Qualitative factors

Let us try to relate the (standardized) sensory data in Table 35.1 to the explanatory variables in Table 35.3. Essentially, this is an analysis-of-variance problem. We try to explain the effects of two qualitative factors, viz. Country and Ripeness, on the sensory responses. Each factor has three levels Country = Greece, Italy,... 

The factors chosen for study were the concentration of the ion-pairing reagent, the solution pH ( quantitative factors) and the acid chosen for pH adjustment (formic, acetic, propionic and trifluoroacetic acids) ( qualitative factor). The effect of these factors was assessed by using responses that evaluated both the HPLC (the number of theoretical plates and the retention time) and MS performance (the total peak area and peak height) for each of the four analytes studied, i.e. 1-naphthyl phosphate (1), 1-naphthalenesulfonic acid (2), 2-naphthalenesulfonic acid (3) and (l-naphthoxy)acetic acid (4). 

The selected factors are either mixture-related, quantitative (continuous), or qualitative (discrete).A mixture-related factor is, for instance, the fraction organic solvent in the buffer system. Examples of quantitative factors are the electrolyte concentration, the buffer pH, the capillary temperature, and the voltage, and of qualitative factors the manufacturer or the batch number of a reagent, solvent, or capillary. Sample concentration (see Table 1) is a factor sometimes included. However, the aim of the method tested is to determine this concentration through the measured signal, from a calibration procedure. Thus, one evaluates the influence of the sample concentration on the sample concentration, which we do not consider a good idea. 

Qualitative factors are also frequently considered in a robustness test. " For CE methods, factors such as the batch or manufacturer of the capillary, reagent or solvent can be selected. When evaluating the influence of such qualitative factor, the analyst should be aware that the estimated effect is only valid or representative for the examined discrete levels and not for any other level of that factor, and certainly not for the whole population. For example, when examining two capillaries X and Y, the estimated effect only allows drawing conclusions about these two capillaries and not about other capillaries available on the market. Such approach allows evaluating whether capillary Y is an alternative for capillary X, used, for instance, to develop the method. 

For qualitative factors, only discrete values are possible, e.g., capillaries X, Y, or Z. As already indicated, this means that only conclusions can be drawn about the examined capillaries and no extrapolation to other capillaries can be made. The most logical in a robustness test is to compare the nominal capillary with an alternative one. 

The factors in Table 3 were selected from a non-aqueous chiral separation method for timolol. One qualitative factor (1), i.e., the type of CE equipment, was examined. Two HPCE systems, A and B, with different software versions for equipment control, data acquisition, and handling were compared. Six quantitative factors ((2) till (7)), for which the extreme levels usually were situated symmetrically around the nominal, also were... 

In this chapter, the possibilities to set up and treat the results of a robustness test were reviewed (Sections I-VIII). Robusmess usually is verified using two-level screening designs, such as FF and PB designs. These designs allow examining the effects of several mixmre-related, quantitative, and qualitative factors, on one or several responses, describing either quantitative and/or qualitative aspects of the analytical method. 

List five quantitative factors. List five qualitative factors. What do the key words type and amount suggest ... 

Full factorial designs have been especially useful for describing the effects of qualitative factors, factors that are measured on nominal or ordinal scales. This environment of qualitative factors is where factorial designs originated. Because all possible factor combinations are investigated in a full design, the results using qualitative factors are essentially historical and have little, if any, predictive ability. 

Because we intend to carry out these experiments in the leisure winter months, our inventory of frozen fruit will be low and we will not have enough of any one type of fruit to be used in all of the experiments. However, we will have available modest amounts of each of twenty types of fruit, so we can randomly assign these fruit types to each experiment and expect to average out any effect caused by variability of the qualitative factor, fruit . A systems view of the experimental arrangement is shown in Figure 15.6. 

Figure 15.7 Factor combinations for a completely randomized design investigating the effect of temperature. Fruit number is an arbitrarily assigned, qualitative factor. Numbers beside factor combinations indicate the time order in which experiments were run.

The randomized paired comparison design discussed in the previous section separates the effect of a qualitative factor, fruit, from the effect of a quantitative factor, temperature (see Section 1.2). The randomized complete block design discussed in this section allows us to investigate more than one purely qualitative variable and to estimate their quantitative effects. 

In the classical statistical literature, one of the two qualitative factors is referred to as the treatments and the other qualitative factor is referred to as the blocks . Hence, the term block designs . In some studies, one of the qualitative factors might be correlated with time, or might even be the factor time itself by carrying out the complete set of experiments in groups (or blocks ) based on this factor, estimated time effects can be removed and the treatment effects can be revealed... 

Figure 15.17 Factor combinations for the randomized complete block design investigating two qualitative factors, type of univalent cation and type of divalent cation. Each factor combination is replicated.

The randomized complete block design has provided a sensitive way of viewing the data from this set of experiments involving two qualitative factors. The linear model using dummy variables ignores much of the variation in the data by again focusing on pairwise differences associated with the different discrete levels of the factors of interest. 

For the example used in Section 15.5, there would be three y s and four x s (or, perhaps, four y s and three t s). If y is associated with the qualitative factor univalent cation , then y would be the average block difference in response between the experiments involving Li and the overall mean y and y, would be the corresponding differences for experiments involving Na and K. Similarly, x g, Xj-, x, and Xgj would be the average treatment differences for experiments involving the divalent cations Mg, Ca, Sr, and Ba. Thus, the full model would be... 

But let me also be quick to point out that the impacts will not be as significant as they at first appear. Hie number of new chemicals is not a complete measure of the output of chemi-cal innovation. It ignores qualitative factors about the chemicals, a very important one of which is the unintended environmental and health effects resulting from the use of the product. 

The above is not a complete statement of the theory of matter of Aristotle, but will, it is hoped, give an idea of the elaborateness and complexity of the Aristotelian concept, and serve to illustrate how far removed was his method of developing the theory from the inductive methods of modern science. The concept of the four elements as qualitative factors in the constitution of other bodies, with their inherent forces of heat, cold, moist, dry, became accepted by later centuries as basic truth. His notion of a fifth element, variously interpreted, also held a place in the thought of later times, but his more complex notions of the nature of the elements and matter had little influence on the later development of natural philosophy. 

Because qualitative factors are not continuous, we cannot use a linear model such as yu = / + >S,jc,x + /J2x2l + ru to describe the behavior of this system. For example, if x, were to represent the factor univalent cation , what value would x, take when Li was used Or Na Or K There is no rational basis for assigning numerical values to xt, so we must abandon the familiar linear models containing continuous (quantitative) factors. 

It would thus appear that it is possible to mark exactly in a great number of carbohydrates the chemical groups which, by establishing contact with complementary groups of the enzyme, orientate the substrate at the enzyme surface. Whereas orientation of the sugar molecule at the surface of the respective catalyst may be regarded as the qualitative factor in enzyme specificity (conditio sine qua non), the ratio... 

Within the set of location factors it is common to distinguish between quantitative and qualitative factors, often without properly defining the difference between them. In the course of this work, factors that have a directly measurable financial impact will be referred to as quantitative factors and all other location factors will be considered of qualitative nature. A further distinction can be drawn between qualifying and ranking factors (cf. Pellerin et al. 2003, p. 268) with the former specifying minimum requirements and the latter being used to rank feasible alternatives. 

Using DEA requires three major steps. In a first step, the DMUs to be considered in the analysis have to be determined. These have to be homogeneous with respect to their tasks and the types of inputs and outputs used. The second step is to select the input and output factors that are to be used for the comparison. DEA also accommodates qualitative factors with the only requirement being that numerical values have to be assigned to all factors. Finally, a mathematical programming model such as the basic formulation provided below is solved separately for every DMU. 

The first step is to determine whether a classical additive model, an outranking approach or DEA should be used. The criteria to be used for the site selection/site ranking task do not lend themselves to a clear classification into input and output parameters. Furthermore, the relatively complex mathematical procedure underlying DEA was perceived to be inappropriate for support of top management decisions that are to a large extent driven by qualitative factors. Hence, DEA was ruled out first. 

The objective weights obtained in the context of the site ranking also illustrate the relative importance of the various location factors for specialty chemicals industry as shown in Figure 34. However, these priorities depend on the type of business considered, the decision context, the scale used and the fact that minimum requirements are assumed to be achieved by all sites included in the analysis. In the application cases, cost performance was considered to be approximately twice as important as qualitative aspects. Within the set of qualitative factors development potential, production know-how and utility availability clearly dominated the site assessment. 

Table 2.4 shows basic statistical designs for all kinds of quantitative and categorical/qualitative factors. 

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