (25, 80, 10) represents the treatment combination having the lowest level of each factor. In a general 2×3 experiment the ordered pair (2, 1) would indicate the cell in which factor A is at level 2 and factor B at level 1. The parentheses are often dropped, as shown in the accompanying table.
The levels of a factor are commonly coded as +1 for the higher level, and −1 for the lower level. For a three-level factor, the intermediate value is coded as 0. [4] To save space, the points in a factorial experiment are often abbreviated with strings of plus and minus signs.
The design matrix for a central composite design experiment involving k factors is derived from a matrix, d, containing the following three different parts corresponding to the three types of experimental runs: The matrix F obtained from the factorial experiment. The factor levels are scaled so that its entries are coded as +1 and −1.
This occurs when the various factor levels are sampled from a larger population. Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments (a multi-variable generalization of simple differences) differ from the fixed-effects model. [13]
Each factor has two levels: for postage (labeled A), they are third-class (low) and first-class (high), for product price (labeled B) the low level is $9.95 and the high level is $12.95, and for envelope size (labeled C) the low level is #10 and the high level is 9x12. From the experiment, the following data are acquired.
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This article describes completely randomized designs that have one primary factor. The experiment compares the values of a response variable based on the different levels of that primary factor. For completely randomized designs, the levels of the primary factor are randomly assigned to the experimental units.
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