Analysis error source

When designing and evaluating an analytical method, we usually make three separate considerations of experimental error. First, before beginning an analysis, errors associated with each measurement are evaluated to ensure that their cumulative effect will not limit the utility of the analysis. Errors known or believed to affect the result can then be minimized. Second, during the analysis the measurement process is monitored, ensuring that it remains under control. Finally, at the end of the analysis the quality of the measurements and the result are evaluated and compared with the original design criteria. This chapter is an introduction to the sources and evaluation of errors in analytical measurements, the effect of measurement error on the result of an analysis, and the statistical analysis of data. 

Ben Yaakov and Lorch [8] identified the possible error sources encountered during an alkalinity determination in brines by a Gran-type titration and determined the possible effects of these errors on the accuracy of the measured alkalinity. Special attention was paid to errors due to possible non-ideal behaviour of the glass-reference electrode pair in brine. The conclusions of the theoretical error analysis were then used to develop a titration procedure and an associated algorithm which may simplify alkalinity determination in highly saline solutions by overcoming problems due to non-ideal behaviour and instability of commercial pH electrodes. 

In those cases where concentrations are not measured directly, the problem of calibration of the in-situ technique becomes apparent. An assurance must be made that no additional effects are registered as systematic errors. Thus, for an isothermal reaction, calorimetry as a tool for kinetic analysis, heat of mixing and/or heat of phase transfer can systematically falsify the measurement. A detailed discussion of the method and possible error sources can be found in [34]. 

FIG. 5.9 Phase angles in an acentric X-N analysis phase angle as calculated with spherical-atom form factors and neutron positional and thermal parameters tpx is the unknown phase of the X-ray structure factors which must be estimated for the calculation of the vector AF. Use of FX — FN introduces a large phase error. Source Coppens (1974). 

Attention has already been given to the errors associated with peak size measurement and with standardization. There are many other places in the chromatographic process where errors enter into quantitative analytical GC. Detailed analysis of most of these error sources is not possible, especially in the confines of this chapter, but they should and will be mentioned and briefly discussed. Most of the error sources are generally obvious it may indeed seem even ridiculous that some have to be mentioned. However, the mere fact that they are obvious tends to slowly place them in the overlooked category. One has to be constantly reminded of these errors until the consideration of them becomes habitual with each problem. 

The list of error sources continues, just to mention a few the ionic strength of the sample, the liquid-junction and residual liquid-junction potentials, temperature effects, instabilities in the galvanic cell, carryover effects, improper use of available corrections (e.g., for pH-adjusted ionized calcium or magnesium). An error analysis goes beyond the limited scope of this paper more details are presented elsewhere [10]. 

As in any measurement, there are error sources whose effects must be quantified. There are two ways to assess error in our analysis. The first, a simple comparison of analytical results with actual elevations (Fig. 9), results in a standard deviation (between measured and actual) of a = 372 m, which is small relative to the elevation changes we consider in major tectonic events. This simple empirical approach to the error depends on the number of samples analyzed and is thus not intrinsic to the technique. The error can be reduced simply by taking more samples... 

The second approach to error assessment is a factor analysis of the various error sources within the procedure. These sources can be ascribed to the three major parameters in Equation (1) above vesicle size, hydrostatic pressure, and sea level atmospheric pressure. 

Stomatal density and index show great potential for paleoelevation reconstructions with low error margins, if additional error sources such as the presence of sun and shade morphotypes and especially uncertainty in sea-level C02 concentrations can be well constrained. Unlike other paleobotanical methods, stomatal frequency analysis is not restricted to angiosperm dominated floras, and has no requirements for a minimum amount of taxa present. The method will be most reliable when applied to fossil taxa that are closely related to extant species, and suitable taxa are most likely to be found for periods when C02 concentrations were not much higher than ambient (380 ppmV). 

Analysis is a lot more complex than the measurement process alone. The measurement step is often the best understood step in the overall analytical process. Error sources are largely situated outside the direct measurement step (Examples 2-4). 

Experimental procedures for quantitative mass spectrometric analysis usually involve several steps. The final error results from the accumulation of the errors in each step, some steps in the procedure being higher error sources than others. A separation can be made between the errors ascribable to the spectrometer and its data treatment on the one hand and the errors resulting from the sample handling on the other. 

The Analysis - which addresses terms encountered whilst undertaking the analysis, including different types of analysis and sources of error. 

Garside, C. (1993). Nitrate reductor efficiency as an error source in seawater analysis. Mar. Chem. 44, 25-30. 

The use of a commercially available software package (QUANT) is described in the analysis of copolymer films by computer assisted infrared spectroscopy. Important features of the software are illustrated by the example of analysis of vinyl acetate/vinyl chloride copolymers. Critical aspects of method development are explained and error sources are examined. Calibration is reported with a correlation coefficient of 0.9998. 

It is notable that such kinds of error sources are fairly treated using the concept of measurement uncertainty which makes no difference between random and systematic . When simulated samples with known analyte content can be prepared, the effect of the matrix is a matter of direct investigation in respect of its chemical composition as well as physical properties that influence the result and may be at different levels for analytical samples and a calibration standard. It has long since been suggested in examination of matrix effects [26, 27] that the influence of matrix factors be varied (at least) at two levels corresponding to their upper and lower limits in accordance with an appropriate experimental design. The results from such an experiment enable the main effects of the factors and also interaction effects to be estimated as coefficients in a polynomial regression model, with the variance of matrix-induced error found by statistical analysis. This variance is simply the (squared) standard uncertainty we seek for the matrix effects. 

Uncertainty can be assessed in various ways, and often a combination of procedures is necessary. In principle, uncertainty can be judged directly from measurement comparisons or indirectly from an analysis of individual error sources according to the law of error propagation ( error budget )- Measurement comparison may consist of a method comparison study with a reference method based on patient samples according to the principles outlined previously or by measurement of certified matrix reference materials (CRMs). 

We encounter several sources of error in the sample decomposition step. In fact, such errors often limit the accuracy that can be achieved in an analysis. The sources of these errors include the following ... 

The noise from I bias has been omitted for simplicity. Using the same parameters as above and Vg = 1 V and B= 1 kHz, the standard deviation of the equivalent input noise of the circuit is 0.63 aF. Since noise follows a Gaussian distribution, there is a 32 percent probability that a particular error sample is larger than this value. Datasheets usually specify a three times larger value, 2 aF, to reduce the probability for larger errors to 0.3%. Note that thermal noise from the amplifier is the only error source included in this analysis. In practice, other error sources are often relevant also. 

Error Analysis What sources of error could have led the lab groups to different final values What modifications could you make in this investigation to reduce the incidence of error ... 

Error Analysis Identify sources of the error that resulted in deviation from the mole ratio given in the balanced chemical equation. 

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