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Statistics systematic errors

Excitation function data can be subjected to several kinds of errors. In addition to random errors e.g. due to counting statistics, systematic errors may occur due to ... [Pg.44]

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. [Pg.44]

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. [Pg.96]

In the maximum-likelihood method used here, the "true" value of each measured variable is also found in the course of parameter estimation. The differences between these "true" values and the corresponding experimentally measured values are the residuals (also called deviations). When there are many data points, the residuals can be analyzed by standard statistical methods (Draper and Smith, 1966). If, however, there are only a few data points, examination of the residuals for trends, when plotted versus other system variables, may provide valuable information. Often these plots can indicate at a glance excessive experimental error, systematic error, or "lack of fit." Data points which are obviously bad can also be readily detected. If the model is suitable and if there are no systematic errors, such a plot shows the residuals randomly distributed with zero means. This behavior is shown in Figure 3 for the ethyl-acetate-n-propanol data of Murti and Van Winkle (1958), fitted with the van Laar equation. [Pg.105]

Ferrenberg A M, Landau D P and Binder K 1991 Statistical and systematic errors in Monte-Carlo sampling J. Stat. Phys. 63 867-82... [Pg.2279]

If all sources of systematic error can be eliminated, there will still remain statistical errors. These errors are often reported as stcindard deviations. What we would particularly like to estimate is the error in the average value, (A). The standard deviation of the average value is calculated as follows ... [Pg.359]

The precision of a result is its reproducibility the accuracy is its nearness to the truth. A systematic error causes a loss of accuracy, and it may or may not impair the precision depending upon whether the error is constant or variable. Random errors cause a lowering of reproducibility, but by making sufficient observations it is possible to overcome the scatter within limits so that the accuracy may not necessarily be affected. Statistical treatment can properly be applied only to random errors. [Pg.192]

If systematic errors due to the analysts are significantly larger than random errors, then St should be larger than sd. This can be tested statistically using a one-tailed F-test... [Pg.690]

Rectification accounts for systematic measurement error. During rectification, measurements that are systematically in error are identified and discarded. Rectification can be done either cyclically or simultaneously with reconciliation, and either intuitively or algorithmically. Simple methods such as data validation and complicated methods using various statistical tests can be used to identify the presence of large systematic (gross) errors in the measurements. Coupled with successive elimination and addition, the measurements with the errors can be identified and discarded. No method is completely reliable. Plant-performance analysts must recognize that rectification is approximate, at best. Frequently, systematic errors go unnoticed, and some bias is likely in the adjusted measurements. [Pg.2549]

Computer simulation is an experimental science to the extent that calculated dynamic properties are subject to systematic and statistical errors. Sources of systematic error consist of size dependence, poor equilibration, non-bond interaction cutoff, etc. These should, of course, be estimated and eliminated where possible. It is also essential to obtain an estimate of the statistical significance of the results. Simulation averages are taken over runs of finite length, and this is the main cause of statistical imprecision in the mean values so obtained. [Pg.56]

The mean deviation from experiment the average difference between computed and experimental values. This statistic is not very meanin since it allows positive and negative errors—underestimations overestimations—to cancel one another. Flowever, a large value usi indicates the presence of systematic errors. [Pg.145]

The statistical error can thus be reduced by averaging over a larger ensemble. How well the calculated average (from eq. (16.9)) resembles the true value, however, depends on whether the ensemble is representative. If a large number of points is collected from a small part of the phase space, the property may be calculated with a small statistical error, but a large systematic error (i.e. the value may be precise, but inaccurate). As it is difficult to establish that the phase space is adequately sampled, this can be a very misleading situation, i.e. the property appears to have been calculated accurately but may in fact be significantly in error. [Pg.375]

The flowsheet shown in the introduction and that used in connection with a simulation (Section 1.4) provide insights into the pervasiveness of errors at the source, random errors are experienced as an inherent feature of every measurement process. The standard deviation is commonly substituted for a more detailed description of the error distribution (see also Section 1.2), as this suffices in most cases. Systematic errors due to interference or faulty interpretation cannot be detected by statistical methods alone control experiments are necessary. One or more such primary results must usually be inserted into a more or less complex system of equations to obtain the final result (for examples, see Refs. 23, 91-94, 104, 105, 142. The question that imposes itself at this point is how reliable is the final result Two different mechanisms of action must be discussed ... [Pg.169]

The precision stated in Table 10 is given by the standard deviations obtained from a statistical analysis of the experimental data of one run and of a number of runs. These parameters give an indication of the internal consistency of the data of one run of measurements and of the reproducibility between runs. The systematic error is far more difficult to discern and to evaluate, which causes an uncertainty in the resulting values. Such an estimate of systematic errors or uncertainties can be obtained if the measuring method can also be applied under circumstances where a more exact or a true value of the property to be determined is known from other sources. [Pg.157]

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 ... [Pg.632]

When specifying atomic coordinates, interatomic distances etc., the corresponding standard deviations should also be given, which serve to express the precision of their experimental determination. The commonly used notation, such as d = 235.1(4) pm states a standard deviation of 4 units for the last digit, i.e. the standard deviation in this case amounts to 0.4 pm. Standard deviation is a term in statistics. When a standard deviation a is linked to some value, the probability of the true value being within the limits 0 of the stated value is 68.3 %. The probability of being within 2cj is 95.4 %, and within 3ct is 99.7 %. The standard deviation gives no reliable information about the trueness of a value, because it only takes into account statistical errors, and not systematic errors. [Pg.10]

If systematic errors can be traced, and perhaps eliminated, and personal errors can be minimized, the remaining random errors can be analyzed by statistical methods. This procedure will be summarized in the following sections. [Pg.378]

Check. Use the Crooks relation (5.35) to check whether the forward and backward work distributions are consistent. Check for consistency of free energies obtained from different estimators. If the amount of dissipated work is large, caution may be necessary. If cumulant expressions are used, the work distributions should be nearly Gaussian, and the variances of the forward and backward perturbations should be of comparable size [as required by (5.35) for Gaussian work distributions]. Systematic errors from biased estimators should be taken into consideration. Statistical errors can be estimated, for instance, by performing a block analysis. [Pg.187]

Perhaps the most challenging part of analyzing free energy errors in FEP or NEW calculations is the characterization of finite sampling systematic error (bias). The perturbation distributions / and g enable us to carry out the analysis of both the finite sampling systematic error (bias) and the statistical error (variance). [Pg.215]

These bounds originate from the systematic errors (biases) due to the finite sampling in free energy simulations and they differ from other inequalities such as those based on mathematical statements or the second law of thermodynamics. The bounds become tighter with more sampling. It can be shown that, statistically, in a forward calculation AA(M) < AA(N) for sample sizes M and N and M > N. In a reverse calculation, AA(M) > AA(N). In addition, one can show that the inequality (6.27) presents a tighter bound than that of the second law of thermodynamics... [Pg.219]

However, this analysis has been performed from a purely statistical perspective, leading to the minimal statistical error for the calculation. The phase space relationship, the staging scheme (conceptual intermediate M), and thus the accuracy of the calculation are not included in Bennett s picture. However, it turns out that the calculation is also optimal from the accuracy point of view. With this optimal choice of C = AA, the weight function w(Au) given by (6.64) has its peak exactly at the crossover between / and g, where AU = AA [cf. (6.15)]. In contrast, the weights for the low-Z w tail of / and high-Zll tail of g are diminished, thus resulting in small systematic error. [Pg.231]

The inspection of the fit residuals, that is, the (normalized) differences between the experimental and fitted data point, is a reliable tool to check for deviations from the fitted model. Residuals should be statistically noncorrelated and randomly distributed around zero. For example, if a bi-exponential decay is fitted to a single exponential function, the residuals will show systematic errors. Therefore, correlations in the residuals may indicate that another fit model should be used. [Pg.138]

A simple statistical test for the presence of systematic errors can be computed using data collected as in the experimental design shown in Figure 34-2. (This method is demonstrated in the Measuring Precision without Duplicates sections of the MathCad Worksheets Collabor GM and Collabor TV found in Chapter 39.) The results of this test are shown in Tables 34-9 and 34-10. A systematic error is indicated by the test using... [Pg.176]


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