Accuracy standard error

Expected protein mass Assay accuracy averages (%) Average. accuracy (%) Standard error (%) df 95% Confidence interval on accuracy ... 

Example 1 Sample Quantity for Composition Quality Control Testing An example is sampling for quality control of a 1,000 metric ton (VFg) trainload of-Ks in (9.4 mm) nominal top-size bentonite. The specification requires silica to be determined with an accuracy of plus or minus three percent for two standard errors (s.e.). With one s.e. of 1.5 percent, V is 0.000225 (one s.e. weight fraction of 0.015 squared). The problem to be solved is thus calculating weight of sample to determine sihca with the specified error variance. 

The standard deviation gives the accuracy of prediction. If Y is related to one or more predictor variables, the error of prediction is reduced to the standard error of estimate S, (the standard deviation of the errors), where... 

The whole calculation can also be extended easily to measurements of different weights, i.e., of different accuracy. Let us denote the standard error in Yij by 6y. The weight wy of a measurement can be defined as... 

Accuracy (systematic error or bias) expresses the closeness of the measured value to the true or actual value. Accuracy is usually expressed as the percentage recovery of added analyte. Acceptable average analyte recovery for determinative procedures is 80-110% for a tolerance of > 100 p-g kg and 60-110% is acceptable for a tolerance of < 100 p-g kg Correction factors are not allowed. Methods utilizing internal standards may have lower analyte absolute recovery values. Internal standard suitability needs to be verified by showing that the extraction efficiencies and response factors of the internal standard are similar to those of the analyte over the entire concentration range. The analyst should be aware that in residue analysis the recovery of the fortified marker residue from the control matrix might not be similar to the recovery from an incurred marker residue. 

In the work described earlier, the applicability of the Weibull model was further tested by assessing the precision of estimation [expressed by the CV defined as the standard error of estimates divided by the estimated value] and the relative accuracy of estimation of the model parameters (based on the difference of the estimates from the actual value, divided by the actual value). Regarding the precision of estimates, for data with SD = 2 the maximum CV value for Wo, b, and c was 13%, 52%, and 16%, respectively, whereas the corresponding numbers for data with SD = 4 were 33%, 151%, and 34%, respectively. As expected, the precision of the estimates decreases as the SD of the data increases, with the poorest precision for the b estimates and the best for the Wo estimates. Additionally, the maximum CV values were associated with low c values (c = 0.5). 

Inner-shell correlation is a substantial part of the absolute correlation energy even for late first-row systems for second-row systems, it in fact rivals the absolute valence correlation energy in importance. However, its relative contribution to molecular TAEs is fairly small in benzene, for instance, it amounts to less than 0.7 % of the TAE. Even so, at 7 kcal/mol, its contribution is important by any reasonable thermochemical standard. By the same token, a 1 % relative error in a 7 kcal/mol contribution is tolerable even by benchmark thermochemistry standards, while the same relative error in a 300 kcal/mol contribution would be unacceptable even by the chemical accuracy standards. 

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). 

The third method for assessing accuracy is to calculate an elemental composition for each LTA s corresponding oxidized ash, based on the reference mineral elemental compositions. Reasonably close agreement between the actual (obtained by ICP-AES) and calculated elemental compositions would substantiate (but not prove) the mineral analysis. The standard error of prediction (SEP) for... 

CVt = 0.25/1.96 = 0.128. The number 0.128 is the largest true precision for a net error at +25% at the 95% confidence level. The number 1.96 is the appropriate t - statistic from the t distribution at the same confidence level. Since the coefficient of variation of pump error is assumed to be 5%, a method should have a CV analysis <0.102 to meet the CV accuracy standard. Tables IV and V7 shows that the infrared technique meets this requirement. 

Assuming normally distributed sampling and analysis errors (and no bias), the NIOSH accuracy standard is met if the true coefficient of variation of the total error, denoted by CVp, is no greater than 0.128. However, estimates of CVp (denoted by CVp), which were obtained in the laboratory validations, are themselves subject to appreciable random errors of estimation. Therefore, a "critical value" for the CVp was needed (i.e. the value not to be exceeded by an experimental CVp if the method is to be judged acceptable). 

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. 

Figure 18.6 Representative standard curve of ICP-AES. Expected concentrations are based on reference standards of certified accuracy. The residual error of measured concentrations is plotted above the standard curve. Error bars represent standard errors of three or more replicate measurements. The linear concentration regime is bracketed by arrows and represents deviations of expected and measured concentrations of less than 5%. Reprinted from Bai et al. (2007).

Accuracy is the closeness of the mean of a set of replicate analyses to the true value of the sample. Often, it is only possible to assess the accuracy of one method relative to another by comparing the means of replicate analyses by the two methods using the t test. The basic assumption, or null hypothesis, made is that there is no significant difference between the mean value of the two sets of data. This is assessed as the number of times the difference between the two means is greater than the standard error of the difference (t value). 

The values were determined at XenoTech (unpublished data). Constants are shown standard error (rounded to 2 significant figures, with standard error values rounded to the same degree of accuracy as the constant), and were calculated using GraFit software, which utilized rates of product formation (triplicate data) at 13 substrate concentrations. 

Apart from the fact that a linear calibration can be performed, bracketing offers excellent precision and accuracy. With the determination of serum cholesterol as an example, Cohen et al. (1980) showed that the replication error on five different serum pools was characterized by a CV of 0.17% with a set-to-set variability of 0.32%. For each serum average, a standard error (considering all causes of variability combined) of 0.16% CV was obtained. The undetected systematic error (bias) in this study was estimated to be smaller than 0.5%, while White et al. (1982), using two different IDMS methods, found serum glucose concentrations to agree within 1%. 

Before continuing with a screening analysis, it is prudent to check the overall accuracy of the approximator in (6) and the validity of its standard error (7) by cross validation (see Jones et al 1998). 

FIGURE 6-14. Theory of error, (a) The standard error curve. (b) Scattering of means and individual measurements about the true value, (c) Impact of reproducibility upon accuracy assuming only random errors. (Figure A and B reprinted from reference 11 with permission.)... 

Standard deviation, standard error, or degree of accuracy can be given in two ways ... 

The data are tabulated and the standard error of the control size class determined to ensure that it is less than 2%. An accuracy factor is calculated for each size class and provided it is always less than the value for the control size class the standard error for the other size classes will be better than this. The completed table is shown as Table 3.5. Although the technique appears onerous, a skilled microscopist can carry out a weight analysis in about an hour. 

Greater accuracy in a mean can be obtained by taking more observations, i.e. by increasing n, since the standard deviation of the mean (or standard error) is o/- /h. Doubling the number of observations will give limits approximately... 

Duplicate or triplicate experiments, each involving twelve or more separate measurements have generally given the mean rate coefficient with a standard error of 0-2 — 0-4% of its value without difficulty. However, the same experimental accuracy leads to a greater error in second-order rate coefficients. 

Fit all the surfaces using kriging and validate the model. Once all the variables (surfaces) have been estimated by kriging, it is important validate the metamodel, i.e. using cross validation that allows us to asses the accuracy of the model without extra sampling [2], A kriging model can be considered correct if all the errors in cross validation are inside the interval [-3,+3] standard errors. 

Figure 12. The ratio Ci /C2 computed for a very rare event in contrast to the system in Fig. 10. For the rare event it is difficult to do the exact calculations. Therefore, accuracy check was done for not so rare events. Error bars are calculated by adding the standard errors for each factor in the numerator and denominator, each of which is given from the standard error of the mean from 20 uncorrelated runs. Here the potential is y = 10 , y = 10 (for Hi), and y = 1.2 x 10 (for H2). kT is 0.1. Since y is 10 and kT is 0.1, it takes only t 0.01 to get across the channel. But after time Z = 1, the probability of a reaction is only 0.0001.

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