Measurement error, sources

Source Amplitude (mV) Bandwidth (Hz) Sensor (Electrodes) Measurement Error Source Selected Applications... 

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. 

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 ... 

Other problems occur in the measurement of pH in unbuffered, low ionic strength media such as wet deposition (acid rain) and natural freshwaters (see Airpollution Groundwatermonitoring) (13). In these cases, studies have demonstrated that the principal sources of the measurement errors are associated with the performance of the reference electrode Hquid junction, changes in the sample pH during storage, and the nature of the standards used in caHbration. Considerable care must be exercised in all aspects of the measurement process to assure the quaHty of the pH values on these types of samples. 

Whenever measured values of diffusivities are available, they should be used. Typically, measurement errors are less than those associated with predictions by empirical or even semitheoretical equations. A few general sources of data are Sec. 2 of this handbook, Schwartzberg and Chao Reid et al. Gammon et al. and Daubert and Danner. Many other more restricted sources are hsted under specific topics later in this subsection. 

The main error sources are noise in the wavefront sensor measurement, imperfect wavefront correction due to the finite number of actuators and bandwidth error due to the finite time required to measure and correct the wavefront error. Other errors include errors in the telescope optics which are not corrected by the AO system (e.g. high frequency vibrations, high spatial frequency errors), scintillation and non-common path errors. The latter are wavefront errors introduced in the corrected beam after light has been extracted to the wavefront sensor. Since the wavefront sensor does not sense these errors they will not be corrected. Since the non-common path errors are usually static, they can be measured off-line and taken into account in the wavefront correction. 

The accuracy with which a wavefront sensor measures phase errors will be limited by noise in the measurement. The main sources of noise are photon noise, readout noise (see Ch. 11) and background noise. The general form of the phase measurement error (in square radians) on an aperture of size d due to photon noise is... 

It is certainly this lack of clarity which leads to the current situation. Flashpoints are usually given without any mention of either the open or closed cup aspects or the make of apparatus. Amongst the thousand or so organic substances listed in Part Two, more than one hundred of them mention oc and cc , which enables comparisons to be made. Nevertheless, a study of the data indicates that the difference between experimental values can reach 56°C for the same substance (for instance, butadiene). It happens quite often that for flashpoints lower values oc than cc values for the same substance are found.The nature of the sources of the level of measurement error in flashpoints can easily be guessed at. 

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 ... 

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. 

The historical background is presented for the asteroid-impact theory that is based on the iridium anomaly found in rocks frm the Cretaceous-Tertiary boundary. Recent measurements of Ir, Pt, and Au abundances from such rocks in Denmark have shown that the element abundance ratios are different from mantle-derived sources and agree with values for chondritic meteorites within one standard deviation of the measurement errors (7-10%). Rare-earth patterns for these rocks are... 

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]. 

For hydrogenations under normal pressure and isobaric conditions, we use a device which registers gas consumption automatically (Fig. 10.3). Possible error sources resulting from such gas consumption measurements and possibilities of their minimization will be discussed. 

A second likely error source in the experimental determination of the appearance energy has also a kinetic origin. As shown in figure 4.4, recombination of the products A+ and B may involve an activation barrier (Etec). Therefore, even if Akin = 0, when Eiec is not negligible the measured appearance energy will be an upper limit of the true (thermodynamic) value. 

A final source of variation in microarray experiments is derived from measurement errors. Measurement errors may occur during the processes of image acquisition and normalization or during the multifactorial data analysis required to extract biological relevance from the collected data. The effect of measurement error can be minimized by ensuring consistency in all aspects of microarray experimentation. If possible, experiments should be performed by the same technician, and subsequent data analyses be applied to all datasets consistently. 

There are several potential sources of error in these methods. The filters routinely used have a relatively high and somewhat variable sulfate content, so that, at concentrations lower than 10 Mg/m and sampling periods less than 24 h, the reliability of tlie sulfate measurement is reduc. Several different types of filtering media adsorb sulfur dioxide during the ftrst few hours of sampling this alters the amount of sulfate observed. This interference can become critical when sampling periods are less than 24 h and the concentration ratio of sulfur dioxide to sulfate is greater than 5 1. Interference can also be introduced by hot-water extraction when reduced sulfur compounds like sulfite are present, because they are oxidized to sulfates in this process. Another possible error source is that some of the various analytic procedures us for sulfate determination may be influenced by other substances also present in the particulate matter. 

Both the air sample matrix C and the matrix of the potential source profiles A were perturbed by measurement error. In Set I only 9 sources were active, among which there was an unreported source. 

Random error is the divergence, due to chance alone, of an observation on a sample from the true population value, leading to lack of precision in the measurement of an association. There are three major sources of random error individual/biological variation, sampling error, and measurement error. Random error can be minimized but can never be completely eliminated since only a sample of the population can be studied, individual variation always occurs, and no measurement is perfectly accurate. 

Finally, the MOS should also take into account the uncertainties in the estimated exposure. For predicted exposure estimates, this requires an uncertainty analysis (Section 8.2.3) involving the determination of the uncertainty in the model output value, based on the collective uncertainty of the model input parameters. General sources of variability and uncertainty in exposure assessments are measurement errors, sampling errors, variability in natural systems and human behavior, limitations in model description, limitations in generic or indirect data, and professional judgment. 

Figure 10.5 Increase of the signal to noise ratio in non-crystallographic symmetry averaging. In (a) is shown a one-dimensional representation of the electron density of a macromolecule. In (b), a graph of the noise that results from the sources of errors in the crystallographic process, including experimental phasing and measurement errors. In (c), the observed density composed of the true electron density with the noise component. In (d), the effect of non-crystallographic symmetry improves the signal from the macromolecule while decreasing the noise level, the dotted lines shows the level of bias.

It is useful to distinguish between variability, parameter uncertainty, and model uncertainty, since they require different treatment in risk analysis (Suter and Barnthouse 1993). Variability refers to actual variation in real-world states and processes. Parameter uncertainty refers to imprecise knowledge of parameters used to describe variability or processes in a risk model this can arise from many sources including measurement error, sampling error, and the use of surrogate measurements or expert judgment. Model uncertainty refers to uncertainty about the structure of the risk model, including what parameters should be included and how they should be combined in the model equations. 

There are two main sources of error propagation in static measurements, errors due to successive dilutions and errors due to initial instrument offset. Other errors which are also applicable to SEC analysis are discussed in (J ). These errors can be propagated using the criteria presented here. If w is the intial mass of polymer and Vj is the amount of solvent added to obtain the desired concentration Ci, the dilution process can be represented by the following set of equations ... 

Some methods are based on the knowledge of the experimental error in the measurement of the original variables. Thus, the number of significant components is that by which the original data matrix is reproduced within the measurement error. This does not usually happen with food data, where analytical error is frequently smaller than the other individual sources of variation. The number of sources of variability in food composition is very high, and it is almost impossible that the experiment has been designed to cover all these sources of variability uniformly. So, some sources of variability appear in only one or a few objects, a minority, which behaves differently from the majority. 

We have presented a statistical experimental design and a protocol to use in evaluating laboratory data to determine whether the sampling and analytical method tested meets a defined accuracy criterion. The accuracy is defined relative to a single measurement from the test method rather than for a mean of several replicate test results. Accuracy here is the difference between the test result and the "true value, and thus, must combine the two sources of measurement error ... 

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). 

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