Relative bias calculations

For the calculation of the bias itself we again use the root of the mean of squares of all biases. In the example shown we have 6 PT results. We calculate the relative bias of these values and then the RMSbias- Finally we combine the RMSbias with the uncertainty of the assigned value and we get the uncertainty component for the bias. 

The national allowable total analytical error, TEa is 6%. According to the European specifications for inaccuracy, the respective allowable bias is maximally 4.2% [15, 16], Table 2 shows the relative biases calculated from the PT results according to the Marchandise equa-... 

The following is an example of a mathematical/statistical calculation of a calibration curve to test for true slope, residual standard deviation, confidence interval and correlation coefficient of a curve for a fixed or relative bias. A fixed bias means that all measurements are exhibiting an error of constant value. A relative bias means that the systematic error is proportional to the concentration being measured i.e. a constant proportional increase with increasing concentration. 

Results. The following calculations are examples to determine whether a fixed or relative bias is found in a calibration curve and in an attempt to separate the random variation from any systematic variations the following lines were calculated ... 

The equation for the best fit straight line from these calculated values is y = —0.028 + 1.0114x. This equation suggests that a constant error of —0.028 is evident regardless of the true concentration and this is a fixed bias of —0.028 and a relative bias of 1.14%. Using these figures it is possible to calculate the bias at any particular concentration. 

The relative bias gives an error of —0.0223% for 0.5 ppm vanadium and 0.086% for 10.0 ppm vanadium metal and this shows that the relative bias exerts a greater influence on the determination than does the fixed bias (see Table 3.7). The estimated error due to relative bias is calculated by taking differences between 1.0114 and 1.000 of the perfect line and correcting for each concentration is used to calculate each predicted concentration. Table 3.7 gives results obtained along with each residual. 

The above calculation states that the true slope lies between 0.9% and 1.4% which shows that a very small systematic increase is observed. The error at 0% is not included, and based on these calculations a small relative bias may exist. 

This line indicates a relative bias of 0.7% which compares well with the best fit line of 1.14% estimated by the best straight line through the centroid. To compare the differences it is necessary to calculate the residual for this line as determined in Table 3.9. 

Tmeness is a measure of the systematic error (<5M) of the calculated result introduced by the analytical method from its theoretical true/reference value. This is usually expressed as percent recovery or relative bias/error. The term accuracy is used to refer to bias or trueness in the pharmaceutical regulations as covered by ICH (and related national regulatory documents implementing ICH Q2A and Q2B). Outside the pharmaceutical industry, such as in those covered by the ISO [20,21] or NCCLS (food industry, chemical industry, etc.), the term accuracy is used to refer to total error, which is the aggregate of both the systematic error (trueness) and random error (precision). In addition, within the ICH Q2R (formerly, Q2A and Q2B) documents, two contradictory definitions of accuracy are given one refers to the difference between the calculated value (of an individual sample) and its true value... 

We are interested in using the BACK equation for hydrogen mixtures. Therefore we have determined equation constants for hydrogen, and these are included in Table I. PVT data (7) at temperatures of 111-2778 K and pressures up to 1020 atm are used in this determination. Neither vapor-pressure nor critical-point data are used to avoid complications owing to quantum effects. It is found necessary to adopt an unusual value of the constant C of 0.241. With this C value the calculated pressure shows a relative root-mean-squared deviation of 0.5% and a relative bias of less than 0.1%. 

Estimated values for the slope a and the intercept h are obtained by way of regression calculations as given in Section 6.5. The fixed bias (B)p is equal to h. and the relative bias (B)n is equal to o - I. The composite bias is given by... 

Relative Bias—Statistically significant relative biases betw n Procedures A and Procedure B were observed in the data from the cooperative program described in Note 9. These biases can be corrected by applying the appropriate correlation equation listed below, that calculates a dry vapor pressure equivalent value for Procedure A (DVPE, Procedure A), from values obtained by Procedure B ... 

Calculate a dry vapor pressure equivalent (DVPE) using the following equation. This corrects the instrument reading for the relative bias found in the 1991 interlaboratory cooperative test program (see Note 9) between the dry vapor pressure measured in accordance with Test Method D 4953, procedure A and this test method ... 

Be/of/ve Bids—-A statisticaOy significant relative bias was observed in the 1991 interiaboratory cooperative test program between the total pressure obtained using this test method and the dry vrqmr pressure obtained using Test Method D 4953, procedure A. This bias is corrected by the use of Eq. (1) (see 13.2), which calculates a DVPE value from the observed total pressure. 

The sample size in a real simulation is always finite, and usually relatively small. Thus, understanding the error behavior in the finite-size sampling region is critical for free energy calculations based on molecular simulation. Despite the importance of finite sampling bias, it has received little attention from the community of molecular simulators. Consequently, we would like to emphasize the importance of finite sampling bias (accuracy) in this chapter. 

For poly(methylene), an exclusion distance (hard sphere diameter) of 2.00 A was used to prevent overlap of methylene residues. The calculation reproduced the accepted theoretical and experimental characteristic ratios (mean square unperturbed end-to-end distance relative to that for a freely jointed gaussian chain with the same number of segments) of 5.9. This wps for zero angular bias and a trans/gauche energy separation of 2.09 kJ mol". ... 

First chemical test measurements have been conducted with the array chip. Figure 6.19 shows the results that have been obtained simultaneously from three microhotplates coated with different tin-dioxide-based materials at operation temperatures of 280 °C and 330 °C in humidified air (40% relative humidity at 22 °C). The first microhotplate (pHPl) is covered with a Pd-doped Sn02 layer (0.2wt% Pd), which is optimized for CO-detection, whereas the sensitive layer on microhotplate 3 contains 3 wt% Pd, which renders this material more responsive to CH4. The material on microhotplate 2 is pure tin oxide, which is known to be sensitive to NO2. Therefore, the electrodes on microhotplate 2 do not measure any significant response upon exposure to CO or methane. The digital register values can be converted to resistance values by taking into account the resistor bias currents [147,148]. The calculated baseline resistance of microhotplate 1 is approximately 47 kQ, that of hotplate 2 is 370 kQ and the material on hotplate 3 features a rather large resistance of nearly 1MQ. 

On the other hand, quantum chemical calculations, at least non-empirical quantum chemical calculations, do not distinguish between systems which are stable and which may be scrutinized experimentally, and those which are labile (reactive intermediates), or do not even correspond to energy minima (transition states). The generality of the underlying theory, and (hopefully) the lack of intentional bias in formulating practical models, ensures that structures, relative stabilities and other properties calculated for molecules for which experimental data are unavailable will be no poorer (and no better) than the same quantities obtained for stable molecules for which experimental data exist for comparison. 

The mode of injection in GC-based methods can affect the recoveries of diazinon. In a study of the determination of organophosphorus pesticides in milk and butterfat, it was found that the recoveries of diazinon from butterfat, calculated relative to organic solutions of standard compounds, were 125% and 84% for splitless and hot on-column injections, respectively (Emey et al. 1993). Recoveries from milk were not dependent on the mode of injection. It was concluded that the sample matrix served to increase diazinon transfer to the GC column by reducing thermal stress imposed on the analytes and by blocking active sites within the injector. Therefore, on-column injection should be used in order to prevent bias when organic solutions of standard compounds are used for quantitation if this is not possible, the matrix must be present at low concentrations or the calibration standards must be prepared in residue-free samples to avoid unknown bias. 

The results of these interlaboratory studies are reported in USEPA Method Validation Studies 14 through 24 (14). The data were reduced to four statistical relationships related to the overall study 1, multilaboratory mean recovery for each sample 2, accuracy expressed as relative error or bias 3, multilaboratory standard deviation of the spike recovery for each sample and 4, multilaboratory relative standard deviation. In addition, single-analyst standard deviation and relative standard deviation were calculated. 

Qualitative NBT ideas provide a straightforward way to think qualitatively about the likely magnitude of the intrinsic barrier for a reaction, or even better for the relative intrinsic barriers of two reactions being compared. If one requires more dimensions, then it will have a larger intrinsic barrier. In general then, the more dimensions there are to a reaction, the larger the intrinsic barrier thus, there is a bias against concerted reactions, but such reactions will be seen when they provide the way to avoid bad intermediates imposed by the stepwise alternatives. Thus, Concerted if necessary but not necessarily concerted. Quantitative NBT provides a convenient, and for most reactions computationally inexpensive, way to calculate rate constants (AG1). Since the predicted rate... 

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