Ratio measurement scales

Four types of measurement scale can be used for assigning values to varying amounts of a property associated with a system input or system output [Summers, Peters, and Armstrong (1977)]. In order of increasing informing power, they are nominal, ordinal, interval, and ratio scales. The characteristics at determine a measurement scale s level of sophistication are name, order, distance, and origin. The characteristics of the four types of measurement scale are shown in Table 1.3. The nominal scale possesses only one of these characteristics the ratio scale possess all four characteristics. 

There are many reasons why it is important to understand which type of measurement scale is being used to describe system inputs and outputs. One reason is that most statistical techniques are not applicable to data arising from all four types of measurement scales the majority of techniques are applicable to data from interval or ratio scales. 

Indicate which type of measurement scale (nominal, ordinal, interval, or ratio) is usually used for the following characteristics time, mass, library holdings, gender, type of heart attack, cholesterol level as measured by a clinical chemical laboratory, cholesterol level as reported by a doctor to a patient, pipet volume, and leaves on a plant. 

Laboratory studies have shown that omega (MAZ structure type) based paraffin hydroisomerization catalyst shows higher activity than mordenite based catalyst and better selectivity, i.e. higher octane due to higher yield of di-branched paraffins compared to mordenite performance (17). The isomerization of a C5/C6 cut at 15 bar results in a final calculated RON of 80.4 for the alumina bound dealuminated PtH-MOR catalyst supplied by IFP with undisclosed (most likely similar) Si/Al ratio, measured at 265 °C compared to a RON value of 80.9 for an alumina bound dealuminated PtH-MAZ catalyst with bulk Si/Al = 16, measured at 250 °C. Both measurements were performed in a bench-scale tubular reactor with a volume of 50 cm3 of 2 mm diameter extrudates with WHSV of 1.5 h and H2/HC of 4. This... 

This apparatus is based on the principle of the detection by flame ionisation. It is especially dedicated to the study of gaseous organic compounds (except formaldehyde, formic acid and carbon suliur). It allows the measurement of the VOC molar ratio in the helium flow (y). The gas analyser is able to perform VOC molar ratio measurements up to 10000 ppm THC. The measuring range may be selected (minimum end of scale value 4 ppm THC). Accuracy and repeatability on each range are better than 1% FSD. 

Figure 2. Nitrogen isotope abundances in solar system materials upper scale gives absolute ratios lower scale gives relative to the terrestrial AIR standard. Heavy bars show observed ranges light bars show measurement...

Figure 5. Xe isotopic compositions in various trapped components Q (PI), ureilite, subsolar as well as P3 in presolar diamonds and N in presolar SiC and graphite (Table 5). More anomalous components are shown in Figure 8. Ratios are normalized to Xe, and shown are deviations in per mill of the Xe/ Xe ratios from the corresponding ratios measured for the solar wind (Table 5 errors for solar wind not included). Values for Xe and Xe in the N component are off scale at -156 and +342.

The He/ He ratios measured in OIB are more variable, with values both below and above that of MORE (Fig. 4). He/ He values below MORE are often associated with basalts containing Pb isotopes more radiogenic than MORE, and probably include recycled components (Kurz et al. 1982 Hanyu and Kaneoka 1998 Earfod et al. 1999). Intraplate volcanic systems with He/" He lower than MORE represent less than 10% of the OIE flux (e.g.. Sleep 1990). It is therefore typically assumed that these OIE do not represent large-scale reservoirs that must be incorporated into global noble gas models. 

This chapter provides an overview of mass spectrometer function and operation. It describes specific instrument types with demonstrated or potential application for measuring radionuclides and surveys the application of these instruments to radionuclide detection. Finally, it discusses the circumstances under which use of mass spectrometers is advantageous, the type of mass spectrometer used for each purpose, and the conditions of sample preparation, introduction and analysis. Its perspective is from a national laboratory active in environmental and non-proliferation monitoring. It emphasizes isotope ratio measurements, but mass spectrometric measurements also provide isotope mass information. Several recent books describe elemental and isotope ratio mass spectrometry in far greater detail than is presented here (Barshick et al., 2000 De Laeter, 2001 Montaser, 1998 Nelms, 2005 Platzner, 1997 Tuniz et al., 1998). High-resolution mass spectrometry forms the basis of the mass scale used for elemental and isotopic masses (Coplen, 2001), but this application of MS falls outside the scope of this chapter. 

Measurement scales S. minimum range should contain at least one selfsimilarity iteration as shown in Refs.. In this case the condition for ratio of maximum, and minimiun, areas of covering quadrates should be fulfilled [39] ... 

It should be noted that the minimum range of the measurement scales of 5 should contain at least one self-similarity iteration. In this case the condition for the ratio of the maximum S and minimum S areas of... 

With LA, MC-ICP-MS isotope ratio measurements can be performed in just a few minutes per sample as compared with the several hours per sample required for TIMS analysis. In addition, LA-MC-ICP-MS can yield spatially resolved isotope ratio characterization. Thus, provenance studies of ceramic paints, glazes, and slips in situ by LA-MC-ICP-MS measurement of lead and/or other isotope ratios are obvious areas for future development. Hints of the potential of this approach are highlighted in a recent study by Huntley [74], which showed that interaction on different spatial scales can be detected via elemental analysis of paste together with lead isotope analysis of glaze paints on Zuni glazed wares. 

Figure 3.5 Use of three-isotope plots to check for spectral interferences in MC-ICP-MS. Each point represents the mean of an isotope ratio measurement of a standard (filled circles) or a sample (empty circle) of natural isotopic composition. Isotope ratios are plotted on the delta scale (5) as relative deviations in parts per thousand from the known isotope ratio of an isotopic reference material of natural isotopic composition. The diagonal line represents the theoretical fractionation curve as defined by the isotopic masses and an exponential fractionation law. (a) Absence of isobaric interferences. Data points from standard and sample plot on the theoretical curve, (b) At least one isotopic signal in the mass spectrum of the standard and the sample is subject to spectral interference from an isobaric nuclide, polyatomic ion, or doubly charged ion. (c) Matrix differences between sample and standard result in an offset of the sample data points from the theoretical fractionation curve.

Fig. 123.2 Oak Ridge National Laboratory georeactor numerical simulation calculated He/ He ratios, normalized to the same ratio in air, as a function of time. For comparison, ranges of values are shown for helium ratios measured in samples from mid-oceanic ridges. Note the ascent of georeactor hehum ratios approaching the present age of earth, indicated by the arrow. Georeactor helium ratios increase as the uranium fuel becomes depleted. Comparably high values are observed in certain deep-source lavas, such as those from Hawaii and Iceland, are evidence that the end of the georeactor s life is approaching, although the time-scale is not precisely known. (Source Maverick s Earth and Universe, Herndon, 2008, with permission)...

In order to realize inter- and intra-laboratory consistency, measured isotope abundance ratios of the sample and reference gases are compared using a d (delta) scale. In the case of carbon isotope ratio measurements, d values are calculated as shown in Equation [6]. The d values for other elements are calculated based on the isotope abundance ratios listed in T able 1. 

Fig. 12.9 Plot of relative volume decrease, open symbols, and relative stress decrease, closed symbols, as a function of log time for vulcanized natural mbber at -26 °C at indicated extension ratios. Stress measurements scaled appropriately.

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