Factorial design quantitative/qualitative

Full factorial designs Categorical / qualitative, quantitative and combined Choice of factors, calculation of main effects and interactions... 

In factorial designs we have n variable factors which we are able to adjust at fixed levels. Sometimes the factors only exist in discrete levels but sometimes we are interested in or are only able to set up these discrete levels. The assignable causes, the factors which we assume will affect the recorded responses, may be quantitative or qualitative features. The quantitative character of temperature, pH, stirring velocity, etc. is obvious. Examples of qualitative factors are the age of membranes in ion selective electrodes or filter devices (with the levels old and new) or a certain medication or noxious agent (present or absent). In this situation the notion version of a factor makes sense (ISO 3534/3 in [ISO STANDARDS HANDBOOK, 1989]). 

An important advantage of two level factorial designs is that some factors can be categorical in nature, that is, they do not need to refer to a quantitative parameter. One factor may be whether a reaction mixture is stirred (+ level) or not (— level), and another whether it is carried out under nitrogen or not. Thus these designs can be used to ask qualitative questions. The values of the b parameters relate directly to the significance or importance of these factors and their interactions. 

One of the most useful symmetrical designs is based on the 4 factorial design (table 2.17), described (using the previous notation) as 4V/4 5 factors at 4 levels are screened in 4 = 16 experiments. We again emphasize that the numbers 0, 1,2, and 3 identify qualitative levels of each variable and have no quantitative significance whatsoever. 

This is why no distinction is drawn here between qualitative and quantitative factors quantitative factors are treated in the same way as qualitative factors (and not the reverse - a mistake made by many users of factorial designs). 

The 2 Factorial Designs are the simplest possible designs, requiring a number of experiments equal to 2, where k is the number of variables under smdy. In these designs each variable has two levels, coded as 1 and +1, and the variables can be either quantitative (e.g. temperature, pressure, amount of an ingredient) or qualitative (e.g. type of catalyst, t3q>e of apparatus, sequence of operations). 

In both the Factorial Design and the Plackett-Burman Design all the variables are studied at two levels. An interesting property is that these designs can be applied to both types of variables. In the case of quantitative variables the — 1 level is usually (but not always) assigned to the lower level and the +r to the higher level in the case of qualitative variables the — 1 and -1-1 levels are arbitrarily assigned. 

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