7.2 Calibration graphs
7.3 Blanks and Detection limit
7.4 Types of sample material
7.5 Validation of own procedures
7.6 Drafting an analytical procedure
7.7 Research plan
7.2.2 Construction and use
7.2.3 Error due to the regression line
7.2.4 Independent standards
7.2.5 Measuring a batch
* This is the so-called "unweighted" regression line. Because normally the standard deviation is not constant over the concentration range (it is usually least in the middle range), this difference in error should be taken into account. This would then yield a "weighted regression line". The calculation of this is more complicated and information about the standard deviation of the y-readings has to be obtained. The gain in precision is usually very limited, but sometimes the extra information about the error may be useful.
1. The standards are made in a solution with the same composition as the extractant used for the samples (with the same dilution factor) so that all measurements are done in the same matrix. This technique is often practised when analyzing many batches where the same standards are used for some time. In this way an incorrectly prepared extractant or matrix may be detected (in blank or control sample).2. The standards are made in the blank extract. A disadvantage of this technique is that for each batch the standards have to be pipetted. Therefore, this type of calibration is sometimes favoured when only one or few batches are analyzed or when the extractant is unstable. A seeming advantage is that the blank can be forced to zero. However, an incorrect extractant would then more easily go by undetected. The disadvantage of pipetting does not apply in case of automatic dispensing of reagents when equal volumes of different concentration are added (e.g. with flow-injection).
3. Less common, but useful in special cases is the so-called standard additions technique. This can be practised when a matrix mismatch between samples and standards needs to be avoided: the standards are prepared from actual samples. The general procedure is to take a number of aliquots of sample or extract, add different quantities of the analyte to each aliquot (spiking) and dilute to the final volume. One aliquot is used without the addition of the analyte (blank). Thus, a standard series is obtained.
Warning. Some instruments can be calibrated with only one or two standards. Linearity is then implied but may not necessarily be true. It is useful to check this with more standards.
|y = bx + a||(6.18; 7.1)|
a = intercept of the line with the y-axis
b = slope (tangent)
x1= concentrations of standards
¯x = mean of concentrations of standards
y1= instrument response to standards
¯y = mean of instrument responses to standards
|a = ¯y - b¯x||(6.21;7.4)|
|y = 0.626x + 0.037||(6.22; 7.5)|
- If the deviations are < 5% the curve can be accepted as linear.
- If a deviation > 5% then the range is decreased by dropping the highest concentration.
- Recalculate the calibration line by linear regression.
- Repeat this test procedure until the deviations < 5%.
|xf ± t.sx||(7.9)|
Note 1. Where the determination of the analyte is part of a procedure with several steps, the error in precision due to this reading is added to the errors of the other steps and as such included in the total precision error of the whole procedure. The latter is the most useful practical estimate of confidence when reporting results. As discussed in Section 6.3.4 a convenient way to do this is by using Equations (6.8) or (6.9) with the mean and standard deviation obtained from several replicate determinations (n> 10) carried out on control samples or, if available, taken from the control charts (see 8.3.2: Control Chart of the Mean). Most generally, the 95% confidence for single values x of test samples is expressed by Equation (6.10):
where s is the standard deviation of the mentioned large number of replicate determinations.Note 2. The confidence interval of ± 0.08 mg/L in the present example is clearly not satisfactory and calls for inspection of the procedure. Particularly the blank seems to be (much) too high. This illustrates the usefulness of plotting the graph and calculating the parameters. Other traps to catch this error are the Control Chart of the Blank and, of course, the technician's experience.
After calibration, at fixed places or intervals (after every 10, 15, 20, or more, test samples) a standard is measured. For this, often a standard near the middle of the working range is used (continuing calibration standard). When the drift is within acceptable limits, the measurement is continued. If the drift is unacceptable, the instrument is recalibrated ("resloped") and the previous interval of samples remeasured before continuing with the next interval. The extent of the "acceptable" drift depends on the kind of analysis but in soil and plant analysis usually does not exceed 5%. This procedure is very suitable for manual operation of measurements. When automatic sample changers are used, various options for recalibration and repeating intervals or whole batches are possible.
Here, too, standards are measured at intervals, usually together with a blank ("drift and wash") and possible changes are processed by the computer software which converts the past readings of the batch to the original calibration. Only in case of serious mishap are batches or intervals repeated. A disadvantage of this procedure is that drift is taken to be linear whereas this may not be so. Autoanalyzers, ICP and AAS with automatic sample changers often employ variants of this type of procedure.
- a blank for the whole method or system and
- a blank for analytical subprocedures (measurements) as part of the whole procedure or system.
1. In many analyses sample results are calculated by subtracting blank readings from sample readings.2. Blank readings can be excellent monitors in quality control of reagents, analytical processes, and proficiency.
3. They can be used to estimate several types of method detection limits.
Note: In analytical chemistry, "lower limit of detection" is often confused with "sensitivity" (see 7.5.3).
|LLD, MDL = 3 × sbl||(7.11)|
|LLQ = 2 × LLD = 6 × sbl||(7.12)|
|LLQ = 10 × sbl||(7.13)|
Note: Noise is defined as the 'difference between the maximum and minimum values of the signal in the absence of the analyte measured during two minutes' (ox otherwise according to instrument instruction). The noise of several instrumental measurements can be displayed by using a recorder (e.g. FES, AAS, ICP, IR, GC, HPLC, XRFS). Although this is not often used to actually determine the detection limit, it is used to determine the signal-to-noise ratio (a validation parameter not discussed here) and is particularly useful to monitor noise in case of trouble shooting (e.g. suspected power fluctuations).
Note that if one would use only 0.5 g of sample (e.g. because of a high N content) the MDL as a relative figure is doubled!
Note 1. There are no strict rules for reporting figures below the LLD or LLQ. Most important is that data can be correctly interpreted and used. For this reason uncertainties (confidence limits) and detection limits should be known and reported to clients or users (if only upon request).The advantage of using the " <" sign for values below the LLD or LLQ is that the value 0 (zero) and negative values can be avoided as they are usually either impossible or improbable. A disadvantage of the " <" sign is that it is a non-numerical character and not suitable in spreadsheet programs for further calculation and manipulation. In such cases the actually found value will be required, but then the inherent confidence restrictions should be known to the user.
Note 2. Because a normal distribution of data is assumed it can statistically be expected that zero and negative values for analytical results occur when blank values are subtracted from test values equal to or lower than the blank. Clearly, only in few cases are negative values possible (e.g. for adsorption) but for concentrations such values should normally not be reported. Exceptions to this rule are studies involving surveys of attributes or effects. Then it might be necessary to report the actually obtained low results as otherwise the mean of the survey would be biased.
7.4.1 Certified reference material (CRM)
7.4.2 Reference material (RM)
7.4.3 Control sample
7.4.4 Test sample
7.4.5 Spiked sample
7.4.6 Blind sample
7.4.7 Sequence-control sample
7.5.1 Trueness (accuracy), bias
7.5.4 Working range
7.5.5 Selectivity and specificity
7.5.7 Ruggedness, robustness
7.5.10 Validation report
1. Validation of standard procedures. The validation of new or existing methods or procedures intended to be used in many laboratories, including procedures (to be) accepted by national or international standardization organizations.2. Validation of own procedures. The in-house validation of methods or procedures by individual user-laboratories.
- Trueness (accuracy), Bias
- Specificity and selectivity
- Working range (including MDL)
- Ruggedness or robustness
¯x = mean of test results obtained for reference sample
m = "true" value given for reference sample
|bias = ¯x - m||(7.15)|
220.127.116.11 Within-laboratory reproducibility
¯x = mean of test results obtained for reference sample
s = standard deviation of x
|R = 2.8 × sR||(7.18)|
|r = 2.8 × sr||(7.19)|
|RL = 2.8 × sL||(7.20)|
si, = the standard deviation of each pair of duplicates
k = number of pairs of duplicates
di = difference between duplicates within each pair
|RL = 1.6 × r||(7.22)|
|RL = 2.8 × scc||(7.23)|
Note: Naturally, instead or reporting the derived validation parameters for precision R, r, or RL, one may prefer to report their primary measure: the standard deviation concerned.
- Prepare a standard solution of the analyte in the relevant matrix (e.g. extractant) at a concentration beyond the highest expected concentration.- Measure this solution and determine the instrument response.
- Dilute this standard solution 10× with the matrix solution and measure again.
- Repeat dilution and measuring until the instrument gives no response.
- Plot the response vs. the concentration.
- Estimate the useful part of the response graph.
(If the dilution steps are too large to obtain a reliable graph, they need to be reduced, e.g. 5×).
¯xs = mean result of spiked samples
¯x = mean result of unspiked samples
¯xadd = amount of added analyte
A: With (+) and without (-) addition of 125 mg CaCO3 to the sample (corresponding with 5% CaCO3 content)
B: Concentration of saturation solution: 1 M (+) and 0.5 M (-) NH4OAc
C: Extraction time: 4 hours (-) and 8 hours (+)
D: Admixture of sea-sand (or celite): with (+) and without (-) 1 teaspoon of sand
E: Washing procedure: 2× (-) or 3×(+) with ethanol 80%
F: Concentration of washing ethanol: 70% (-) or 80% (+)
G: Purity of NH4OAc: technical grade (-) and analytical grade (+)
S YA+ = sum of results Yi, where factor A has + sign (i.e. Y1, + Y2 + Y3 + Y4; n=4)
S YA- = sum of results Yi, where factor A has - sign (i.e. Y5 + Y6 + Y7+ Y8; n=4)
1. With a t-test (6.4.3) using in principle the table with "two-sided" critical t values (App. 1, n=4). When clearly an effect in one direction is to be expected, the one-sided test is applicable.2. By checking if the effect exceeds the precision of the original procedure (i.e. if the effect exceeds the noise of the procedure). Most realistic and practical in this case would be to use scc, the within-laboratory standard deviation taken from a control chart (see Sections 18.104.22.168 and 8.3.2). Now, the standard deviation of the mean of four measurements can be taken as (see 6.3.4), and the standard deviation of the difference between two such means (i.e. the standard deviation of the effect calculated with Eq. 7.26) as . The effect of a factor can be considered significant if it exceeds 2× the standard deviation of the procedure, i.e..
|Effect >1.4 × scc||(7.27)|
Note. Obviously, when this standard deviation is not available such as in the case of a new method, then an other type of precision has to be used, preferably the within-laboratory reproducibility (see 7.5.2).
- Parameters to be validated
- Description of the procedures (with reference to relevant SOPs)
1. Weigh 5.0 g of sample into a 250 ml bottle.
2. Add 100 ml of extracting solution and close bottle.
3. Shake overnight.
4. Etc., etc.
- Descriptive title, purpose, and identification details Study director and further personnel Sponsor or client- Work plan with starting date and duration Materials and methods to be used Study protocol and SOPs (including statistical treatments of data)
- Protocols for interim reporting and inspection Way of reporting and filing of results Authorization by the management (i.e. signature)
- A work plan or subroutines can often be clarified by means of a flow diagram. Some of the most used symbols in flow diagrams for procedures in general, including analytical procedures, are given in Figure 7-3. An example of a flow sheet for a research plan is given in Fig 7-4.
VAL 09-2 - Validation of CEC determination with NH4OAc
METH 006 - Determination of nitrogen in soil with micro-Kjeldahl
STANDARD OPERATING PROCEDURE
Page; 1 # 2
|No.: VAL 09-2||Version: 1||Date: 96-09-19|
|Title: Validation of CEC determination with NH4OAc (pH 7)||File:|
|A:||With (+) and without (-) addition of 125 mg CaCO3 (corresponding with 5% CaCO3 content)|
|B:||Concentration of saturating solution: 1 M (+) and 0.5 M (-) NH4OAc|
|C:||Extraction time: 4 hours (-) and 8 hours (+)|
|D:||Admixture of seasand (or celite): with (+) and without (-) 1 teaspoon of sand|
|E:||Washing procedure: 2× (-) or 3× (+) with ethanol 80%|
|F:||Concentration of ethanol for washing free of salt: 70% (-) or 80% (+)|
|G:||Parity of NH4OAc: technical grade (-) and analytical grade (+)|
METHOD VALIDATION FORM
Page: 1 # 1
|No.: VAL RES 09-2||Version: 1||Date: 96-11-23|
|Title: Validation data CEC-NH4OAc (METH 09-2)||File:|
|2.1 Bias (Accuracy):||Result of calculation -with Eq. (7.14) or (7.16) of Guidelines.|
|Repeatability:||Result of calculation with Eq. (7.17) or (7.19).|
|Within-lab reproducibility:||Result of calculation with Eq. (7.23) (if Control Charts are available).|
|2.3 Working range:||Result of calculation as examplified by Table 7-1 in Section 7.3.2 of Guidelines.|
|2.4 Ruggedness:||Results of calculations with Eq. (7.26) or (7.29),|
|2.5 Interferences:||In this case mainly drawn from Ruggedness test|
|2.6 Practicability:||Special equipment necessary: mechanical extractor substantial amounts of ethanol required washing procedures not always complete, particularly in high-clay samples, requiring thorough check.|
|2.7 General observations:|
|QA Officer (sign.):||Date of Expiry:|
|QA Officer (sign.):||Date of Expiry:|
METHOD VALIDATION FORM
Page: 1 # 1
|No.: METH 006||Version: 2||Date: 96-03-01|
|Title: Determination of nitrogen in soil with micro-Kjeldahl||File:|
ISO 3696 Water for analytical laboratory use. Specification and test methods,
ISO 11464 Soil quality Pretreatment of samples for physico-chemical analysis.
|F 001||Administration of SOPs|
|APP 066||Operation of Kjeltec 1009 digester|
|APP 067||Operation of ammonia distillation unit|
|APP 072||Operation of Autoburette ABU 13 and Titrator TTT 60 (facultative)|
|RF 008||Reagent Book|
|METH 002||Moisture content determination|
4.1 Digester (Kjeldahl digestion tubes in heating block)
4.2 Steam-distillation unit (Fitted to accept digestion tubes)
4.3 Burette 25 ml
5.1 Sulphuric acid - selenium digestion mixture. Dissolve 3.5 g selenium powder in 1 L concentrated (96%, density 1.84 g/ml) sulphuric acid by mixing and heating at approx. 350°C. on a hot plate. The dark colour of the suspension turns into clear light-yellow. When this is reached, continue heating for 2 hour5.2 Hydrogen peroxide, 30%.
5.3 Sodium hydroxide solution, 38%. Dissolve 1,90 kg NaOH pellets in 2 L water in a heavy-walled 5 L flask. Cool the solution with the flask stoppered to prevent absorption of atmospheric CO2. Make up the volume to 5 L with freshly boiled and cooled deionized water. Mix well.
5.4 Mixed indicator solution. Dissolve 0.13 g methyl red and 0.20 g bromocresol green in 200 ml ethanol.
5.5 Boric acid-indicator solution, 1%. Dissolve 10 g H3BO3 in 900 ml hot water, cool and add 20 ml mixed indicator solution. Make to 1 L with water and mix thoroughly.
5.6 Hydrochloric acid, 0.010 M standard. Dilute standard analytical concentrate ampoule according to instruction.
|QA Officer (sign.):||Date of Expiry:|
1. Weigh 1 g of sample (accuracy 0.01 g) into a digestion tube. Of soils, rich in organic matter (>10%), 0.5 g is weighed in (see Remark 1). In each batch, include two blanks and a control sample.2. Add 2.5 ml digestion mixture.
3. Add successively 3 aliquots of 1 ml hydrogen peroxide. The next aliquot can be added when frothing has subsided. If frothing is excessive, cool the tube in water.
Note:. In Steps 2 and 3 use a measuring pipette with balloon or a dispensing pipette,
4. Place the tubes on the heater and heat for about 1 hour at moderate temperature (200°C).
5. Turn up the temperature to approx. 330°C (just below boiling temp.) and continue heating until mixture is transparent (this should take about two hours).
6. Remove tubes from heater, allow to cool and add approx., 10 ml water with a wash bottle while swirling.
1. Add 20 ml boric acid-indicator solution with measuring cylinder to a 250 ml beaker and place beaker on stand beneath the condenser tip.2. Add 20 ml NaOH 38% with measuring cylinder to digestion tube and distil for about 7 minutes during which approx. 75 ml distillate is produced.
Note: the distillation time and amount of distillate may need to be increased for complete distillation (see Remark 2).
3. Remove beaker from distiller, rinse condenser tip, and titrate distillate with 0.01 M HCl until colour changes from green to pink.
Note: When using automatic titrator: set end-point pH at 4.60.
1. The described procedure is suitable for soil samples with a nitrogen content of up to 10 mg N. This corresponds with a carbon content of roughly 10% C. Of soils with higher contents, less sample material is weighed in. Sample sizes of less than 250 mg should not be used because of sample bias.2. The capacity of the procedure with respect to the amount of N that can be determined depends to a large extent on the efficiency of the distillation assembly. This efficiency can be checked, for instance, with a series of increasing amounts of (NH4)2SO4 or NH4Cl containing 0-50 mg N.
a = ml HCl required for titration of sample
b = ml HCl required for titration of blank
s = air-dry sample weight in gram
M = molarity of HCl
1.4 = 14 × 10-3 × 100% (14 = atomic weight of nitrogen)
mcf = moisture correction factor
|9.1 Bias:||-3.1% rel. (sample ISE 921, ¯x=2.80 g/kg N, n=5)|
|9.2 Within-lab reproducibility:||RL = 2.8×scc = 2,5% rel. (sample LABEX 38,¯x =2.59 g/kg N, n=30)|
|9.3 Method Detection Limit:||0.014 mg N or 0.0014% N|
- the result(s) of the determination with identification of the corresponding sample(s);
- a reference to this SOP (if requested a brief outline such as given under clause 3: Principle);
- possible peculiarities observed during the test;
- all operations not mentioned in the SOP that can have affected the results.
Hesse, P.R. (1971) A textbook of soil chemical analysis. John Murray, London.Bremner, J.M. and C.S. Mulvaney (1982) Nitrogen Total. In: Page, A.L., R.H. Miller & D.R. Keeney (eds.) Methods of soil analysis. Part 2. Chemical and microbiological properties, 2nd ed. Agronomy Series 9 ASA, SSSA, Madison. ISO 11261 Soil quality - Determination of total nitrogen - Modified Kjeldahl method.