True quantity value

Example 5 The true value of a quantity is 30.00, and cr for the method of measurement is 0.30. What is the probability that a single measurement will have a deviation from the mean greater than 0.45 that is, what percentage of results will fall outside the range 30.00 0.45 ... 

The probable largest inconsistency in all measurements is the fact that, regardless of the instruments used and the methods applied, we never find the true value of the quantity that is being measured. It is possible to improve the... 

True value of a quantity This characterizes a perfectly defined quantity, in the conditions existing at the time the value was observed. 

Error of measurement This is the discrepancy between the result of measurement and the true value of the quantity. 

True value A theoretical value that exactly relates a quantity for specific conditions. 

When a quantity is measured with the greatest exactness of which the instrument, method, and observer are capable, it is found that the results of successive determinations differ among themselves to a greater or lesser extent. The average value is accepted as the most probable. This may not always be the true value. In some cases the difference may be small, in others it may be large the reliability of the result depends upon the magnitude of this difference. It is therefore of interest to enquire briefly into the factors which affect and control the trustworthiness of chemical analysis. 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

Figure 10-1 illustrates two statements that experience has shown to be generally valid for analytical results obtained by wet methods (1) The true value a and the mean x are different quantities, and one cannot be predicted from the other. (2) No conclusions about the frequency distribution can be drawn from a or from x. One more generalization applies to comparative x-ray methods, be they absorption (3.10) or emission (7.8) methods If the comparison is properly carried out, questions of accuracy will never arise properly includes the use of a... 

Material certification study Study that assigns a reference value ( true value ) to a quantity (concentration or property) in the test mate-... 

Suppose N independently repeated samples xi, x2,..., xjv are obtained to measure the value of a quantity X, where x represents an estimate of its true value x. Usually the best estimate of x is provided by the mean or average of x, x(N). The reliability of the estimator x can be characterized by the mean square error, (e.g., [29, 30])... 

An error is the difference between an individual result and the true value of the quantity being measured. Since true values cannot be known exactly, it follows, from the above definition, that errors cannot be known exactly either. Errors are usually classified as either random or systematic. 

Accuracy is the closeness of the agreement between the result of a measurement and the true value of the quantity being measured. Accuracy is the property of a single measurement result. It tells us how close a single measurement result is to the true value and therefore includes the effect of both precision and bias. 

If a large number of readings of the same quantity are taken, then the mean (average) value is likely to be close to the true value if there is no systematic bias (i.e., no systematic errors). Clearly, if we repeat a particular measurement several times, the random error associated with each measurement will mean that the value is sometimes above and sometimes below the true result, in a random way. Thus, these errors will cancel out, and the average or mean value should be a better estimate of the true value than is any single result. However, we still need to know how good an estimate our mean value is of the true result. Statistical methods lead to the concept of standard error (or standard deviation) around the mean value. 

New chemicals must have time to prove themselves in the marketplace. Often, the true value of an innovation is not known for many years after its introduction. The initial use of a new product is industry s opportunity to appreciate the chemical s properties and explore its potential. A new chemical often initially produced in small quantities, may become a large scale venture after many years with significant and occasionally unanticipated applications. 

Two terms refer to the quality and reproducibility of our measurements of variables. The first, accuracy, is an expression of the closeness of a measured or computed value to its actual or true value in nature. The second, precision, reflects the closeness or reproducibility of a series of repeated measurements of the same quantity. 

Uncertainty of a Certified Value Estimate attached to a certified value of a quantity which characterizes the range of values within which the true value" is asserted to lie with a stated level of confidence. 

In some textbooks, a confidence interval is described as the interval within which there is a certain probability of finding the true value of the estimated quantity. Does the term true used in this sense indicate the statistical population value (e.g., p if one is estimating a mean) or the bias-free value (e.g., 6.21% iron in a mineral) Could these two interpretations of true value be a source of misunderstanding in conversations between a statistician and a geologist ... 

Accuracy is the closeness of a result to a true value. This again is the combination of tmeness and precision and defines measurement uncertainty. (See also chapter 12). Accuracy is greater when the quantity value is closer to the tme value... 

A result obtained by using several independent methods in several expert laboratories on one measurand Is regarded as conventional true value of a quantity... 

Error (of measurement) is the sum of random and systematic errors of one measurement. Since a true value cannot be determined, in practice a reference quantity value is used. Each individual result of a measurement will have its own associated error. 

The ability to quantity is generally expressed in terms of the signal or analyte (true) value that will produce estimates having a specified relative standard deviation (RSD), commonly... 

The closeness or proximity of a measured value to the true value for a quantity being measured. Unless the magnitude of a quantity is specified by a formal SI definition, one typically uses reference standards to establish... 

PARROT allows for the fact that, in addition to the experimental quantities z which exhibit significant deviations from their true value, there is another set of quantities u° which are considered free from significant inaccuracy. Also, independent and dependent variables are defined, where independent variables are measured values which can be considered to define the conditions for the equilibriiun state while dependent variables are regarded as the responses of the system to the these prescribed conditions. Independent variables should come primarily from the u° set, but if recourse has to be made to the zf set the latter can be further divided into two sets, one which contains independent variables xf and the other containing dependent variables y°. Whether a measured independent variable should be included in the Uj or x, set depends on the sensitivity of the yi quantities to fluctuations in that value. If the fluctuations in the y, quantities are less than the accuracy of the experimental measurement when the u,- or value is varied within its own accuracy limit, then it should be included in the xk set. 

The information communicated by the risk assessor needs to provide an assessment of the overall degree of uncertainty and confidence in the analysis. The nature of the uncertainty for sensitive variables should be communicated, for example, variability, descriptive errors, data gaps, uncertainty about a quantity s true value, and... 

Other than the operations that emphasize certain aspects of the data, there are destructive influences that reduce our knowledge of the features of the data under investigation. These influences introduce deviations from the true values of the quantity being measured called experimental error, or simply error. Many of these degrading operations are selective, in that their... 

Measurement uncertainty is the most important criterium in both method validation and IQC. It is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand [14]. The measurand refers to the particular quantity or the concentration of the analyte being measured. The parameter can be a standard deviation or the width of a confidence interval [14, 37]. This confidence interval represents the interval on the measurement scale within which the true value lies with a specified probability, given that all sources of error are taken into account [37]. Within this interval, the result is regarded as being accurate, that is, precise and true [11]. 

The accuracy of an analytical method is estimated as the percentage difference (bias) between the mean values generated by the method and the true or known concentrations. Accuracy is usually synonymous with systematic errors. Systematic errors cause all the results in a series of replicates to deviate from the true value of the measured quantity in a particular sense (i.e., all the results are too high or all are too low) (20). Accuracy has also been used in recent years to refer to any error causing a single measurement to deviate from the true value (i.e., to encompass elements of random and systematic errors) (21). 

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