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Such an experiment has 2×3=6 treatment combinations or cells. Similarly, a 2×2×3 experiment has three factors, two at 2 levels and one at 3, for a total of 12 treatment combinations. If every factor has s levels (a so-called fixed-level or symmetric design), the experiment is typically denoted by s k, where k is the number of factors. Thus a ...
Before performing a Yates analysis, the data should be arranged in "Yates' order". That is, given k factors, the k th column consists of 2 (k - 1) minus signs (i.e., the low level of the factor) followed by 2 (k - 1) plus signs (i.e., the high level of the factor). For example, for a full factorial design with three factors, the design matrix is
The alias structure determines which effects are confounded with each other. For example, the five-factor 2 5 − 2 can be generated by using a full three-factor factorial experiment involving three factors (say A, B, and C) and then choosing to confound the two remaining factors D and E with interactions generated by D = A*B and E = A*C.
Let X 1 be dosage "level" and X 2 be the blocking factor furnace run. Then the experiment can be described as follows: k = 2 factors (1 primary factor X 1 and 1 blocking factor X 2) L 1 = 4 levels of factor X 1 L 2 = 3 levels of factor X 2 n = 1 replication per cell N = L 1 * L 2 = 4 * 3 = 12 runs. Before randomization, the design trials look like:
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
Statisticians [2] [3] describe stronger multifactorial DOE methods as being more “robust”: see Experimental design. As DOE software advancements gave rise to solving complex factorial statistical equations, statisticians began in earnest to design experiments with more than one factor (multifactor) being tested at a time.
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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.