Replicate analysis

Before a procedure can provide useful analytical information, it is necessary to demonstrate that it is capable of providing acceptable results. Validation is an evaluation of whether the precision and accuracy obtained by following the procedure are appropriate for the problem. In addition, validation ensures that the written procedure has sufficient detail so that different analysts or laboratories following the same procedure obtain comparable results. Ideally, validation uses a standard sample whose composition closely matches the samples for which the procedure was developed. The comparison of replicate analyses can be used to evaluate the procedure s precision and accuracy. Intralaboratory and interlaboratory differences in the procedure also can be evaluated. In the absence of appropriate standards, accuracy can be evaluated by comparing results obtained with a new method to those obtained using a method of known accuracy. Chapter 14 provides a more detailed discussion of validation techniques. 

If Sm is significantly greater than Sj, then we only need to collect and analyze a single sample. The number of replicate analyses, r, needed to minimize the error due to the method is given by an equation similar to equation 7.7... 

Unfortunately, the simple situations just described are often the exception. In many cases, both the sampling variance and method variance are significant, and both multiple samples and replicate analyses of each sample are required. The overall error in this circumstance is given by... 

As expected, since the relative method variance is better than the relative sampling variance, a sampling strategy that favors the collection of more samples and few replicate analyses gives the better relative error. 

When an analyst performs a single analysis on a sample, the difference between the experimentally determined value and the expected value is influenced by three sources of error random error, systematic errors inherent to the method, and systematic errors unique to the analyst. If enough replicate analyses are performed, a distribution of results can be plotted (Figure 14.16a). The width of this distribution is described by the standard deviation and can be used to determine the effect of random error on the analysis. The position of the distribution relative to the sample s true value, p, is determined both by systematic errors inherent to the method and those systematic errors unique to the analyst. For a single analyst there is no way to separate the total systematic error into its component parts. 

Partitioning of random error, systematic errors due to the analyst, and systematic error due to the method for (a) replicate analyses performed by a single analyst and (b) single determinations performed by several analysts. 

A newly proposed method is to be tested for its singleoperator characteristics. To be competitive with the standard method, the new method must have a relative standard deviation of less than 10%, with a bias of less than 10%. To test the method, an analyst performs ten replicate analyses on a standard sample known to contain 1.30 ppm of the analyte. The results for the ten trials are... 

Constructing a Precision Control Chart The most common measure of precision used in constructing a precision control chart is the range, R, between the largest and smallest results for a set of j replicate analyses on a sample. 

Replicate Analyses. Confidence in the test result is improved by reducing the measurement variabihty. This variabihty in repeat analyses is known as precision. One method to improve the precision of the measurement is to perform complete rephcate analyses of the same sample beginning with the sample preparation (26). This is appropriate when the sample is known to be representative of the material sampled. When this is not the case, multiple samples should be taken for analysis. 

Hence, on increasing the number of replicate determinations both the values of and s/yfn decrease with the result that the confidence interval is smaller. There is, however, often a limit to the number of replicate analyses that can be sensibly performed. A method for estimating the optimum number of replicate determinations is given in Section 4.15. 

Example 8. Ascertain the number of replicate analyses desirable (a) for the determination of approximately 2 per cent Cl" in a material if the standard deviation for determinations is 0.051, (b) for approximately 20 per cent Cl- if the standard deviation of determinations is 0.093. 

It must be stressed, however, that the whole object may be the analytical sample, e.g. a specimen of moon-rock. Ideally this sample would be analysed by non-destructive methods. Occasionally the bulk material may be homogeneous (some water samples) and then only one increment may be needed to determine the properties of the bulk. This increment should be of suitable size to provide samples for replicate analyses. 

In experiments with water-soluble inhibitors, the subsample was stirred under nitrogen during post-addition of an aqueous solution of the inhibitor followed by an aqueous sodium nitrite solution. Aliquots were weighed into 1-oz ointment jars, covered with nitrogen, sealed, and stored at 37 for later replicate analyses. Preparation of the positive control subsample was identical except that water was added in place of inhibitor. 

Figure 1.116. Lead isotopic variation in Japanese Neogene ores. The majority of data fall in a relatively narrow range which is no more than twice the experimental uncertainty indicated by the replicate analyses of NBS-SRM-981 standard (Sasaki et al., 1982).

An example of adequate sample homogenization is given in Table 4. The experiment was conducted with two replicate treated soil samples. Each replicate was analyzed in duplicate. Three different sample aliquots (2, 5 and 10 g) were used from each replicate. Analyses of controls and fortified samples were also conducted concurrently with treated samples to evaluate method performance (i.e., extraction recoveries). These results show that residue values are the same regardless of sample size. Thus, thorough homogenization of soil samples coupled with mgged analytical methodology provides for satisfactory residue analysis. 

Because of these complications, regardless of the very high within-run precision attainable via TIMS or ICP-MS, the true precision of the runs (as opposed to the internal or within run precision provided by the TIMS or ICP-MS operating software) can only be reliably established by replicate analyses of natural samples. One useful approach is to establish the external variance of a measurement technique by subtracting the internal variance from the total (= run-to-run) variance from replicate analyses, e.g.. 

The error correlation between two quantities can be determined empirically, from a number (N) of replicate analyses of pairs of the two quantities (say x and y), and evaluating the expression for the linear correlation (Rickmers and Todd 1967)... 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

Sakamoto [243] determined picomolar levels of cobalt in seawater by flow injection analysis with chemiluminescence detection. In this method flow injection analysis was used to automate the determination of cobalt in seawater by the cobalt-enhanced chemiluminescence oxidation of gallic acid in alkaline hydrogen peroxide. A preconcentration/separation step in the flow injection analysis manifold with an in-line column of immobilised 8-hydroxyquinoline was included to separate the cobalt from alkaline-earth ions. One sample analysis takes 8 min, including the 4-min sample load period. The detection limit is approximately 8 pM. The average standard deviation of replicate analyses at sea of 80 samples was 5%. The method was tested and inter calibrated on samples collected off the California coast. 

When the samples were returned to the laboratory the pH was adjusted to approximately pH 8 using concentrated ammonia (Ultrapure, G. Frederick Smith). Chelating cation exchange resin in the ammonia form (20 ml Chelex 100,100 - 200 mesh, Bio-Rad) was added to the samples and they were batch extracted on a shaker table for 36 hours. The resin was decanted into columns, and the manganese eluted using 2N nitric acid [129]. The eluant was then analysed by graphite furnace atomic absorption spectrophotometry. Replicate analyses of samples indicate a precision of about 5%. 

In order to evaluate the precision of this method, replicate analyses were carried out by Lee et al. [627] using the proposed procedure, for trace elements in a seawater sample taken from the Kwangyang Bay (Korea). The results showed satisfactory precision ranging from 0.2 xg/l for cadmium to 250 xg/l for iron. 

The precision of the method was tested by carrying out replicate analyses (10) on 150 ml aliquots of two seawater samples from the Irish Sea. Mean ( sd) arsenic concentrations of 2.63 0.05 and 2.49 0.05 pg/1 amounts of were found. The recovery of arsenic was checked by analysing 150 ml aliquots of arsenic-free seawater which had been spiked with known amounts of arsenic (V). The results of these experiments shows that there is a linear relationship between absorbance and arsenic concentration and that arsenic could be recovered from seawater with an average efficiency of 98.0% at levels of 1.3-6.6 pg/1. Analagous experiments in which arsenic (III) was used gave similar recoveries. 

Measurement bias is determined by comparing the mean of measurement results obtained for a reference material, using the method being validated, with the assigned property values for that reference material. The number of replicate analyses required (n) depends on the precision of the method (.s ) and the level of bias (8) that needs to be detected [12]. A useful approximation is shown in the following equation ... 

Table 4.7 Responses from ten replicate analyses at different concentration levels...

In a series of replicate analyses of a sample the following data (%) were obtained ... 

Preparation of a calibration curve has been described. From the fit of the least-squares line we can estimate the uncertainty of the results. Using similar equations we can determine the standard deviation of the calibration line (similar to the standard deviation of a group of replicate analyses) as... 

Figure 13.1 Illustration of the terms accuracy and precision in analytical chemistry. In each case, for a pair of hypothetical measured elements x and y, the cross shows the true value, the circles the results of three replicate analyses.

Ou et al. [42] used methanol-ultrasonic extraction followed by clean-up with aluminium oxide, and enrichment with a C-18 SPE column for the determination of LAS in plant tissues by HPLC. Both efficiency and accuracy of the overall method were high, with a mean recovery of 89% (84-93% for LAS concentrations ranging from 1 to 100 mg kg-1) and a repeatability of 3% relative standard deviation for six replicate analyses. With a 2 g sample for analysis, LAS levels of 0.5 mg kg-1 in plants could be detected with the proposed method. 

Six sets of results from five laboratories were obtained for the analyses of NPEO in three cartridges. All laboratories used MS for quantitative analysis, except laboratory 5, which used LC-FL. Laboratory 1 used an LC with an APCI interface laboratories 2 and 4 used LC-ESI-MS and laboratory 3 used FIA-MS analysis. All laboratories performed three independent replicate analyses, i.e. analysed three replicate cartridges of each type of spike. 

The results of replicate analyses of the same sample will usually show some variation about a mean value and if only one measurement is made, it will be an approximation of the true value. 

There is therefore a considerable advantage in making a limited number of replicate analyses rather than a single analysis but, in practice, it is necessary to balance the improved confidence that can be placed in the data against the increased time and effort involved. 

Thirty replicate analyses of the protein content of a sample ga e the following results. Calculate the standard deviation of the results. 

It may be possible to demonstrate a high degree of precision in a set of replicate analyses done at the same time and in such a situation the within batch imprecision would be said to be good. However, comparison of replicate samples analysed on different days or in different batches may show greater variation and the between batch imprecision would be said to be poor. In practice this may more closely reflect the validity of the analytical data than would the within batch imprecision. 

Accuracy is the closeness of the mean of a set of replicate analyses to the true value of the sample. In practice most methods fail to achieve complete accuracy and the inaccuracy of any method should be determined. It is often only possible to assess the accuracy of one method relative to another which, for one reason or another, is assumed to give a true mean value. This can be done by comparing the means of replicate analyses by the two methods using the f test. An example of such a comparison is given in Procedure 1.3 with the comment that only a limited number of replicates are used solely to simplify the calculation. 

Some authors use the word trueness instead of accuracy to describe the closeness of the mean of many replicate analyses to the true value. This allows the word accuracy to carry a more general meaning which relates to the accuracy or difference of a single result from the true value, as a conse-... 

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