Appendix G: Common Sources and Values of Uncertainty

The following tables summarise some typical examples of uncertainty components. The tables give:

  • The particular measurand or experimental procedure (determining mass, volume etc)
  • The main components and sources of uncertainty in each case
  • A suggested method of determining the uncertainty arising from each source.
  • An example of a typical case

The tables are intended only to summarise the examples and to indicate general methods of estimating uncertainties in analysis. They are not intended to be comprehensive, nor should the values given be used directly without independent justification. The values may, however, help in deciding whether a particular component is significant.

Determination Uncertainty Components Cause Method of determination Typical values
Example Value
Mass Balance calibration uncertainty Limited accuracy in calibration Stated on calibration certificate, converted to standard deviation 4-figure balance 0.5 mg
Linearity  
  1. experiment, with range of certified weights
  2. Manufacturer's specification
   ca. 0.5x last significant digit
Readability Limited resolution on display or scale From last significant digit   0.5x last significant digit/
Daily drift Various, including temperature Standard deviation of long term check weighings. Calculate as RSD if necessary.   ca. 0.5x last significant digit.
Run to run variation Various
  ca. 0.5x last significant digit.
Density effects

(conventional basis)Note 1

 Calibration weight/sample density mismatch causes a difference in the effect of atmospheric buoyancy Calculated from known or assumed densities and typical atmospheric conditions Steel, Nickel

Aluminium

Organic solids

Water

Hydrocarbons

 1 ppm

20 ppm

50-100 ppm

65 ppm

90 ppm
Density effects

(in vacuo basis)Note 1

 As above. Calculate atmospheric buoyancy effect and subtract buoyancy effect on calibration weight. 100 g water

10 g Nickel

 +0.1g (effect)

<1 mg (effect)
Volume (liquid) Calibration uncertainty Limited accuracy in calibration Stated on manufacturer's specification, converted to standard deviation.

For ASTM class A glassware of volume V, the limit is approximately V0.6/200

 10 ml (Grade A) 0.02 / = 0.01 ml*

* Assuming rectangular distribution
Temperature Temperature variation from the calibration temperature causes a difference in the volume at the standard temperature. T./(2) gives the relative standard deviation, where T is the possible temperature range and the coefficient of volume expansion of the liquid. is approximately 2 x10-4 K-1 for water and 1 x 10-3 K-1 for organic liquids. 100 ml water 0.03 ml for operating within 3°C of the stated operating temperature
Run to run variation Various Standard deviation of successive check deliveries (found by weighing) 25 ml pipette Replicate fill/weigh:

s = 0.0092 ml
Reference material concentration Purity Impurities reduce the amount of reference material present. Reactive impurities may interfere with the measurement. Stated on manufacturer's certificate. Reference certificates usually give unqualified limits; these should accordingly be treated as rectangular distributions and divided by .

Note: where the nature of the impurities is not stated, additional allowance or checks may need to be made to establish limits for interference etc.

 Reference potassium hydrogen phthalate certified as 99.9±0.1% 0.1/ = 0.06%
Concentration (certified) Certified uncertainty in reference material concentration. Stated on manufacturer's certificate. Reference certificates usually give unqualified limits; these should accordingly be treated as rectangular distributions and divided by . Cadmium acetate in 4% acetic acid. Certified as (1000±2) mg l-1. 2/ = 1.2 mg l-1 (0.0012 as RSD)*

*Assuming rectangular distribution
Concentration (made up from certified material) Combination of uncertainties in reference values and intermediate steps Combine values for prior steps as RSD throughout. Cadmium acetate after three dilutions from 1000 mg l-1 to 0.5 mg l-1

as RSD
Absorbance Instrument calibration

Note: this component relates to absorbance reading versus reference absorbance, not to the calibration of concentration against absorbance reading

 Limited accuracy in calibration. Stated on calibration certificate as limits, converted to standard deviation    
Run to run variation Various Standard deviation of replicate determinations, or QA performance. Mean of 7 absorbance readings with s=1.63 1.63/ = 0.62
Sampling Homogeneity Sub-sampling from inhomogeneous material will not generally represent the bulk exactly.

Note: random sampling will generally result in zero bias. It may be necessary to check that sampling is actually random.
  1. Standard deviation of separate sub-sample results (if the inhomo-geneity is large relative to analytical accuracy).
  2. Standard deviation estimated from known or assumed population parameters.
 Sampling from bread of assumed two-valued inhomogeneity

(See example a4)

 For 15 portions from 72 contaminated and 360 uncontaminated bulk portions: RSD = 0.58
Extractrion recovery Mean recovery Extraction is rarely complete and may add or include interferents. Recovery calculated as percentage recovery from comparable reference material or representative spiking. Uncertainty obtained from standard deviation of mean of recovery experiments.

Note: recovery may also be calculated directly from previously measured partition coefficients.

 Recovery of pesticide from bread; 42 experiments, mean 90%, s=28%

(See example a4)

 28/= 4.3% (0.048 as RSD)
Run to run variation in recovery Various Standard deviation of replicate experiments. Recovery of pesticides from bread from paired replicate data. (See example a4) 0.31 as RSD.

Note: For fundamental constants or SI unit definitions, mass determinations by weighing are usually corrected to the weight in vacuum. For almost all other practical situations, weight is quoted on a conventional basis as defined by OIML [h.18]. The convention is to quote weights at an air density of 1.2 kg m-3 and a sample density of 8000 kg m-3 . The convention corresponds to weighing steel at normal sea level atmospheric conditions. The important implication is that the correction to conventional mass is zero either when the sample density is 8000 kg m-3 or the air density is 1.2 kg m-3 . Since the air density is nearly always close to the latter value, the correction to conventional weight can normally be neglected. The standard uncertainty values given for density-related effects on a conventional weight basis in the table above are sufficient for preliminary estimates for weighing on a conventional basis without buoyancy correction at sea level.