8 The \(2^k\) factorial design
The most important special case of the factorial design has \(k\) factors, each at only two levels. The levels may be quantitative (two temperatures) or qualitative (two machines, the presence and absence of a catalyst); they are called low and high, and coded \(-1\) and \(+1\), or simply \(-\) and \(+\). A complete replicate has \(2^k\) runs, the smallest number with which \(k\) factors can be studied in a full factorial. These designs are used above all for screening: early in an investigation, when many factors are candidates and the aim is to find the few that matter.
8.1 The \(2^2\) design
8.2 The \(2^3\) design and the table of signs
8.3 The general \(2^k\) design
8.4 A single replicate
8.5 Centre points
8.6 Practice problems
8.2 The \(2^3\) design and the table of signs
8.3 The general \(2^k\) design
8.4 A single replicate
8.5 Centre points
8.6 Practice problems
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