Measurement errors avoidance

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

Since the Wenner formula [Eq. (24-41)] was deduced for hemispherical electrodes, measuring errors appear for spike electrodes. To avoid errors in excess of 5%, the depth of penetration must be less than a 5. Soil resistivity increases greatly under frost conditions. While electrodes can be driven through thin layers of frost, soil resistivity measurements deeper than 20 cm in frozen ground are virtually impossible. 

The fouling of the probe when inserted into a duct or pipe acts as an isolating layer and increases the measurement error. To avoid this conduction error, the probe should be a poor heat conductor. In measuring surface temperatures, the probe should not have an insulating effect, as this will change the temperature in the measuring point. 

For preparation of solvent mixtures, the single solvents should be measured out separately and then properly mixed in a vessel with a ground glass stopper (avoidance of volume contraction and measuring errors). 

In the previous development it was assumed that only random, normally distributed measurement errors, with zero mean and known covariance, are present in the data. In practice, process data may also contain other types of errors, which are caused by nonrandom events. For instance, instruments may not be adequately compensated, measuring devices may malfunction, or process leaks may be present. These biases are usually referred as gross errors. The presence of gross errors invalidates the statistical basis of data reconciliation procedures. It is also impossible, for example, to prepare an adequate process model on the basis of erroneous measurements or to assess production accounting correctly. In order to avoid these shortcomings we need to check for the presence of gross systematic errors in the measurement data. 

Sample variabilities and the measurement error must be considered (risk analysis, cf. Section I.C) to avoid that an analyte signal yo will be measured outside the calibrated range. Thus, the range shall be chosen a little wider than the expected range of analyte concentrations. 

A method of employing a tube carrying a modest electric current as a resistance thermometer, while the heat source is a condensing vapor, has been reported for boiling work (M8). The method was originally developed as a scheme for avoiding temperature-measurement errors with condenser tubes (J6). 

A key feature of the competitive isotope fractionation measurements is the use of natural abundance O2. Isotope effects are, therefore, determined for the reactions of the most abundant isotopologues 160-160 and 180-160. It is the intermolecular competition of these species that is reflected in the isotope effect. Aside from the obvious advantage of not requiring costly enriched materials, the competitive measurements also avoid the error that could arise from small leaks in the vacuum manifold and dilution due to ambient air. 

Pinching is avoided. It has been recommended to pilot-test at total reflux (16). At finite reflux, pinching can convert small measurement errors into major errors in efficiency estimates (130). However, finite reflux testing is useful in supplementing a total reflux test and providing information on pinch-point location. 

The direct determination of the polymer content adsorbed onto the solid surface avoids the systematic measuring error arising from particle-initiated PVFA-co-PVAm flocculation which can be important by the determination of the PVFA-co-PVAm amount in the supernatant solution after the adsorption [23], Figure 1 shows a wide-scan XPS spectrum of PVFA-co-PVAm (degree of hydrolysis > 90%, pH = 8) adsorbed onto copper. 

Using standard solutions for quantifying concentrations in an unknown sample may give rise to measurement errors due to the influence of food matrix remnants in the injection solution. Ion suppression or enhancement is a typical matrix effect seen in mass spectrometry. Matrix-matched standards are generally used in order to avoid such possible matrix interferences. Standard addition is a valid alternative for dealing with matrix effects. On the other hand, standard addition or matrix based calibration curves require more manipulation, which is time- and money-consuming, whereas a greater risk of manipulation errors ensues. 

Numerous reports are available [19,229-248] on the development and analysis of the different procedures of estimating the reactivity ratio from the experimental data obtained over a wide range of conversions. These procedures employ different modifications of the integrated form of the copolymerization equation. For example, intersection [19,229,231,235], (KT) [236,240], (YBR) [235], and other [242] linear least-squares procedures have been developed for the treatment of initial polymer composition data. Naturally, the application of the non-linear procedures allows one to obtain more accurate estimates of the reactivity ratios. However, majority of the calculation procedures suffers from the fact that the measurement errors of the independent variable (the monomer feed composition) are not considered. This simplification can lead in certain cases to significant errors in the estimated kinetic parameters [239]. Special methods [238, 239, 241, 247] were developed to avoid these difficulties. One of them called error-in-variables method (EVM) [239, 241, 247] seems to be the best. EVM implies a statistical approach to the general problem of estimating parameters in mathematical models when the errors in all measured variables are taken into account. Though this method requires more information than do ordinary non-linear least-squares procedures, it provides more reliable estimates of rt and r2 as well as their confidence limits. 

Figure 8 Schematic layout of a typical 90° Raman depolarization experiment showing the positions of the polarization analyzer and the scrambler. The analyzer may simply be a polaroid sheet, which can be rotated by 90° to allow the parallel ( ) and perpendicular ( ) components of the scattered light to pass through to the detector. The function of a scrambler is to change linear into circular polarization of the light entering the Raman spectrometer slit in order to avoid measurement errors due to the variable spectrometer transmittance of the light polarized in different directions...

This approach yields good results when the compounds lead to spectra, which are significantly different, otherwise it loses precision when the spectra are in close proximity as a small measurement error can lead to a large variation in the result. To avoid this risk the instruments housing diode arrays use many tens of data points. Although the system to be resolved (expression 9.14) becomes over-determined but this leads to better results. 

We now present temperature measurements of the vibrational properties of the T) phase. Type II diamonds were used for mid-IR measurements to avoid interference with the characteristic absorption of the sample. The representative absorption spectra at different temperatures (see Fig. 14) clearly show the presence of a broad 1700 cm IR band (compare with Fig. 12). Its presence was also observed in the sample heated to 495 K at 117 GPa (see below). The position of the band and its damping (if fitted as one band) does not depend on pressure and temperature within the error bars. The Raman spectrum of the Tj phase obtained on heating (see below) does not show any trace of the molecular phase (see Fig. 12(b)). Careful examination of the spectrum in this case showed a weak broad band at 640 cm and a shoulder near 1750 cm (both indicated by arrows in Fig. 12(b)). For an amorphous state, the vibrational spectrum would closely resemble a density of phonon states [63] with the maxima corresponding roughly to the zone boundary acoustic and optic vibrations of an underlying structure [3-5, 55], which is consistent with our observations. The only lattice dynamics... 

Thermocouples were fabricated from commercial thermocouple wire by stripping the insulation approximately 1 cm from the end. The two wires were then twisted together, doubled over, and soldered. After fabrication, the thermocouple was tested for electrical continuity and for temperature measurement fidelity. Thermocouples made from the same spool of wire were found to provide closely identical signals giving a relative temperature measurement error of less than 0.05 K. Thermocouples were made from 0.25 mm diameter wire to allow insertion of the thermocouple in the capillaries. Because of the fine wire, all operations described in this note require considerable care to avoid breaking the wire. 

If the range of temperatures is adequate, and measurement errors are small enough to establish the temperature coefficients of the equilibrium constant, then this single ramping can be used to calculate all of the equilibrium constant, the desorption, and the adsorption rate constants for the system. In practice the best operating conditions for this type of run are at high values of transit time, i.e. under conditions where Wfc is large but there is a premium on accurate data to avoid the instabilities that result from the form of the equations used. 

Most applications depend on the understanding of the limitations of the detection principles and of the equipment used, which helps to avoid trivial errors. For this reason, after a short introduction to the theoretical fundamentals, different types of instrumentation are compared with respect to sample handling and error avoidance. Besides absorption, the suitability of fluorescence, reflectance, and interferometry are demonstrated. Some new applications by use of fiber optics and diode array technology are given. Measurements in turbid solution are introduced and a few clinical examples are mentioned. Finally, principles of multicomponent analysis are discussed. 

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