Comparison of measured values

The f-test in this form can only be applied under the condition that the variances of the two sample subsets, sf and sf, do not differ significantly. This has to be checked by the F-test beforehand. The test statistic f has to be compared to the related quantile of the (-distribution h-a,v where v = mx + n2 — 2. 

If the variances sf and sf, differ significantly, a generalized (-lest (tw test) according to Welch [1937] can be applied  

The comparison is done again with b a v, but in this case it is 

If more than two means have to be compared, the (-lest cannot be applied in a multiple way. Instead of this, an indirect comparison by analysis of variance (ANOVA) has to be used, see (3) below. 

The decision, if a mean of a sample, y, differs randomly or significantly from a prescribed mean, p, leads to the question, if the confidence interval of the experimental mean, cnf(y), includes the mean p or not, i.e., is the absolute difference y — p smaller or larger than the interval AJ = s b a,v/Jn  

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Comparison of Measured Values of Amid AF OISA with % S3... 

In contrast to variable testing (comparison of measured values or analytical values), attribute testing means testing of product or process quality (nonconformity test, good-bad test) by samples. Important parameters are the sample size n (the number of units within the random sample) as well as the acceptance criterion naccept, both of which are determined according to the lot size, N, and the proportion of defective items, p, within the lot, namely by the related distribution function or by operational characteristics. 

Fig. 1 (a) Comparison of measured values of for two P-phospholyl-NHPs at different temperatures in solution (data denoted as squares or diamonds, respectively solid lines represent fits of the temperature dependent variation) with values measured in the solid state (dashed horizontal lines). (b) Explanation of the observed variation in solution as a consequence of a dynamic equilibrium between trans- and gauche-rotamers. (Data from [45])... 

Based on our experiments such substitute has been found. The exact specification on the substitute is know-how of the Institute of hydromechanics National Academy of Sciences of the Ukraine at Kiev. The comparison of measured values of dynamic viscosity of the methanol solution substitute and the data available in the literature for real methanol solution are presented in Figure 3 (the value C is the weight concentration of methanol in a solution). Since the measurements were realised within the temperature range T = 18-20°C, a fairly good agreement between methanol and its substitute was proved. Of course, to use the substitute is not limited on this temperature range it should be used also for very low temperatures. The preliminary measurements with the substitute used as the carrier fluid also confirmed results illustrated in Figure 1. 

Comparison of Measured Values of KPA at 10°C for 2,3-Dichlorobiphenyl in Five Different Grass and Herb Species with the Predicted Value from the Linear KOA Model.3... 

Figure 5. Comparison of measured values of Sorg between the ASTM and electron-optical techniques. Not all 56 points can be differentiated because some are coincident...

Comparison of Measured Values of aGr With Those Calculated From Various Models... 

The recording of monitoring results and related information should be such as to satisfy the objectives of the monitoring programme, which include the requirement to carry out a comparison of measured values with appropriate derived levels and, where appropriate, to calculate the annual dose to the average individual of the critical group and the collective doses. 

The most recendy developed model is called UNIQUAC (21). Comparisons of measured VLE and predicted values from the Van Laar, Wilson, NRTL, and UNIQUAC models, as well as an older model, are available (3,22). Thousands of comparisons have been made, and Reference 3, which covers the Dortmund Data Base, available for purchase and use with standard computers, should be consulted by anyone considering the measurement or prediction of VLE. The predictive VLE models can be accommodated to multicomponent systems through the use of certain combining rules. These rules require the determination of parameters for all possible binary pairs in the multicomponent mixture. It is possible to use more than one model in determining binary pair data for a given mixture (23). 

This gives two choices ia interpreting calculated NRR values, ie, a direct comparison of NRR values for different options or a comparison of the NRR value of each option with a previously defined NRR cutoff level for acceptabiUty. The NPV, DTC, and NRR can be iaterpreted as discounted measures of the return, iavestment, and return rate, analogous to the parameters of the earher example. These three parameters characterize a venture over its entire life. Additional parameters can be developed to characterize the cash flow pattern duting the early venture years. Eor example, the net payout time (NPT) is the number of operating years for the cumulative discounted cash flow to sum to zero. This characterizes the early cash flow pattern it can be viewed as a discounted measure of the expected operating time that the investment is at risk. 

Reference electrodes are used in the measurement of potential [see the explanation to Eq. (2-1)]. A reference electrode is usually a metal/metal ion electrode. The electrolyte surrounding it is in electrolytically conducting contact via a diaphragm with the medium in which the object to be measured is situated. In most cases concentrated or saturated salt solutions are present in reference electrodes so that ions diffuse through the diaphragm into the medium. As a consequence, a diffusion potential arises at the diaphragm that is not taken into account in Eq. (2-1) and represents an error in the potential measurement. It is important that diffusion potentials be as small as possible or the same in the comparison of potential values. Table 3-1 provides information on reference electrodes. 

The Gibbs equation allows the amount of surfactant adsorbed at the interface to be calculated from the interfacial tension values measured with different concentrations of surfactant, but at constant counterion concentration. The amount adsorbed can be converted to the area of a surfactant molecule. The co-areas at the air-water interface are in the range of 4.4-5.9 nm2/molecule [56,57]. A comparison of these values with those from molecular models indicates that all four surfactants are oriented normally to the interface with the carbon chain outstretched and closely packed. The co-areas at the oil-water interface are greater (heptane-water, 4.9-6.6 nm2/molecule benzene-water, 5.9-7.5 nm2/molecule). This relatively small increase of about 10% for the heptane-water and about 30% for the benzene-water interface means that the orientation at the oil-water interface is the same as at the air-water interface, but the a-sulfo fatty acid ester films are more expanded [56]. 

Verification of this structure is provided by the comparison with calculated intensity curves. In Fig. 6 curve A represents the model described above and curve B a similar model with the C=C bond distance equal to 1.38 A., as given by the original table of covalent radii. Each of these curves reproduces closely the qualitative aspect of the photographs curve A also shows quantitative agreement, whereas curve B shows a systematic difference of about 3%. The quantitative comparison of measured ring diameters and r values for the maxima and minima of curve A is shown in Table VIII. 

The quantitative comparison of measured. To values and 5 values calculated for models A for mesitylene and hexamethylbenzene is given in Tables XII and XIII. With omission of the innermost maximum and minimum, the unreliable third minimum, and the very weak fifth maximum for each substance, the average values sa/s0 = 1.000 and 1.002, respectively, are found. These correspond to the interatomic distances C — = 1.54 0.01 A. and Car-Car = 1.39 A. in both substances, the 0 —Qa distance being equal to the single-bond distance in aliphatic compounds and the Car—distance to that in benzene to within the probable error of the determination. 

Figure 6.3 Ag-Au solid solution. Comparison of measured hardnesses and values calculated from heats of mixing. Data from Sachs and Weerts (1930).

If the values of 2ktn and v are known, one can easily calculate the rate constant kpli. Such measurements were performed for several hydrocarbons [5]. The comparison of the values of kp]j(2/t, ii) 12 measured by the co-oxidation and oxidation of hydrocarbons with hydroperoxides are given in Refs. [5,9]. The dependence of the initiated oxidation rate on the added concentration of hydroperoxide [R1OOH] is described by the equation [5] ... 

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