Interpretation fractional factorials

The decision to select a larger design with more experiments could depend on the statistical interpretation one would like to apply (see Section 3.4.7). If the same six factors are examined in a fractional factorial design,... 

Multiple-factor interaction effects can be used to determine a critical effect value for the interpretation of full and fractional factorial designs [29] ... 

A number of software packages or expert systems for ruggedness testing has been developed. RES (commercialized under the name Shaiker ) is an expert system created by Van Leeuwen et al. [4,23] and has been validated and evaluated [42,43]. It uses fractional factorial and Plackett-Burman designs and allows to test the factors at two or three levels. The interpretation criteria used here are the predefined values (see Section 3.4.8). 

Merck also proposed recently an expert system called Ruggedness Method Manager for ruggedness tests of chromatographic assay methods. The system uses fractional factorial designs. Besides the factors to be examined, interactions that possibly also could be relevant have to be defined by the user. The system then calculates a design in which the main effects are not confounded with one of the specified interactions. The interpretation criterion to identify statistically significant effects is not known to the authors of this chapter. 

The fractional factorial designs, including the Latin squares, are generally used for screening possible experimental variables in order to find which are the most important for further study. Their use is subject to some fairly severe assumptions which should be known and taken into consideration when interpreting the data ... 

Interpretation of a fractional factorial experiment always requires careful study of the results, engineering or scientific knowledge about the process being studied, and sometimes the judicious use of Occam s razor.1 Confirmation experiments... 

Assume that you have run a fractional factorial design 2 (4 = 12, 5 = 13, 6 = 23), showing that the variables 1 and 5 are probably not significant, the following interpretation of the estimated effects can be attempted. 

Table 2 is a half-fraction of a full 2 design. Looking carefully at these experiments one can see that the combination of each set of three variables, for example B, C, and D. constitutes a full 2 design. One says then that the full factorial for By C, and D is embedded in the half-fraction factorial design. This also means that, if D is found to be unimportant, one can interpret the experiment as a full factorial design for factors A, B, and C without any confounding between interactions of the remaining factors. 

Appropriate designs might be based on factorial designs (full or fractional) or a central composite design. Response surface methods frequently rely on visualization of the data for interpretation. 

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