Precision of an Analysis

Uncertainty expresses the range of possible values that a measurement or result might reasonably be expected to have. Note that this definition of uncertainty is not the same as that for precision. The precision of an analysis, whether reported as a range or a standard deviation, is calculated from experimental data and provides an estimation of indeterminate error affecting measurements. Uncertainty accounts for all errors, both determinate and indeterminate, that might affect our result. Although we always try to correct determinate errors, the correction itself is subject to random effects or indeterminate errors. 

Analysis of Duplicate Samples An effective method for determining the precision of an analysis is to analyze duplicate samples. In most cases the duplicate samples are taken from a single gross sample (also called a split sample), although in some cases the duplicates must be independently collected gross samples. The results from the duplicate samples, Xi and X2, are evaluated by determining the difference, d, or the relative difference, d) between the samples... 

Increases precision of an analysis (indirect or statistical control of variability). 

The precision of an analysis is often expressed as the relative standard deviation ( RSD) (Equation 3). 

The precision of an analysis is most conveniently defined in terms of percent relative standard deviation. The standard deviation is relatively easily calculated following a series of discrete measurements either of absorbance or of concentration. The relative standard deviation is then defined as the standard deviation expressed as a percentage of the mean of the data used to calculate the standard deviation. 

The precision of an analysis is limited by counting statistics which in turn depend on the operating conditions (counting time, probe current and voltage), the element analysed and its matrix (atomic number, line used for analysis). For light elements (boron, carbon, oxygen) there are additional uncertainties regarding the value of the correction parameters (in particular absorption coefficients). 

There are several steps that can be taken to ensure accuracy in analytical procedures. Most of these depend on minimizing or correcting errors that might occur in the measurement step. We should note, however, that the overall accuracy and precision of an analysis might be limited not by the measurement step but by factors such as sampling, sample preparation, and calibration, as discussed earlier in this chapter. 

The standard deviation is a measure for the magnitude of the random error of an analysis, which depends on the method and sample composition. The relative random error s describes the precision of an analysis, which increases with decreasing relative random error ... 

Since radioactive decay follows Poisson statistics, a lower limit to the precision of an analysis can be obtained by a single measurement. In practice, counting statistics generally is the limiting uncertainty, since chi-squared tests often show that the single-measurement precision is an excellent predictor of sample-to-sample repeatability. 

More often than not, the accuracy and precision of an analysis is limited by the sampling rather than the measurement step. The overall variance of an analysis is the sum of the sampling variance and the variance of the remaining analytical operations, that is. 

The relationship between p, , and K for different ds is shown on Figure 1. p-Values are on a percentage scale, giving a water analyst direct recovery data for 1 1 solvent water ratios with equilibrated solvents. The p-value for unequilibrated systems is easily translated to the theoretical amount extracted, , for any solvent water ratio again on a percentage basis. The acciuracy and precision of an analysis is expressed on a percentage basis. Using the distribution ratio K precludes this last use. 

The precision of an analysis at or near the detection limit is usually poor compared with the precision at higher concentrations. This makes the uncertainty in the detection limit and in concentrations slightly above the detection limit also high. For this reason, many regulatory agencies define another limit, the limit of quantitation (LOQ), which is higher than the LOD and should have better precision. 

An internal standard is a known amount of a nonanalyte element or compound that is added to all samples, blanks, and standard solutions. Calibration with internal standardization is a technique that uses the signal from the internal standard element or compound to correct for interferences in an analysis. Calibration with internal standardization improves the accuracy and precision of an analysis by compensating for several sources of error. 

The precision of an analysis is often expressed in terms of the relative standard deviation (in percent, %RSD) or the coefficient of variation (COV). These values are calculated from the standard deviation, s, and mean, x, of the data set ... 

I very anq cal measurement i rnade upuf t turn components. One eompon die sig - /> t nol, carries informatian about.j analyte that is of interest Mthe scientist The Siond, ccdlek-noise, is made up ofextrcuieSas atformc on that is unwanted because it degrades the accuracy and precision of an analysis and also ff ces a lower limit on the amount of analyte that can be detected. In this chapter we ddicribe sc ve of the common sources of noise and how dtpir effects can be minimized... 

Indicator variables can easily be added to a calibration if one has reason to question the influence of one or more controllable factors on the accuracy or precision of an analysis. A factor can be designated absent or present with assigned values of 0 or 1, or additional indicator variables can be used to designate more than two possibilities. The evaluation of the statistics produced by incorporating indicator variables provides quantitative evidence of the effect that one or more factors may have on a given analytical procedure or process. Thus, this can be a route to... 

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