Error, in measurement

Statement that a periodic signal must be sampled at least twice each period to avoid a determinate error in measuring its frequency. 

The relative measurement error in concentration, therefore, is determined by the magnitude of the error in measuring the cell s potential and by the charge of the analyte. Representative values are shown in Table 11.7 for ions with charges of+1 and +2, at a temperature of 25 °C. Accuracies of 1-5% for monovalent ions and 2-10% for divalent ions are typical. Although equation 11.22 was developed for membrane electrodes, it also applies to metallic electrodes of the first and second kind when z is replaced by n. 

The degree of accuracy can be assessed from the error in measurement. If Rg is the true ratio (64.5) and R is the mean, then... 

Thus, the variance of the desired quantity Y can be found. This gives an independent estimate of the errors in measuring the quantity Y from the errors in measuring each variable it depends upon. 

The resistance must be measured with extreme care and accuracy, since a small error in measuring the resistance will cause a much larger error in determining the temperature rise. When the temperature of the winding is to be determined by the resistance, the temperature of the winding before the test, measured either by thermometer or by ETD, may be considered as the cold temperature for the resistance measured. The machine must be left cold for at least 12 to 24 hours, depending upon the size of the machine, to obtain a stable reading. 

In group (b), AU values are determined according to the data in Section 3.6.2.2 for circular defects. Examples are shown in Figs. 3-28 and 3-29. Figure 3-31 shows that in fact practically symmetrical voltage cones can occur, as predicted in Eq. (3-48) [47]. Errors in measurement must take into account the information in... 

A weighted least-squares analysis is used for a better estimate of rate law parameters where the variance is not constant throughout the range of measured variables. If the error in measurement is corrected, then the relative error in the dependent variable will increase as the independent variable increases or decreases. 

Basically, there may be three reasons for the inconsistency between the theoretical and experimental friction factors (1) discrepancy between the actual conditions of a given experiment and the assumptions used in deriving the theoretical value, (2) error in measurements, and (3) effects due to decreasing the characteristic scale of the problem, which leads to changing correlation between the mass and surface forces (Ho and Tai 1998). 

Before the slit. Motion of the image delivered by the telescope with respect to the slit causes both a loss of throughput and an error in the barycentre of the spectral lines recorded on the detector, unless the object uniformly fills the slit (which implies low throughput). This can cause errors in measurement of radial velocities. For MOS, there is the particular problem of variations in the image scale or rotations of the mask. These can cause errors which depend on position in the field resulting in spurious radial trends in the data. Fibre systems are almost immune to this problem because the fibres scramble posifional information. 

In order to discuss how we can use statistical methods to estimate the errors in measuring the displacement we use the notation h u a). This is the condi-... 

Error in measuring the gain or efficiency of the electron multiplier or ion counter... 

It should be noted that in a vapour phase the liquid layer on the surface of a sensitive element of the sensor (zinc oxide) must be sufficiently thin, so that it would not produce any influence on the diffusion flux of oxygen through this layer. Possible lack of the film continuity (the presence of voids) does not prevent determination of concentration of oxygen in the bulk of the cell by the vapour - gas method. In this case, one deals with a semi-dry method. On the contrary, the presence of a thick liquid layer causes considerable errors in measuring t, because of different distribution of oxygen in a system gas - liquid layer -semiconductor film (this distribution is close to that in the system semiconductor film - liquid), in addition to substantial slowing down of oxygen diffusion in such systems. 

Minimisation of sample preparation is the main bottleneck in polymer/additive analysis. The importance of sample preparation increases with miniaturisation of the separation techniques. However, there is no point in improving instrumentation when the true sources of errors in measurement are sampling, sample inhomogeneity or sample instability. 

Electrophoresis involves the movement of a charged particle through a liquid under the influence of an applied potential difference. A sample is placed in an electrophoresis cell, usually a horizontal tube of circular cross section, fitted with two electrodes. When a known potential is applied across the electrodes, the particles migrate to the oppositely charged electrode. The direct current voltage applied needs to be adjusted to obtain a particle velocity that is neither too fast nor too slow to allow for errors in measurement and Brownian motion, respectively. It is also important that the measurement is taken reasonably quickly in order to avoid sedimentation in the cell. Prior to each measurement, the apparatus should be calibrated with particles of known zeta potential, such as rabbit erythrocytes. 

After all this fancy mathematics, we need a word of caution. It is extremely dangerous to apply the state estimate as presented in this chapter. Why The first hint is in Eq. (9-32). We have assumed perfect knowledge of the plant matrices. Of course, we rarely do. Furthermore, we have omitted actual terms for disturbances, noises, and errors in measurements. Despite these drawbacks, material in this chapter provides the groundwork to attack serious problems in modem control. 

A critical attitude towards the results obtained in analysis is necessary in order to appreciate their meaning and limitations. Precision is dependent on the practical method and beyond a certain degree cannot be improved. Inevitably there must be a compromise between the reliability of the results obtained and the use of the analyst s time. To reach this compromise requires an assessment of the nature and origins of errors in measurements relevant statistical tests may be applied in the appraisal of the results. With the development of microcomputers and their ready availability, access to complex statistical methods has been provided. These complex methods of data handling and analysis have become known collectively as chemometrics. 

Sources of Error 1. Experimental error in measurement 2. Measuring tools not reliable or not sensitive enough 3. Activity of ions as proposed by Debye and Huckel which states an effective concentration called activity which takes into account interionic attractions resulting in a decrease in the magnitude of colligative properties, especially for concentrated solutions. 

The excited state of a molecule can last for some time or there can be an immediate return to the ground state. One useful way to think of this phenomenon is as a time-dependent statistical one. Most people are familiar with the Gaussian distribution used in describing errors in measurement. There is no time dependence implied in that distribution. A time-dependent statistical argument is more related to If I wait long enough it will happen view of a process. Fluorescence decay is not the only chemically important, time-dependent process, of course. Other examples are chemical reactions and radioactive decay. 

How to best describe this broadening we expect to occur One way is by analogy to random error in measurements. We know or assume there is a truly correct answer to any measurement of quantity present and attempt to determine that number. In real measurements there are real, if random, sources of error. It is convenient to talk about standard deviation of the measurement but actually the error in measurement accumulates as the sum of the square of each error process or variance producing mechanism or total variance = sum of the individual variances. If we ignore effects outside the actual separation process (e.g. injection/spot size, connecting tubing, detector volume), this sum can be factored into three main influences ... 

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