Source of errors

The main task here is the revealing of the sources of errors and character of their behaviour. 

The main sources of error which define the accuracy are counting statistics in tracer concentration measurements, the dispersion of the tracer cloud in the flare gas stream, and the stationarity of the flow during measurements. 

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

Tlierc are two major sources of error associated with the calculation of free energies fi computer simulations. Errors may arise from inaccuracies in the Hamiltonian, be it potential model chosen or its implementation (the treatment of long-range forces, e j lie second source of error arises from an insufficient sampling of phase space. 

Provided that the balance is functioning correctly, the main source of error is in the weights themselves these should be calibrated by one of the standard methods so that their relative values are known, and they should be carefully cleaned with tissue paper and checked from time to time. To make the best use of the balance, weighing should be carried out by the method of swings, but for this purpose it is necessary first to determine the sensitivity of the balance. 

The chief danger and main source of error in a combustion is that of moving the Bunsen forward a little too rapidly and so causing much of the substance to burn very rapidly, so that a flash-back occurs. This usually causes an explosion wave to travel back along the tube towards the purification train, some carbon dioxide and water vapour being carried with it. If these reach the packing of the purification train they will, of course, be absorbed there and the results of the estimation will necessarily be low. 

However, this convergence is not monotonic. Sometimes, the smallest calculation gives a very accurate result for a given property. There are four sources of error in ah initio calculations ... 

For very-high-accuracy ah initio calculations, the harmonic oscillator approximation may be the largest source of error. The harmonic oscillator frequencies... 

Side chain generation is often a source of error. It will be most reliable if certain rules of thumb are obeyed. Start with structurally conserved side chains and hold them fixed. Then look at the energy and entropy of rotamers for the remaining side chains. Conventional conformation search techniques are often used to place each side chain. 

The parameters in the original parameterization are adjusted in order to reproduce the correct results. These results are generally molecular geometries and energy differences. They may be obtained from various types of experimental results or ah initio calculations. The sources of these correct results can also be a source of error. Ah initio results are only correct to some degree of accuracy. Likewise, crystal structures are influenced by crystal-packing forces. 

By proper design of experiments, guided by a statistical approach, the effects of experimental variables may be found more efficiently than by the traditional approach of holding all variables constant but one and systematically investigating each variable in turn. Trends in data may be sought to track down nonrandom sources of error. 

The control chart is set up to answer the question of whether the data are in statistical control, that is, whether the data may be retarded as random samples from a single population of data. Because of this feature of testing for randomness, the control chart may be useful in searching out systematic sources of error in laboratory research data as well as in evaluating plant-production or control-analysis data. ... 

The stoichiometry must be exact. Coprecipitation by solid-solution formation, foreign ion entrapment, and adsorption are possible sources of error. 

Mercury porosimetry is generally regarded as the best method available for the routine determination of pore size in the macropore and upper mesopore range. The apparatus is relatively simple in principle (though not inexpensive) and the experimental procedure is less demanding than gas adsorption measurements, in either time or skill. Perhaps on account of the simplicity of the method there is some temptation to overlook the assumptions, often tacit, that are involved, and also the potential sources of error. 

A number of potential sources of error must be taken into account. In the volumetric method the following items need attention (a) constancy of the level of liquid nitrogen (b) depth of immersion of the sample bulb ( S cm) (c) temperature of sample (monitoring with vapour pressure thermometer close to sample bulb) (d) purity of adsorptive (preferably 99-9 per cent) (e) temperature of gas volumes (doser, dead space), controlled to 01 C. 

The critical value for f(0.05,4), as found in Appendix IB, is 2.78. Since fexp is greater than f(0.05, 4), we must reject the null hypothesis and accept the alternative hypothesis. At the 95% confidence level the difference between X and p, is significant and cannot be explained by indeterminate sources of error. There is evidence, therefore, that the results are affected by a determinate source of error. 

In this experiment students measure the length of a pestle using a wooden meter stick, a stainless-steel ruler, and a vernier caliper. The data collected in this experiment provide an opportunity to discuss significant figures and sources of error. Statistical analysis includes the Q-test, f-test, and F-test. 

The difference between precision and accuracy and a discussion of indeterminate and determinate sources of error is covered in the following paper. 

The regression models considered earlier apply only to functions containing a single independent variable. Analytical methods, however, are frequently subject to determinate sources of error due to interferents that contribute to the measured signal. In the presence of a single interferent, equations 5.1 and 5.2 become... 

Determine the uncertainty for the gravimetric analysis described in Example 8.1. (a) How does your result compare with the expected accuracy of 0.1-0.2% for precipitation gravimetry (b) What sources of error might account for any discrepancy between the most probable measurement error and the expected accuracy ... 

The equivalence point of a redox titration occurs when stoichiometrically equivalent amounts of analyte and titrant react. As with other titrations, any difference between the equivalence point and the end point is a determinate source of error. 

When standardizing a solution of NaOH against potassium hydrogen phthalate (KHP), a variety of systematic and random errors are possible. Identify, with justification, whether the following are systematic or random sources of error, or if they have no effect. If the error is systematic, then indicate whether the experimentally determined molarity for NaOH will be too high or too low. The standardization reaction is... 

Miscellaneous Methods At the beginning of this section we noted that kinetic methods are susceptible to significant errors when experimental variables affecting the reaction s rate are difficult to control. Many variables, such as temperature, can be controlled with proper instrumentation. Other variables, such as interferents in the sample matrix, are more difficult to control and may lead to significant errors. Although not discussed in this text, direct-computation and curve-fitting methods have been developed that compensate for these sources of 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 goal of a collaborative test is to determine the expected magnitude of ah three sources of error when a method is placed into general practice. When several analysts each analyze the same sample one time, the variation in their collective results (Figure 14.16b) includes contributions from random errors and those systematic errors (biases) unique to the analysts. Without additional information, the standard deviation for the pooled data cannot be used to separate the precision of the analysis from the systematic errors of the analysts. The position of the distribution, however, can be used to detect the presence of a systematic error in the method. 

A variety of statistical methods may be used to compare three or more sets of data. The most commonly used method is an analysis of variance (ANOVA). In its simplest form, a one-way ANOVA allows the importance of a single variable, such as the identity of the analyst, to be determined. The importance of this variable is evaluated by comparing its variance with the variance explained by indeterminate sources of error inherent to the analytical method. 

The "feedback loop in the analytical approach is maintained by a quality assurance program (Figure 15.1), whose objective is to control systematic and random sources of error.The underlying assumption of a quality assurance program is that results obtained when an analytical system is in statistical control are free of bias and are characterized by well-defined confidence intervals. When used properly, a quality assurance program identifies the practices necessary to bring a system into statistical control, allows us to determine if the system remains in statistical control, and suggests a course of corrective action when the system has fallen out of statistical control. 

The principal tool for performance-based quality assessment is the control chart. In a control chart the results from the analysis of quality assessment samples are plotted in the order in which they are collected, providing a continuous record of the statistical state of the analytical system. Quality assessment data collected over time can be summarized by a mean value and a standard deviation. The fundamental assumption behind the use of a control chart is that quality assessment data will show only random variations around the mean value when the analytical system is in statistical control. When an analytical system moves out of statistical control, the quality assessment data is influenced by additional sources of error, increasing the standard deviation or changing the mean value. 

The shortcomings of microhardness tests include numerous sources of errors not found in macrohardness tests such as friction, vibration, inertia, windage, and the skiH of the test operator. 

Friction due to lack of vertical positioning of the tube is a source of error, as is sensitivity to the surface condition of the test piece. Samples of small mass cannot be tested except when supported on a heavy anvil. 

Sources of Error. pH electrodes are subject to fewer iaterfereaces and other types of error than most potentiometric ionic-activity sensors, ie, ion-selective electrodes (see Electro analytical techniques). However, pH electrodes must be used with an awareness of their particular response characteristics, as weU as the potential sources of error that may affect other components of the measurement system, especially the reference electrode. Several common causes of measurement problems are electrode iaterferences and/or fouling of the pH sensor, sample matrix effects, reference electrode iastabiHty, and improper caHbration of the measurement system (12). 

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