Nominal scale data

Since we have no idea how large the steps are between scores, we obviously cannot claim that all steps are of equal size. In fact, it is not even necessarily the case that the difference between scores of —2 and 0 is greater than that between +1 and +2. So, neither of the special characteristics of an constant interval scale apply to this data. 

The name ordinal reflects the fact that the various outcomes form an ordered sequence going from one extreme to its opposite. Such data are sometimes referred to as ordered categorical . In this case the data are usually discontinuous, individual cases being scored as — 1, +2 etc., with no fractional values. 

In this case there is no sense of measuring a characteristic. With this data we use a system of classifications, with no natural ordering. For example, one of the factors that might influence the effectiveness of treatment could be the specific manufacturer of a medical device. Therefore, all patients would be classified as users of Smith , Jones or Williams equipment. There is no natural sequence to these they are just three different makes. 

With ordinal data we did at least know that a case scored as (say) +2 is going to be more similar to one scored +1 than to one scored 0 or — 1. However, with nominal data, we have no reason to expect Smith or Jones equipment to have any special 

Quite commonly there are just two categories in use. Obvious cases are male/ female, alive/dead or success/failure. In these cases, the data are described as dichotomous . 

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Show how we describe nominal scale data (data that consist of categorizations rather than measurements)... 

Emphasise the inefficient nature of nominal scale data... 

In this chapter we will start to look at data where no measurements are made on individuals. Instead, each individual is placed in a category and the numbers in each category are then counted. A classic example is where we look at a medical treatment and declare each patient s outcome as successful or unsuccessful . We then count the number of successes and failures. This type of data was introduced in Chapter 1 as nominal scale data. 

The inefficiency of nominal scale data is further exacerbated when one of the categories is rare. For example, a drug may produce a side-effect in a small proportion of users. In the example that follows, we will assume a 4 per cent occurrence rate. If we studied 500 patients that might sound like a perfectly adequate number. 

Nominal scale Data are simply descriptive a series of categories, which are identified and labeled using a name or a number, is listed samples are classified into groups on basis of the frequencies of each category. They contain very little information because no quantitative relationships are established. 

Normally, these surveys generate only ordinal or nominal scaled data. An additional possibility of a large multinational firm is to ask market researchers of the foreign affiliates. This has the advantage, that the R D department does not have to disclose the innovation project to experts outside the company. The indicators must be quantified for a set of countries that can be expected to be possible lead markets. Possible countries are not only industrialised countries but newly industrialised countries as well (Brazil, Singapore, South Africa). The set of countries should be representative to all environments and should include the expectations of all project team members about the lead markets, for better internal acceptance of the result. If these countries are not included in the analysis members might oppose the result because of the exclusion. 

The student collected one data pair for each business day for the past nine-months. Each data pair consisted of (1) the amount of money issued by her department in computer-generated checks on that day, and (2) the amount of money in checks that cleared the banks on that day. Table 10.1 is a four-column list of the 177 pairs of data she collected. Each entry gives (1) the sequence, or acquisition number ( Seq ), starting with Thursday, August 8, and increasing by one each business day, five business days a week (2) a nominal scale (that can also be used as an ordinal or interval scale) for the day of the week ( D ), where 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, and 5 = Friday (3) the amount of money issued in checks ( Iss ) and (4) the amount of money in checks that cleared ( Clr ). 

Another important feature of mathematical modeling techniques is the nature of the response data that they are capable of handling. Some methods are designed to work with data that are measured on a nominal or ordinal scale this means the results are divided into two or more classes that may bear some relation to one another. Male and female, dead and alive, and aromatic and nonaromatic, are all classifications (dichotomous in this case) based on a nominal scale. Toxic, slightly toxic, and non-toxic are classifications based on an ordinal scale since they can be written as toxic > slightly toxic > non-toxic. The rest of this section is divided into three parts methods that deal with classified responses, methods that handle continuous data, and artificial neural networks that can be used for both. 

Analysis will then probably progress to hypothesis testing — looking to see whether the answer provided to one question influences the pattern of answers to another question. As so many questionnaire data are nominal scale, contingency chi-tests tend to dominate. 

Discriminant analysis, also known as the linear learning machine, is intended for use with classified dependent data. The data may be measured on a nominal scale (yes/no, active/inactive, toxic/non-toxic) or an ordinal scale (1,2,3,4 active, medimn, inactive) or may be derived from continuous data by some rule (such as low if <10, high if > 10). The objective of... 

The word ordinal means ordering the objects according to their ranks. Hence, any rankable data set has ordinal scale. In the ordinal scales, each description is expressed by words that include uncertainty. One can count and order, but not measure ordinal data. For instance, the nominal scale in Table 7.1 can be converted into ordinal scale as in Table 7.3, where aforementioned percentages are attached to each category. 

Nominal scale, i.e. a classification of the data by applying a classification scheme. A classification scheme is a taxonomy, when it consists of a complete set of mutually exclusive classes. Sex is an example of a taxonomy with two classes (male/female). 

The first four criteria are derived from feedback-control theory. A SHE performance indicator must be observable and quantifiable, i.e. it must be possible to observe and measure performance by applying a recognised data-collection method and scale of measurement. The nominal scale is the simplest type. This means that we must be able to tell whether the result represents a deviation from a norm or not. Usually, the SHE performance indicators are expressed on a ration scale of measurement. A typical example is the LTI-rate, i.e. the number of lost-time injuries per one million hours of work. 

In the previous Section, we distinguished between two different types of data on accidents and near accidents, i.e. coded data (applying a nominal, ordinal, interval or ratio scale) and free-text descriptions. We will here discuss the principal difference between qualitative or free-text data on the one hand, and coded data on the other hand. We will focus on the trade-off between using free-text descriptions and coding the data according to a coding schedule (i.e. a nominal scale). 

All relevant data about the accidents and near accidents are stored in a coded format. This coding may take place during data collection, see Section 13.4. Nominal scales of measurement are applied in coding the descriptions of losses, the sequence of event and causal factors, etc. The ISA, ILCI and MAIM accident models presented in Chapters 5 and 13 have typically been developed for this purpose. Table 15.2 shows a coding schedule based on the ILCI model. 

The application of accident-concentration analysis is not meaningful for small data sets. There must be at least in the region of 50 accident cases. Useful types of data in accident-concentration analysis are location, activity, equipment, accident type, type of injury and part of body affected. The analysis is facilitated if some of the data is coded (i.e. presented on a nominal scale of measurement), especially if large quantities of data are handled. The coding should, however, not be done at the cost of the details in the information. The free-text description of the sequence of events should always be available. 

Shoiild the particles have a tendency to cohere slightly during sedimentation, each sampling time, representing a different nominal detention time in the clarifier, will produce different suspended-sohds concentrations at similar rates. These data can be plotted as sets of cui ves of concentration versus settling rate for each detention time by the means just described. Scale-up will be similar, except that detention time will be a factor, and both depth and area of the clarifier will influence the results. In most cases, more than one combination of diameter and depth will be capable of producing the same clarification result. 

Detention efficiency. Conversion from the ideal basin sized by detention-time procedures to an actual clarifier requires the inclusion of an efficiency factor to account for the effects of turbulence and nonuniform flow. Efficiencies vaiy greatly, being dependent not only on the relative dimensions of the clarifier and the means of feeding but also on the characteristics of the particles. The cui ve shown in Fig. 18-83 can be used to scale up laboratoiy data in sizing circular clarifiers. The static detention time determined from a test to produce a specific effluent sohds concentration is divided by the efficiency (expressed as a fraction) to determine the nominal detention time, which represents the volume of the clarifier above the settled pulp interface divided by the overflow rate. Different diameter-depth combinations are considered by using the corresponding efficiency factor. In most cases, area may be determined by factors other than the bulksettling rate, such as practical tank-depth limitations. 

FIG. 18 83 Efficiency curve for scale-up of barch clarification data to determine nominal detention time in a continuous clarifier,... 

In non-metric MDS the analysis takes into account the measurement level of the raw data (nominal, ordinal, interval or ratio scale see Section 2.1.2). This is most relevant for sensory testing where often the scale of scores is not well-defined and the differences derived may not represent Euclidean distances. For this reason one may rank-order the distances and analyze the rank numbers with, for example, the popular method and algorithm for non-metric MDS that is due to Kruskal [7]. Here one defines a non-linear loss function, called STRESS, which is to be minimized ... 

The parameter ad is included to allow for catalyst deactivation as shown by Liebman. The data for the example (physical constants) are shown in Table 1. All temperatures and concentrations were scaled using a nominal reference concentration (Ar = 1 x 10-6 gmol cm-3) and a nominal reference temperature (Tr = 100.0 K). 

Fig. 7 Relative integrated intensities under the peaks (left scale) and relative degree of crystallinity (right scale) obtained from wide-angle X-ray scattering data for D7732C2310 quenched from T = 115 to 30°C. The cooling rate was 30°Cmin 1. The arrow indicates the nominal point at which the final temperature was reached. For convenience, the amorphous peak intensity has been divided by 5. (Reprinted with permission from [ 107]. Copyright 2003 American Chemical Society)...

Quantitative methodology uses large or relatively large samples of subjects (as a rule students) and tests or questionnaires to which the subjects answer. Results are treated by statistical analysis, by means of a variety of parametric methods (when we have continuous data at the interval or at the ratio scale) or nonparametric methods (when we have categorical data at the nominal or at the ordinal scale) (30). Data are usually treated by standard commercial statistical packages. Tests and questionnaires have to satisfy the criteria for content and construct validity (this is analogous to lack of systematic errors in measurement), and for reliability (this controls for random errors) (31). 

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