Total systematic error

When an analyst performs a single analysis on a sample, the difference between the experimentally determined value and the expected value is influenced by three sources of error random error, systematic errors inherent to the method, and systematic errors unique to the analyst. If enough replicate analyses are performed, a distribution of results can be plotted (Figure 14.16a). The width of this distribution is described by the standard deviation and can be used to determine the effect of random error on the analysis. The position of the distribution relative to the sample s true value, p, is determined both by systematic errors inherent to the method and those systematic errors unique to the analyst. For a single analyst there is no way to separate the total systematic error into its component parts. 

The bias error is a quantity that gives the total systematic error of a measuring instrument under defined conditions. As mentioned earlier, the bias should be minimized by calibration. The repeatability error consists of the confidence limits of a single measurement under certain conditions. The mac-curacy or error of indication is the total error of the instrument, including the... 

Bias is the total systematic error (there may be more than one component contributing to total systematic error). It is the (positive or negative) difference (A) of the population mean (p, the limiting value of the arithmetic mean for u-a qo) from the (known or assumed) trae value (x). A = p - t. Therefore bias is the lack of traeness. 

If the exact value x0 is known (e.g. analysis of a standard of known composition), the total systematic error e is characteristic of the accuracy of the series of measurements made with the method used (Table 21.1). 

Figure 2.7 The method evaluation function (MEF) report for 2-(2-butoxyethoxy) ethanol (high cone, level) with plots of the ideal MEF, residuals and the total systematic error.

EXAMPLE 11.5 Assume that you estimate the total systematic error in the melting temperature measurement of Example 11.3 as 0.20 °C at the 95% confidence level. Find the total expected error. 

The total systematic error can sometimes be zero. Suppose, for example, a balance with a systematic error of -0.01 g is used for the weighings involved in making a standard solution. Since the weight of the solute used is found from the difference between two weighings, the systematic errors cancel out. It should be pointed out that this applies only to an electronic balance with a single internal reference weight. Carefully considered procedures, such as this, can often minimize the systematic errors, as described in Chapter 1. 

Bias The difference between the expected and experimental result also called the total systematic error. Biases should be corrected for, or minimized in, validated methods. An improperly calibrated balance that always reads 0.0010 g too high will impart bias to results. 

Description Bias is the total systematic error of a measurement result (in contrast to random error). 

The overall uncertainty of an experimental result maybe given as a function of the random and systematic errors. For methods of estimating individual bias components and propagated errors to predict the total systematic error, the reader is referred to Currie and DeVoe (1977) or Peters et al. (1974). Methods for estimating propagation of errors in products, quotients, sums, or differences are provided in Cans (1992), Kline (1985), and Topping (1962). Statistical methods for addressing measurements that appear to be outliers (i.e., extreme values that are not part of the population) are presented in McCuen (1992). 

Even within a particular approximation, total energy values relative to the method s zero of energy are often very inaccurate. It is quite common to find that this inaccuracy is almost always the result of systematic error. As such, the most accurate values are often relative energies obtained by subtracting total energies from separate calculations. This is why the difference in energy between conformers and bond dissociation energies can be computed extremely accurately. 

The electron alfinity (FA) and ionization potential (IP) can be computed as the difference between the total energies for the ground state of a molecule and for the ground state of the appropriate ion. The difference between two calculations such as this is often much more accurate than either of the calculations since systematic errors will cancel. Differences of energies from correlated quantum mechanical techniques give very accurate results, often more accurate than might be obtained by experimental methods. 

The data used to construct a two-sample chart can also be used to separate the total variation of the data, Otot> into contributions from random error. Grand) and systematic errors due to the analysts, Osys. Since an analyst s systematic errors should be present at the same level in the analysis of samples X and Y, the difference, D, between the results for the two samples... 

The total cerium content in the single crystal samples on the basis of rare-earth elements is determined by photometry after Ce(III) oxidation by ammonium persulfate. The Ce(III) content is calculated from the difference. Comparison of the determination results of the total cerium content obtained by photometric and atomic emission methods for Li GdlBO ljiCe demonstrated the elaborated procedure precision and systematic error absence. 

I he origins of the above two errors are chfferent in cause and nature. A sim ple example is, when the mass of a weight is less than its nominal value, a systematic error occurs, which is constant in absolute value and sign. This is a pure systematic error. A ventilation-related example is, when the instrument faaor of a Pitot-static tube, which defines the relationship between the measured pressure difference and the velocity, is incorrect, a systematic error occurs. On the other hand, if a Pitot-static tube is positioned manually in a duct in such a way that the tube tip is randomly on either side of the intended measurement point, a random error occurs. This way, different phenomena create different ty pes of error. I he (total) error of measurement usually is a combination of the above two types. 

The question may be asked. What is the reason in dividing the errors into two categories. I he answer is the totally different way of dealing with these different types. Systematic error can be eliminated to a sufficient degree, whereas random error cannot. The following section shows how to deal with these errors. 

Systematic error, as stated above, can be eliminated— not totally, but usually to a sufficient degree. This elimination process is called calibration. Calibration is simply a procedure where the result of measurement recorded by an instrument is compared with the measurement result of a standard. A standard is a measuring device intended to define, to represent physically, to conserve, or to reproduce the unit of measurement in order to transmit it to other measuring instruments by comparison. There are several categories of standards, but, simplifying a little, a standard is an instrument with a very high accuracy and can for that reason be... 

When comparing calculated results to thermodynamic quantities extrapolated to zero Kelvin, the zero point energy needs to be added to the total energy. As with the frequencies themselves, this predicted quantity is scaled to eliminate known systematic errors in frequency calculations. Accordingly, if you have not specified a scale factor via input to the Reodlsotopes option, you will need to multiply the values in the output by the appropriate scale factor (see page 64). 

For measurements by AS, the errors of the isotope ratio will be dominated by counting statistics for each isotope. For measurements by TIMS or ICP-MS, the counting-statistic errors set a firm lower limit on the isotopic measurement errors, but more often than not contribute only a part of the total variance of the isotope-ratio measurements. For these techniques, other sources of (non-systematic) error include ... 

It is not always possible to tell strictly the difference between random and systematic deviations, especially as the latter are defined by random errors. The total deviation of an analytical measurement, frequently called the total analytical error , is, according to the law of error propagation, composed of deviations resulting from the measurement as well as from other steps of the analytical process (see Chap. 2). These uncertainties include both random and systematic deviations, as a rule. 

It is clear that in this microcalorimeter, only a fraction of the outside wrall of the inner vessel is covered by thermoelectric elements. Consequently, only a part of the total heat flux emitted by the cell is detected. This may be the cause of a systematic error which, however, can be avoided if the heat transfer via the thermoelectric elements constitutes a constant fraction of the total, irrespective of the process taking place in the calorimeter cell. The present version of the Petit microcalorimeter can be used only at moderate temperatures (<100°C), mainly because some components of the thermoelectric elements wrould be damaged at higher temperatures. 

The total optical path difference between the two arms of the interferometer, for a sample length of about 50 mm, is of the order of 10 mm or less, minimizing the systematic error due to laser frequency fluctuations. To reduce the thermal effects on the interferometer assembly, the interferometer support plate is stabilized to a temperature slightly higher than room temperature and insulated from air currents by a polystyrene foam shield. The temperature variation of the interferometer support is kept below 0.1 K. 

A computer program has been used to calculate the magnitude of systematic errors incurred in the evaluation of equivalence points in hydrochloric acid titrations of total alkalinity and carbonate in seawater by means of Gran plots. Hansson [13] devised a modification of the Gran procedure that gives improved accuracy and precision. The procedure requires approximate knowledge of all stability constants in the titration. 

Because measurements always contain some type of error, it is necessary to correct their values to know objectively the operating state of the process. Two types of errors can be identified in plant data random and systematic errors. Random errors are small errors due to the normal fluctuation of the process or to the random variation inherent in instrument operation. Systematic errors are larger errors due to incorrect calibration or malfunction of the instruments, process leaks, etc. The systematic errors, also called gross errors, occur occasionally, that is, their number is small when compared to the total number of instruments in a chemical plant. 

This systematic error affects the usefulness of these series in determining the constant a, but they still provide valuable data for use in determining dependence of the equilibrium on temperature, fraction neutralization, and total anion concentration. 

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