Variability of measurements

Expected Variability of Measurement (Coefficient Distribution of Variation) (Model) 95% Confidence Interval About the Mean Estimate (percent) ... 

In this expression, x is the independent variable of measurement, whether it be wavelength, wave number, or other parameter. The quantity UM(x) is the flux, as measured by the spectrometer, after it has passed through the absorbing sample. The quantity BM(x) represents the flux that has passed over an identical path but in the absence of an absorbing sample. The term Dm(x) represents any additive offsets that might be introduced by stray flux, errors in electronic amplification and digital conversion, or other causes. We call the resulting measured transmittance TM(x). 

The uncertainty applicable to a measurement contains components for repeatability and reproducibility [9,19, 20], caused in part by variability of measurement-relevant parameters. The uncertainty also depends on the individual making the measurement, the laboratory facilities used, and the environment during the measurement. Without some quality control over measurements, statements on relevant traceability can have little meaning. Such controls provide a laboratory with confidence in its operators and credibility to the outside. 

Nendza (1998) and Doucette (2003) have discussed reasons for the variability of measured values. These include soil inhomogeneity, lack of attainment of equilibrium, sorption of the test chemical onto vessel walls, volatilization of the test chemical, instability of the test chemical in both water and soil, pH and buffer capacity of the aqueous phase, presence of solubilizing agents and co-solutes, and incomplete phase separation prior to analysis. 

Statistical The process by which that variability of measurements or of data outputs of control - a system is controlled to the extent necessary to produce stable and... 

The slope of the dose-response curve depends on many factors, such as the variability of measurement of the response and the variables contributing to the response. The greater the number of animals or individual measurements and the more precise the measurement of the effect, the more accurate are the parameters determined from the dose-response curve. The slope of the curve also reflects the type of response. Thus when the response reflects a potent single effect, such as avid binding to an enzyme or interference with a vital metabolic function as is the case with cyanide or fluoroacetate for example, the dose-response curve will be steep and the value of the slope will be large. Conversely, a... 

The significance of the estimated coefficients was tested by using the Student s -distribution at the 0.05 level of significance. The multiple correlation coefficient (R) was derived from the total variability of measured properties and the residual variability of the calculated values. Variability was expressed as sums of squares. These calculations were performed for every property studied. 

Precision is the estimate of variability of measurements. It is often confused with, or used interchangeably (and incorrectly) with, accuracy. Accuracy reflects systematic error precision reflects random error. The concept is really more complex since the systematic error term also is subject to random variability, but for our purpose we can treat the two attributes of analytical methods as separate characteristics. 

The data-quality requirements for QSAR models relate to several aspects of the experimental procedure, data transformation and the selection of the appropriate test compounds. Only if the input data of a QSAR meet the highest quality standards may a sound model be derived. Because the accuracy of predictions can never be better than the variability of the respective measurements (usually 20% and more), validity assessment of the activity and effects data is crucial in QSAR derivations. The data should be generated by tests that are methodologically and mechanistically defined. The latter is not trivial for parameters such as biodegradability, soil sorption and ecotoxicity. With regard to the considerable variability of measurements, inter- and also intra-laboratory, the test results, especially when collected from different literature sources, should be critically evaluated with respect to ... 

Control charts may be utilized to monitor the variability of measurements from the quality control check standards and independent reference standards in order to optimally detect abnormal situations and ensure a stable measurement process. 

The surface energies Ygg obtained experimentally by Zisman s method are remarkably similar to the average value obtained from Equation 5 throughout the range of Ygg regardless of the liquids used. The accuracy of both approaches in the determination of Ygg appears to be limited more by the notorious variability of measurements of 9 than by other factors. 

VARIABLES TO BE SUPPLIED ARRAY OF MEASURED INOEP VARIABLES ARRAY OF ERROR VARRIANCES CF INDEP VECTOR OF FIRST MEASURED DEPENDENT ERROR VARRIANCES OF FIRST VARIABLES... 

The effectiveness of the approach is demonstrated on two rqjresentative NDT techniques intapretation of data acquired with an ultrasonic rail inspection system and interpretation of eddy-current data from heat exchangers in (petro-)chemical industry. The results show that it is possible to provide a high level of automation in combination with efficient operator support for highly variable NDT measurements where up to now use of automated interpretation was only limited. 

The proposed measurement system consist of measuring impedance variations, resistance and inductance, using a coil surrounding a cylindrical hallow sample, in with standard defects were created homy a variable length and width... 

The NAs such as DNA usually used in the experiments consist of 10" -1 o nucleotides. Thus, they should be considered as macrosystems. Moreover, in experiments with wet NA samples macroscopic quantities are measured, so averaging should also be performed over all nucleic acid molecules in the sample. These facts justify the usage of the macroscopic equations like (3) in our case and require the probabilities of finding macromolecular units in the certain conformational state as variables of the model. 

In another type of measurement, the parallel between mechanical and electrical networks can be exploited by using variable capacitors and resistors to balance the impedance of the transducer circuit. These electrical measurements readily lend themselves to computer interfacing for data acquisition and analysis. 

Knoop developed an accepted method of measuring abrasive hardness using a diamond indenter of pyramidal shape and forcing it into the material to be evaluated with a fixed, often 100-g, load. The depth of penetration is then determined from the length and width of the indentation produced. Unlike WoodeU s method, Knoop values are static and primarily measure resistance to plastic flow and surface deformation. Variables such as load, temperature, and environment, which affect determination of hardness by the Knoop procedure, have been examined in detail (9). 

In most process plant situations where feedforward control is appropriate, a combination of the feedforward and feedback control is usually used. The feedforward portion reduces the impact of measured disturbances on the controlled variable while the feedback portion compensates for model inaccuracies and unmeasured disturbances. This control strategy is referred to as feedforward control with feedback trim. 

Statistical quaUty control charts of variables are plots of measurement data, preferably the average result of repHcate analyses, vs time (Fig. 2). Time is often represented by the sequence of batches or analyses. The average of all the data points and the upper and lower control limits are drawn on the chart. The control limits are closely approximated by the sum of the grand average plus for the upper control limit, or minus for the lower control limit, three times the standard deviation. 

The ordered set of measurements made on each sample is called a data vector. The group of data vectors, identically ordered, for all of the samples is called the data matrix. If the data matrix is arranged such that successive rows of the matrix correspond to the different samples, then the columns correspond to the variables as in Figure 1. Each variable, or aspect of the sample that is measured, defines an axis in space the samples thus possess a data stmcture when plotted as points in that / -dimensional vector space, where n is the number of variables. 

The purpose of translation is to change the position of the data with respect to the coordinate axes. Usually, the data are translated such that the origin coincides with the mean of the data set. Thus, to mean-center the data, let be the datum associated with the kth measurement on the /th sample. The mean-centered value is computed as = x.f — X/ where xl is the mean for variable k. This procedure is performed on all of the data to produce a new data matrix the variables of which are now referred to as features. 

Nature In some types of applications, associated pairs of obseiwa-tions are defined. For example, (1) pairs of samples from two populations are treated in the same way, or (2) two types of measurements are made on the same unit. For applications or tnis type, it is not only more effective but necessary to define the random variable as the difference between the pairs of observations. The difference numbers can then be tested by the standard t distribution. 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodyuamics are internal energy and entropy These properties, together with the two laws for which they are essential, apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly... 

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