Relative percent difference

Whereas precision (Section 6.5) measures the reproducibility of data from replicate analyses, the accuracy (Section 6.4) of a test estimates how accurate the data are, that is, how close the data would represent probable true values or how accurate the analytical procedure is to giving results that may be close to true values. Precision and accuracy are both measured on one or more samples selected at random for analysis from a given batch of samples. The precision of analysis is usually determined by running duplicate or replicate tests on one of the samples in a given batch of samples. It is expressed statistically as standard deviation, relative standard deviation (RSD), coefficient of variance (CV), standard error of the mean (M), and relative percent difference (RPD). 

Calibrations were carried out for the GC/PID or the GC/MS daily. Calibration standards were prepared based on standard reference materials obtained from Supelco Chromatography products. A check standard was analyzed every ten samples to assure calibration and accuracy. A reagent blank was included in each analytic batch of samples. Blanks were made from reagent or make-up water and matrix similar to the sample. A spiked sample was analyzed every twenty samples. This was done by splitting an appropriate sample into two subsamples and adding a known quantity of TCE to one of the split samples. The purpose of a spiked sample is to determine the extent of matrix bias or interference on TCE recovery and sample to sample precision. Accuracy was assessed by analysis of external reference standards (separate from calibration standards) and by percent recoveries of spiked samples. Precision was assessed by means of replicate sample analysis. It is expressed as relative percent difference (RPD) in the case of duplicates or relative standard deviation (RSD) for triplicate (or more) analyses. Recovery was 96% or more for all spiked samples, and RPD/RSD are less than 7% for all samples. 

In routine tests of environmental samples, many repeat analyses of a sample aliquots are not possible. Therefore, the precision of the test required is measured by a scale known as relative percent difference (RPD). This is determined from the duplicate analysis performed under identical conditions on two aliquots of one of the samples in a batch. It is calculated by dividing the difference of test results by the average of test results and expressing as percent. Thus,... 

There are two types of control charts accuracy chart and precision control chart. Accuracy control charts are prepared from the percent spike recoveries data obtained from multiple routine analysis. Precision control charts may be prepared from the relative percent difference (RPD) of analyte concentrations in the samples and their duplicate analytical data. Alternatively, RPDs are calculated for percent recoveries of the analytes in the matrix spike and matrix spike duplicate in each batch and twenty (or any reasonable number of data points) are plotted against the frequency or number of analysis. If the samples are clean and the analytes are not found, the aliquots of samples must be spiked with the standard solutions of the analytes and the RPD should be determined for the matrix spike recoveries. Ongoing data quality thus can be checked against the background information of the control chart. Sudden onset of any major problem in the analysis can readily be determined from the substantial deviation of the data from the average. 

Precision is the agreement between the measurements of the same property under a given set of conditions. Precision or random error is a quantitative parameter that can be calculated in several different ways as the standard deviation relative standard deviation (RSD) or as relative percent difference (RPD). The first two are common statistical parameters that are used for the evaluation of multiple replicate measurements, whereas RPD is used for measuring precision between two duplicate measurements. Equation 1 in Table 2.2 illustrates the method for calculating RPD as a measure of precision. 

Precision 1 Relative Percent Difference Xi7Xrf xioo Xi + Xd 2 Xj—sample measurement xd—duplicate measurement... 

LCS/LCSD denotes laboratory control sample/laboratory control sample duplicate. RPD denotes relative percent difference. 

Similar to an LCS, but in this case the actual sample analyzed is being spiked with the analytes of interest. Data will give an indication of possible matrix interferences, and relative percent differences (RPD) can be calculated (30%—50% depending on matrix and analyte). Matrix spikes and matrix spike duplicates (MS/MSD) should be run with each new matrix. 

Duplicates To verify appropriate Verify the relative percent difference... 

In order to provide information on the precision of the analysis in the sample matrix, the laboratory must perform a duplicate analysis on one sample of each matrix in each SDG. The samples to be analyzed in duplicate may be specified by the Region in advance however, if no samples are so specified, the laboratory must select a sample of each matrix for duplicate analyses. The precision of the analysis is determined as the relative percent difference of the concentrations as specified in Section 14. 

Calculate the precision of each detected analyte in the original and duplicate analyses, expressed as the Relative Percent Difference (RPD), according to the following equation ... 

If we make the simplifying assumption that the density factor in (27-6) is unity, and if (for broad applicability) we consider the relative-percent difference in composition of the two kinds of particles, lOOfP — P jPt, we can calculate the curves... 

Calculate the net heating value (NHV) of methane, chloroform, benzene(g), chlorobenzene, and hydrogen sulfide. This assumes that the water product is in the vapor state. Compare these values with those calculated using Dulong s equation. Calculate the relative percent difference between the true NHVs as determined by thermodynamic calculations and the estimated values calculated using Dulong s equation. Dulong s equation can be written as follows ... 

In addition to the QA/QC performed by the laboratory, an independent QA/QC program administered by the data users is essentid in evalutating data quality. The "Field" QA/QC checks usually consist of travel blanks, field blanks, decontamination blanks, co-located samples, split samples, and blind standards. Split samples are most important for evaluating laboratory precision and blind standards are most important in assessing laboratory accuracy. The relative percent difference between split samples exceeded the 20 percent criteria at least once for Al, Sb, Be, Cd, Co, Cu, Fe, Mo, and Ag. Overall, few values exceeded the 20% criteria. 

Certified materials were used to evaluate the accuracy of the technique. These included coal, coal fly ash, soil, and crude oil. Table 3 shows that measured concentrations of mercury in the SRMs agree well with certified values. With only one exception, the Relative Percent Difference (RPD) is within 5 % of the certified values. The one exception is for a value that is less than half of the claimed detection limit for the published method. Six repetitions were made for each material. The expanded uncertainty of each measurement is calculated by multiplying the value for of one experimentally derived standard deviation of the data times the critical value. The critical value of 2.57 is determined from a Student s t-distiibution [12] with 5 degrees of fi-eedom and a confidence level of 95 %. 

If required, the relative percent difference (RPD) for a pair of duplicate analyses may be computed using Eq. (10.28) ... 

Assuming n = 1, T = 298 K (25°C), and a = 0.5, the ratios of the current density and exchange current density, Rjafei arid R, are calculated for negative q values and are compared in Table 5.2 along with the relative percent difference between the two ratios. 

Matrix Spike Duplicate (MSD) Sample (Tier II only)—Every batch or 20 samples, whichever is more frequent, precision data is generated using a matrix spike duplicate. Acceptance criteria is 20 % RPD (relative percent difference) for the duplicate analyses. 

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