Scaling magnitude estimation

Children aged 8-9 were shown to be able to estimate the intensity of sweetness in a suitable way compared to adults, by comparing category scale, magnitude estimation and hand separation (James et al, 2003). A nine-point scale was successfully applied to the evaluation of the intensity of sweetness and creaminess in children aged 8-10 and 11-14 years, but the researchers used pair comparisons to evaluate perceptions in children aged 5-7 years (Lavin and Lawless, 1998). A five-point scale was used to describe perception of sweetness intensity throughout the age span from 6 years ... 

Large-scale biomass production will come at a considerable cost to the society. We have already given an order of magnitude estimate for wood plantations. When biomass raw material is processed that competes with the food chain, as vegetable oils and sugars, the situation is even worse. For instance Smil [4] mentions that if the US vehicles were to run solely on corn derived ethanol the country would have to plant corn on an area 20% larger than is currently cropland . 

Hadronic vacuum polarization in the external field approximation for the pointlike proton also was calculated in [33]. Such a calculation may serve only as an order of magnitude estimate since both the external field approximation and the neglect of the proton form factor are not justified in this case, because the scale of the hadron polarization contribution is determined by the same yo-meson mass which determines the scale of the proton form factor. Again a more accurate calculation is feasible but does not seem to be warranted, and only an estimate of the hadronic polarization contribution appears in the literature [7]... 

Current models allow order-of-magnitude estimations but lack the fine-scale estimation capabilities that account for the variation of soil properties. The most... 

Criticism of the 9-point scale used in the AHP includes aspects such as its being bounded, lacking theoretical validation for the verbal equivalents used and especially the ratio scale property (cf. Belton 1986, p. 11). In practice, it can be observed that the values between 7 and 9 are only infrequently assigned because of a perceived lack of difference to the values 5 and 6. Alternative ratio scales and their performance relative to the traditional AHP scale can for example be found in Leskinen (2000) and Pohonen and Hamalainen (1998) while Schoner and Wedley (1989) suggest to use the magnitude estimation method instead. 

Many studies have attempted to compare the results of magnitude estimation versus some of the more standard scaling techniques or semi-structure or unstructured line techniques and different results have arisen from these various studies (5-8). Based on my experience, the more important consideration is the degree of training of the panel utilized in trained panel work rather than the type of scale that is used. However, magnitude estimation results do tend to show more differences when the differences are very small than do other methods. 

Sensations of oral chemical heat, as induced by pepper-derived compounds are amenable to psychophysical investigation and sensory evaluation by supra-threshold scaling techniques such as magnitude estimation and anchored graphic rating scales. 

The quickest way to make an order-of-magnitude estimate of plant cost is to scale it from the known cost of an earlier plant that used the same technology or from published data. This requires no design information other than the production rate. The capital cost of a plant is related to capacity by the equation... 

Arguments based on quite different scaling theory assumptions yield much the same order-of-magnitude estimates. For r - oo and fixed x= icr,2, where k is an inverse correlation length, Kcr/, we can use (4.82) with... 

The objective of this section is to identify the characteristic quantities for a generic mass transfer problem and the physical properties of the fluid (i.e., p and Hi, mix), which can be combined to represent the dimensions and an order-of-magnitude estimate of each term in the mass transfer equation. The characteristic scalar quantities are the average flnid velocity (n), a length scale L, and the inlet molar density of reactant A, Cao-... 

Introduce dimensionless variables (i.e., C, = Cps fi, etc.) and write each mass transfer rate process in terms of these dimensionless variables and the corresponding dimensional scaling factor. This scaling factor contains all the dimensions of, as well as an order-of-magnitude estimate for, the particular mass transfer rate process. For example, the left-hand side of equation (10-4) is written as follows, where all the variables are dimensionless ... 

The next objective is to identify a time constant for each important mass transfer rate process and solve the system of equations for the two-phase CSTR in terms of these time constants. This approach allows one to develop generic solutions in dimensionless form. For example, six time constants can be defined for (1) convection in the liquid phase (r), (2) chemical reaction in the liquid phase (X), and (3-6) interphase mass transfer for each component (0y, j = B,C1,M,H). Obviously, these six time constants produce five dimensionless ratios. Remember that time constants represent order-of-magnitude estimates of the time scales of mass transfer rate processes. The time constant for convective mass transfer in the liquid phase is equivalent to the liquid s residence time ... 

Giovanni, M.E. and Pangbom, R.M. 1983. Measurement of taste intensity and degree of liking of beverages by graphic scales and magnitude estimation. J. Food. Sci. 48, 1175-1182. 

Tables I, II, III and IV show the data base for the four sets of experiments reported there. Note that in each experiment a group of non-expert panelists evaluated each of the sets of odor mixtures twice, using magnitude estimation scaling. Thus, the tables each present numbers which are averages of approximately 32-36 ratings, depending upon the particular study. Furthermore, note that in Tables l-IV, the panelists profiled each stimulus on a variety of sensory characteristics.

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