Ordinal scales

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. 

It is not necessary that the interval length in each category should be equal, but in various lengths as in this table. Ordinal scales allow one to order the items in terms of which one has less and more of the quality represented by the variable, but still they do not allow one to say how much more. One can say that 

Description Without Very minor Minor Moderate Severe Very severe CoUapse 

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Flavor Intensity. In most sensory tests, a person is asked to associate a name or a number with his perceptions of a substance he sniffed or tasted. The set from which these names or numbers are chosen is called a scale. The four general types of scales are nominal, ordinal, interval, and ratio (17). Each has different properties and allowable statistics (4,14). The measurement of flavor intensity, unlike the evaluation of quaUty, requires an ordered scale, the simplest of which is an ordinal scale. 

Fig. 4-1. Calculated intensity-wavelength distributions for continuous spectra produced by electron bombardment of various targets. The ordinate scale is arbitrary.

An application of Eq. (19) is shown in Fig. 4, which gives the solubility of solid naphthalene in compressed ethylene at three temperatures slightly above the critical temperature of ethylene. The curves were calculated from the equilibrium relation given in Eq. (12). Also shown are the experimental solubility data of Diepen and Scheffer (D4, D5) and calculated results based on the ideal-gas assumption (very large errors are incurred when corrections for gas-phase nonideality are neglected. 

Speciation of plutonium leached from the glass cubes is shown in Figure 1. The first bar represents the total amount of insoluble plutonium and is the summation of suspended plutonium (the difference between the values for filtered and unfiltered waters) and sorbed plutonium—viz., the amount removed from the cubes by a 0.1 M perchloric acid wash, normalized to the volumes of leachant solutions so that it is comparable to the other values in the graphs. For simplicity, the insoluble fractions are combined in one bar, whereas the various oxidation states in the soluble fraction are represented by separate bars. It should be noted that the ordinate scale varies among the graphs. 

The conventional control chart is a graph having a time axis (abscissa) consisting of a simple raster, such as that provided by graph or ruled stationary paper, and a measurement axis (ordinate) scaled to provide six to eight standard deviations centered on the process mean. Overall standard deviations are used that include the variability of the process and the analytical uncertainty. (See Fig. 1.8.) Two limits are incorporated the outer set of limits corresponds to the process specifications and the inner one to warning or action levels for in-house use. Control charts are plotted for two types of data ... 

Residuals On/Off) permits the residuals to be superimposed at a chosen ordinate and with a given magnification relative to the ordinate scale. 

The substrates used were PC citrus pectin E orange peel G glucose, Gly gycerol, APG polygalacturonic acid. Results of two cultures (1 and 2) are presented. On ordinates, specific activities (Activity Units par p,g of extracellular proteins) are presented. Note the ordinates scale differs from one histogramme to another. 

Fig. 5.—The partial degradation of decamethylene adipate polyester with small percentages of decamethylene glycol (experiments 8, 13, and 17), or with lauryl alcohol (experiment 19), at 109°C, catalyzed with 0.1 equivalent percent of p-toluenesulfonic acid. The fraction of added glycol, or alcohol, unassimilated has been calculated indirectly from melt viscosity measurements and is plotted on the logarithmic ordinate scale.2 ...

Fig. 107.—Tensile strengths of natural rubber plotted against the degree of cross-linking with bis-azo vulcanizing agent (O), expressed as equivalent percent (pXlOO). Upper curve ( ) sample prepared using one equivalent percent of bis-azo compound plus monoreactive ethyl azodi-carboxylate for the total degrees of modification of the units indicated on the ordinate scale. (Flory, Rabjohn, and Shaffer.

Table 32.1 describes 30 persons who have been observed to use one of four available therapeutic compounds for the treatment of one of three possible disorders. The four compounds in this measurement table are the benzodiazepine tranquillizers Clonazepam (C), Diazepam (D), Lorazepam (L) and Triazolam (T). The three disorders are anxiety (A), epilepsy (E) and sleep disturbance (S). In this example, both measurements (compounds and disorders) are defined on nominal scales. Measurements can also be defined on ordinal scales, or on interval and ratio scales in which case they need to be subdivided in discrete and non-overlapping categories. 

Fig. 6 Gaussian convolution of an experimental profile (a) raw spectrum (b) after convolution by a Gaussian of width 5 points (c) after convolution by a Gaussian of 30 points. The ordinate scale is arbitrary. 

Fig. 32. CD spectra of c-myci.143 protein at three temperatures as indicated. The ordinate scale is the mean residue ellipticity in units of 103 deg cm2/dmol. From McEwan et al. (1996). Biochemistry 35, 9584-9593, with permission. 1996, American Chemical Society.

Fig. 2. a) Symmetric (5) and antisymmetric (A) levels of trimethylene energy variation with increase of angle a (abscissa, degrees), b) The same for the oxyallyl radical. The vertical line is 1 eV on the energy ordinate scale. 

Fig. 3 Fourier transform (FT) infrared (upper) and FT-Raman (lower) spectra of aspirin. The left ordinate scale is representative of the Raman intensity, whereas the right ordinate scale represents IR transmission units. 

Fig. 28. Time-resolved phosphorescence spectra of quinoxaline in durene host observed at 1.38 K and at (a) 30 msec, (b) 450 msec, and (c) 1500 msec after excitation cutoff. The ordinate scale is normalized with respect to the 0 - 0" band. The numbers shown in (c) represent the vibrational frequencies (in wavenumber unit) measured from the 0 - 0" band (21639 cm r). The arrows indicate the bands whose relative intensities are remarkably enhanced at later times after the excitation cutoff. (From Yamauchi and Azumi, Ref. >)...

Relative primary productivity, POC fluxes at 105 and 3000 m, and POC sediment accumulation rates versus latitude in the central equatorial Pacific Ocean. Data are normalized to the maximum value in each transect. Survey 1 was conducted during February-March 1992 under El Nino conditions and Survey 2 from August to September 1992 under non-El Nino conditions at longitudes ranging from 135 to 140°W. Ordinate scale is reset to 1.0 at each maximum, and the absolute magnitude (mmolCm ij-i) of each parameter is given next to its maximum. Source-. From Flernes, P. J., et al. (2001). Deep-Sea Research I 48, 1999-2023. 

When the statistieally sophisticated psychologists realized what I was doing, they had a field day pointing out my failings unjustified assumptions, violations of statistical theory and other mathematical crimes. They talked about ordinal scales versus ratio scales and scolded me for not using analysis of variance instead of Chi-square and Student s T tests of significance. 

The ordinal scale possesses the characteristic of order, but it does not make use of the distance property. In a ranked group of twelve workers, for example, the numerical distance between the best worker ( 1) and the next-to-the-best worker ( 2) is the same as the numerical distance between the two middle-ranked workers ( 5 and 6), but the ordinal scale does not imply that worker 5 is as much better than worker 6 as worker 1 is better than worker 2. Reward systems based on rank is a topic of much current interest [Scherkenbach (1986), Scherkenbach (1991), Scholtes (1988), and W. Deming (1986)]. 

When arranged according to increasing dipole moment, the solvent names are expressed on an ordinal scale as 1,7, 4, 2, 8, 6, 9, 5, 3. Figure 2.12 plots percent... 

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. 

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