Interval 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. 

Measurement uncertainty is the most important criterium in both method validation and IQC. It is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand [14]. The measurand refers to the particular quantity or the concentration of the analyte being measured. The parameter can be a standard deviation or the width of a confidence interval [14, 37]. This confidence interval represents the interval on the measurement scale within which the true value lies with a specified probability, given that all sources of error are taken into account [37]. Within this interval, the result is regarded as being accurate, that is, precise and true [11]. 

Measurement issues also undermine the adequacy of the EDP model in some circumstances. It has been noted by Teas (1993) that when interval level scales are used to assess expectations and satisfaction, a performance expectation discrepancy of, for example, -2 (minus 2) can be realised in a number of ways. Working with a 7- point scale -2 may result when expectations were... 

Because these measurements have constant sized steps (intervals), the measurement scale is described as a constant interval scale and the data as interval scale . Although the weights quoted in Figure 1.1 are exact integers, weights of 1.5 or 3.175 g are perfectly possible, so the measurement scale is said to be continuous . 

Back in Chapter 1, data were described as interval (measurements on a regular scale), ordinal (measurements on a scale of undefined steps) and nominal (classifications). We have dealt extensively with two of these, but ordinal data have thus far been ignored. 

A dimension is a quantity such as time, mass, temperature, or distance, that can be expressed munerically in terms of one or more standard rmits. Dimensions have homogeneous linear scales so that a 2-meter interval measured at the begimiing of a 1-kilometer traverse is identical in length to a 2-meter interval measured near the end of the traverse. The magnitude of a dimension is expressed in terms of a pure number and a unit of measure. Units are standards to whieh dimensional quantities are compared to obtain a numerical ratio, which is the pure number. For example, comparison of... 

Halting interval HIC is the temperature interval measured in°C that cuts the time at the temperature of the TI or RTI in half. HIC is a measure of the slope of the temperature-time curve. It is not a constant, but changes with temperature even when the temperature-time curve is linear. In many practical cases, the error in the HIC is sufficiently small in the temperature range of interest [252], For practical reasons, HIC is expressed in°C, while the time axis has a I/T scale with absolute temperature in K. 

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. 

The main predictions of the scaling theory [40], concerning the dynamics behavior of polymer chains in tubes, deal with a number of characteristic times the smallest time rtube measures the interval of essentially Rouse relaxation before the monomers feel the tube constraints significantly, 1 < Wt < Wrtube = and diffusion of an inner monomer is... 

In order to analyze this type of plot, the analyst must manually change the time scale to obtain discrete frequency curve data. The time interval between the recurrences of each frequency can then be measured. In this way, it is possible to isolate each of the frequencies that make up the time-domain vibration signature. 

The absorbance and the percentage transmission of an approximately 0.1M potassium nitrate solution is measured over the wavelength range 240-360 nm at 5 nm intervals and at smaller intervals in the vicinity of the maxima or minima. Manual spectrophotometers are calibrated to read both absorbance and percentage transmission on the dial settings, whilst the automatic recording double beam spectrophotometers usually use chart paper printed with both scales. The linear conversion chart, Fig. 17.18, is useful for visualising the relationship between these two quantities. 

It should be noted that when we compare the brightness of a LGS to a NGS, the result depends on the spectral bandwidth, because the LGS is a line source, whereas the NGS is a continuum one. The magnitude scale is a logarithmic measure of flux per spectral interval (see Ch. 15). This means that a (flat) continuum source has a fixed magnitude, no matter how wide the filter is. In contrast, the magnitude of a line source is smaller for narrower bandpasses. It is therefore advisable to use the equivalent magnitude only for qualitative arguments. The photon flux should be used in careful system analyses. 

If we coimect the positions of the same inflexion points over various values of straight lines, we create an interval tree of scales, as shown in Fig. 7 for the signals of Fig. 5. The interval tree allows us to generate two very important pieces of information about the trends of a measured variable ... 

Equation (6a) implies that the scale (dilation) parameter, m, is required to vary from - ac to + =. In practice, though, a process variable is measured at a finite resolution (sampling time), and only a finite number of distinct scales are of interest for the solution of engineering problems. Let m = 0 signify the finest temporal scale (i.e., the sampling interval at which a variable is measured) and m = Lbe coarsest desired scale. To capture the information contained at scales m > L, we define a scaling function, (r), whose Fourier transform is related to that of the wavelet, tf/(t), by... 

Having completed the decomposition and reconstruction of a function at a finite number of discrete values of scale, let us turn our attention to the discretization of the translation parameter, u, dictated by the discrete-time character of all measured process variables. The classical approach, suggested by Meyer (1985-1986), is to discretize time over dyadic intervals, using the sampling interval, t, as the base. Thus, the translation parameter, u, can be expressed as... 

In Section II we defined the trend of a measured variable as a strictly ordered sequence of scaling episodes. Since each scaling episode is defined by its bounding inflexion points, it is clear that the extraction of trends necessitates the localization of inflexion points of the measured variable at various scales of the scale-space image. Finally, the interval tree of scale (see Section II) indicates that there is a finite number of distinct sequences of inflexion points, implying a finite number of distinct trends. The question that we will try to answer in this section is, How can you use the wavelet-based decomposition of signals in order to identify the distinct sequences of inflexion points and thus of the signal s trends ... 

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