Percent relative error

Accuracy is a measure of how closely the result of an experiment agrees with the expected result. The difference between the obtained result and the expected result is usually divided by the expected result and reported as a percent relative error... 

Rearranging and multiplying through by 100 gives the percent relative error in concentration as... 

Since empirical force fields do not accurately estimate the true interatomic forces, it is difficult a priori to say how accurate the fast multipole approximation to the exact Coulomb potential and forces (exact in terms of the sum over partial charges) should be. Probably a good rule is to make sure that at each atom the approximate electrostatic force is within a few percent relative error of the true electrostatic force, obtained by explicitly summing over all atom pairs, i.e., IF — FJ < 0.05 F , for all atoms i, where F is the... 

Often, the relative error is a more useful quantity than the absolute error. The percent relative error is given by the expression... 

A method of analysis yields weights for gold that are low by 0.4 mg. Calculate the percent relative error caused by this uncertainty if the weight of gold in the sample is (a) 700 mg. 

The color change of a chemical indicator requires an overtitration of 0.04 mL. Calculate the percent relative error if the total volume of titrant is (a) 50.00 mL. (b) 10.0 mL. 

A loss of 0.4 mg of Zn occurs in the course of an analysis for that element. Calculate the percent relative error due to this loss if the weight of Zn in the sample is... 

Often another estimate of the LOQ is used, the experimental limit of quantitation (ELOQ). Tliis value is defined as the lowest biological sample standard concentration that has been analyzed and that has a defined relative error and a defined RSD (e.g., 15 percent relative error and 15 percent RSD). 

The estimates are the maximum likelihood estimates determined by NONMEM. %RSE is the percent relative error calculated by dividing the asymptotic standard error by the parameter estimate. Statistical significance is the significance level as determined by the log likelihood difference. NT = not tested. 

Recommended analysis and acceptance criteria apply to each sample concentration HQC = high-quality control sample LLOQ — lower limit of quantification sample LQC = low-quality control sample MQC — middle quality control sample ULOQ — upper limit of quantification sample) %CV — percent coefficient of variation %RE — percent relative error [4]... 

The trueness of the method can be represented by the percent relative error (bias). At concentration level j, it is given by... 

Precision and Accuracy. Precision and accuracy are assay performance characteristics that describe the random (statistical) errors and systematic errors (bias) associated with repeated measurements of the same sample under specified conditions [3-5]. Precision is typically estimated by the percent coefficient of variation (% CV, also referred to as relative standard deviation or RSD) but may certainly also be reported as standard deviations. Method accuracy is expressed as the percent relative error (% RE) and is determined by the percent deviation of the weighted samples mean from samples with nominal reference values. A collection of validation sample statistics can be found in References 9,11, and 25. 

Figure 2.16 Ringbom plot of permanganate solution measured at 526 nm in a 1.00 cm cell. %RE = percent relative error in concentration for a 1% error in transmittance. The magnitude of %RE is shown for three ranges of Mn concentration. Mn concentration is in units of ppm Mn in solution (1 ppm = 1 p,g Mn/mL solution).

Accuracy can be evaluated based on a determination of the percent relative error provided that a known value is available. A certified reference standard constitutes such a standard. Accuracy is calculated and reported in terms of a percent relative error according to... 

Include all calibration data, ICVs, and sample unknowns for both instrumental methods. Perform a statistical evaluation in a manner that is similar to previous experiments. Use EXCEL or LSQUARES (refer to Appendix C) or other computer programs to conduct a least squares regression analysis of the calibration data. Calculate the accuracy (expressed as a percent relative error for the ICV) and the precision (relative standard deviation for the ICV) from both instrumental methods. Calculate the percent recovery for the matrix spike and matrix spike duplicate. Report on the concentration of Cr in the unknown soil samples. Be aware of all dflution factors and concentrations as you perform calculations ... 

Accuracy can be evaluated based on a determination of the percent relative error according to... 

The manual count, as given by Putman et al. (2005), is 1038 tTable 4.1T Thus, the percent relative error (PRE) is ... 

PRE is the percent relative error for the numerically calculated value. 

You should be able to get the exact solution for this simple ODE and compare your answers. Calculate the percent relative error (PRE) for the estimated value of y at t = 5. 

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