Normal Distribution accuracy level

The critical value of CVp has to be lower than the maximum permissible true value (e.g. lower than CVp 0.128 when there is no bias). The maximum permissible value of the true CVp will be referred to as its "target level". In order to have a confidence level of 95% that a subject method meets this required target level, on the basis of CVp estimated from laboratory tests, an upper confidence limit for CVp is calculated which must satisfy the following criterion reject the method (i.e. decide it does not meet the accuracy standard) if the 95% upper confidence limit for CVp exceeds the target level of CVp. Otherwise, accept the method. This decision criterion was implemented in the form of the Decision Rule given below which is based on assumptions that errors are normally distributed and the method is unbiased. Biased methods are discussed further below. 

This indicates that to know the measurement random error it is not sufficient to know its magnitude only (confidence interval of measurement error) but also the significance level that facilitates the confidence estimate of the obtained measurements. Using the error mean square as a measurement accuracy property is convenient because that value in a normal distribution is associated with a confidence or confidence coefficient of 0.68 probability. The doubled error mean square 2S has... 

The third source arises from the extraction efficiency for the removal of solute from water, a technique common to most methods. Peters (6), has shown this to introduce another negative bias within 8 percent therefore a beta distribution with a 95-percent confidence level of -8 percent was selected. Finally, the accuracy of the detection method was modeled by a normal distribution with a 95-percent confidence level of +2 percent as recommended by Mallon and Harrison ( 7). 

O Figure 11-1, taken from Bak et al. (2000), illustrates the accuracy of equilibrium geometry dipole moments calculated for a series of small molecules. In Bak et al. (2000), the dipole moments of 11 molecules were studied at various levels of approximation using a sequence of basis sets, with the CCSD(T)/aug-cc-pVQZ results providing the benchmark values. The normal distribution of errors with respect to the reference values, shown in O Fig. 11-1, demonstrates the systematic improvements of the computed results with increasing basis set and improved treatment of electron correlation effects. 

This method employs the classical statistics to calculate the variance with a set of model outputs from a set of input parameters that are randomly generated. The number of runs depends on the model and the assumed input parameter distribution. According to Harr (25), the required number of MC simulations, N, for, m, independent variables is estimated as, N=(h /4 r, where h is the standard deviation in a normal distribution corresponding to the confidence interval, and is the maximum allowable system error in estimating the confidence interval. For example, if a required confidence interval is 99% with 1% system error, h is 2.58, e is 0.01, and (16,641)" is estimated. Therefore computing time is the major disadvantage of this method. Cawlfield and Wu (24) required over 400,000 computer runs to achieve a good level of accuracy for a one-dimensional transport code for a reactive contaminant. 

Some of the more sophisticated techniques offer detailed information or levels of accuracy that are not required in day-to-day operations. However, when operational upsets cannot be handled by normal methods, details of the emulsion properties have to be understood. For example, subtle changes in the size distribution of the dispersed phase (while total oil, water, and solids remain constant) can be important in determining process performance. An oil-in-water or water-in-oil emulsion can invert during processing as one or the other phase is removed, and the point in the process when this inversion occurs can have implications for the efficiency of the operation. The addition of diluent to reduce oil-phase viscosity, for instance, is much more efficient if oil is the continuous phase. 

The accuracy with which total body water can be measured depends on the uniformity of distribution of the deterium oxide throughout the water compartments of the body and the precision with which the concentration of deuterium can be measured in a given body fluid. As early as 1959 it was demonstrated that salivary glands concentrated deuterium above the level in serum, following the administration of label to normal pregnant women [236]. This fact has been repeatedly questioned by various workers [237] on the grounds of possible contamination of the salivary distillate, required for deuterium analysis by the falling drop method employed. More recently the use of isotope mass spectrometry has provided unequivocal evidence that in both the rat [238] and man... 

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