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Details of the FACTEX Procedure |

*Block factors* are unavoidable factors that are known to affect
the response, but in a relatively uninteresting way. For example, in the
chemical experiment, the technician operating the equipment
might have a noticeable effect on the yield of the process. The operator
effect might be unavoidable, but it is usually not very interesting. On
the other hand, factors whose effects are directly of interest are called
*design factors*. One goal in designing an experiment is to avoid
getting the effects of the design factors mixed up, or *confounded*,
with the effects of any block factors.

When constructing a design by orthogonal confounding, all factors
formally have the same number of levels *q*, where *q* is a prime
number or a power of a prime number. Usually, *q* is two,
and the factor levels are chosen to represent
high and low values.

However, this does not mean, for example, that a design for two-level
factors is restricted to no more than two blocks. Instead, the values of
several two-level factors can be used to index the values of a single
factor with more than two levels. As an example, the values of three
two-level factors (*P _{1}*,

P_{1} |
P_{2} |
P_{3} |
F |

0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 |

0 | 1 | 0 | 2 |

0 | 1 | 1 | 3 |

1 | 0 | 0 | 4 |

1 | 0 | 1 | 5 |

1 | 1 | 0 | 6 |

1 | 1 | 1 | 7 |

The method for constructing an orthogonally confounded design for
*q*-level factors in *q*^{m} runs distinguishes between the first *m*
factors and the remaining factors. Each of the *q*^{m} different combinations of the
first *m* factors occurs once in the design in an order similar to the
preceding table. For this reason, the first *m* factors are called the
*run-indexing factors*.

Table 15.7 summarizes the different types of factors discussed in this section.

Block factor | Unavoidable factor whose effect is not of direct interest |

Block pseudo-factor | Pseudo-factor used to derive levels of a block factor |

Derived factor | Factor whose levels are derived from pseudo-factors |

Design factor | Factor whose effect is of direct interest |

Pseudo-factor | Formal factor combined to derive the levels of a real factor |

Run-indexing factors | The first m design factors, whose q^{m} combinations |

index the runs in the design |

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