Uncertainty standard addition

Furthermore, there is the problem that the signal level to whieh one extrapolates need not necessarily be y = 0 if there is any interference by a matrix component, one would have to extrapolate to a level y > 0. This uncertainty can only be cleared if the standard addition line perfectly coincides with the calibration line obtained for the pure analyte in absence of the matrix, i.e. same slope and 100% recovery, see also Figure 3.2. This problem is extensively treated in Refs. 97-101. A modification is presented in Ref. 102. 

Normally the population standard deviation a is not known, and has to be estimated from a sample standard deviation s. This will add an additional uncertainty and therefore will enlarge the confidence interval. This is reflected by using the Student-t-distribution instead of the normal distribution. The t value in the formula can be found in tables for the required confidence limit and n-1 degrees of freedom. 

Recovery tests, for example the recovery of a standard addition to a sample in the validation process, can be used to estimate the systematic error. In this way, validation data can provide a valuable input to the estimation ofthe uncertainty. 

The standard addition method of calibration (see Chapter 1) is often used to combat the uncertainties of varying interference effects in electrothermal atomization. However, care should be taken with this approach, as errors from spurious blanks and background may go undetected. It must also be emphasized that the technique of standard additions does not correct for all types of interference. 

IDMS is based on measurements of masses and isotope ratios only. Some important advantages, compared with other calibration strategies, such as external calibration and standard additions, are that instrumental instabilities such as signal drift and matrix effects will have no influence in the final concentration in the sample, high accuracy and small measurement uncertainties are enabled, possible loss of substance of the isotope-diluted sample will have no influence on the final result and there is no need to resort to an external instrumental calibration or standard additions to the sample. 

Blrt Standard addition. Selenium from 0.108 g of Brazil nuts was converted into the fluorescent products in Reaction 18-15. which was extracted into 10.0 mL of cyclohexane. Then 2.00 mL of the cyclohexane solution was placed in a cuvet for fluorescence measurement. Standard additions of fluorescent product containing 1.40 rg Se/mL are given in the table below. Construct a standard addition graph like Figure 5-6 to find the concentration of Se in the 2.00-mL unknown solution. Find the wt% of Se in the nuts and its uncertainty and 95% confidence interval. 

A. Li was determined by atomic emission with the method of standard addition. Use a graph similar to Figure 5-6 to find the concentration of Li and its uncertainty in pure unknown. The Li standard contained 1.62 pg Li/mL. 

Standard addition. To measure Ca in breakfast cereal, 0.521 6 g of crushed Cheerios was ashed in a crucible at 600°C in air for 2 h.22 The residue was dissolved in 6 M HC1, quantitatively transferred to a volumetric flask, and diluted to 100.0 mL. Then 5.00-mL aliquots were transferred to 50-mL volumetric flasks. Each was treated with standard Ca2+ (containing 20.0 pg/mL), diluted to volume with H20, and analyzed by flame atomic absorption. Construct a standard addition graph and use the method of least squares to find the x-intercept and its uncertainty. Find wt% Ca in Cheerios and its uncertainty. 

The risk interpretation of biomonitoring results will tend to have additional uncertainties. That is because, in addition to the standard uncertainties encountered in risk assessment, there is the uncertainty of extrapolating from a blood or urinary concentration to an external dose. There will be variability both in the timing between sample draw and most recent exposure and in the relationship between blood concentration and dose. Those kinds of variability are compounded by uncertainty in the ability of a PK calculation or model to convert biomarker to dose accurately. For example, reliance on urinary biomarker results expressed per gram of urinary creatinine leads to an uncertain calculation of total chemical excretion per day because of the considerable variability in creatinine clearance per day. That complicates an otherwise simple approach to estimating dose. Furthermore, the conversion requires knowledge of fractional excretion via various pathways, which may not be present for a large sample of humans. The uncertainties created by these factors can be bounded via sensitivity and Monte... 

Figure 3.6. (a) Example of a well-proportioned standard addition curve, as well as of the possible difference between a traditional standard curve and a standard addition curve. (b) Example of a disproportional standard addition curve, which may result in a large uncertainty. 

In practice, the value of k is never obtained as such, because the meter is adjusted so that the standard reads the correct value for its pX, the scale being Nernstian. As k contains in addition to the reference electrode potentials, a liquid-junction potential and an asymmetry potential, frequent standardization of the system is necessary. The uncertainty in the value of the junction potential, even when a salt bridge is used, is of the order of 0.5 mV. Consequently the absolute uncertainty in the measurement of pX is always at least 0.001/(0.059// ) or 0.02 if n = I, i.e. a relative precision of about 2% at best. For the most precise work a standard addition technique (p. 32) and close temperature control are desirable. All measurements should be made at constant ionic strength because of its effect on activities. Likewise,... 

Since RDDR values are unavailable for dogs (EPA 1994), ATSDR used a default uncertainty factor of 3 for extrapolating from animals to humans as it incorporates the differences in physiology between dogs and humans. A default factor of 3 was used rather than the standard factor of 10 because of similarities in renal physiology between the two species, i.e., both acidify the urine by active transport of bicarbonate. Additional uncertainty factors of 3 for use of a minimal 1 O AFT. and 10 for human intraspecies variability are used to calculate the intermediate-duration intermediate MRL. 

Values are means standard errors for 2 years of data. Numbers of observations range from 15 (HNO3) to 26 (particles) to 128 (precipitation) to 730(802). In comparing these deposition rates it must be recalled that any such estimates are subject to considerable uncertainty. The standard errors given provide only a measure of uncertainty in the calculated sample means relative to the population means hence additional uncertainties in analytical results, hydrologic measurements, scaling factors, and deposition velocities must be included. The overall uncertainty for wet deposition fluxes is about 20% and that for dry deposition fluxes is approximately 50% for SOj", Ca ", K", and approximately 75% for NOj" and... 

Refractive index and specific refractive index increments - (k = dn/dc) of polymers in solution have been studied extensively in connection with light scattering measurements and size exclusion chromatography applications to polymer characterization for which refractometers are used as standard concentration detectors. Contrary to the observations made in the infrared region (12), refractive index increments have been shown to be a function of the molecular weight of the polymers (2) and, in some cases, of the copolymer composition (17). Therefore, the assumptions of linearity and additivity (Eq. 1 to 4) have to be verified for each particular polymer system. In the case of styrene/acrylonitrile copolymers, there is an additional uncertainty due to the... 

Where the method scope covers a range of sample matrices and/or analyte concentrations, an additional uncertainty term Rs is required to take account of differences in the recovery of a particular sample type, compared to the material used to estimate Rm. This can be evaluated by analysing a representative range of spiked samples, covering typical matrices and analyte concentrations, in replicate. The mean recovery for each sample type is calculated. Rs is normally assumed to be equal to 1. However, there will be an uncertainty associated with this assumption, which appears in the spread of mean recoveries observed for the different spiked samples. The uncertainty, u(Rs), is therefore taken as the standard deviation of the mean recoveries for each sample type. 

The nature of the samples means that a CRM to estabhsh accuracy in a proper metrological way may not exist. Usually, recovery studies will be done with spiked samples. There is concern about the purity of standards used here, and also about the spedation of redox active spedes such as transition metal elements. Standard addition is a method that extrapolates beyond the cahbration range, and is therefore prone to high uncertainty. The low levels of analyte makes it difficult to estabhsh a true concentration. 

Having estimated the uncertainty as outlined, additional uncertainty sources should be considered. If the comparison was undertaken within a short time period, one might consider adding an additional long-term imprecision component as a variance component to the standard uncertainty expression. 

A measured value is complete only when it is accompanied by a statement of its uncertainty and is required in order to decide whether or not the result is adequate for its intended purpose. The uncertainty value must be suitably small to show that the reported results can be accepted with confidence and to ascertain whether or not it is consistent with similar results. There is an uncertainty in the concentration of the calibration samples used both in synthetic calibration samples and calibrations of standard addition. Weighing and volumes, which are a must in most analytical methods, must include weighing errors volumes must include volume errors to take into account uncertainties associated with these steps of the analysis. These and others must also be included in the overall calculation of the analytical error. 

Spreadsheet Summary In Chapter 12 ot Applications of Microsoft Excel in Analytical Chemistry, we investigate the multiple standard additions method for determining solution concentration. A least-squares analysis of the data leads to the determination of the concentration of the analyte as well as the uncertainty of the measured concentration. 

Normally, there is also an uncertainty in the concentrations of the calibration samples used both in the case of calibration with synthetic calibration samples as well as in calibration by standard additions. In both cases these errors can also be included in the calculation of the analytical error [34]. 

When weighing an amount of sample M there is a weighing error additional uncertainty cry in the volume to be taken into account. The resulting relative standard deviation can be calculated as ... 

Also in the case of calibration by standard additions, the uncertainty in the amount added in the case of one standard addition can be taken into account. When... 

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