created with mindgenius business 2005® 3. sampling (elo) “a defined procedure whereby a part of a...

Created with MindGenius Business 2005Created with MindGenius Business 2005®®

3. Sampling (ELO) “A defined procedure whereby a part of a substance, material or product is taken to provide for testing or calibration a representative sample of the whole. Sampling may also be required by the appropriate specification for which the substance, material or product is to be tested or calibrated.”

ie The sample(s) must be REFLECTIVE of the TRUE situationBackground Reading: Quality Assurance in Analytical Chemistry, Chapter 3For an example relevant to your analyses, see BS EN ISO 707:2008 Milk and milk products – Guidance on sampling


Sampling Strategies (1)Depend on: Types of parent material

Homogeneous or heterogeneous Static (stable and contained) or dynamic (cannot be resampled)

Concentration Trace (prone to heterogeneity and contamination) Principal component (% uncertainty much lower)

Packaging Bulk (eg a silo) Packaged (eg cornflakes) Items (eg tablets)

Results required Quantitative (how much) Qualitative or compliance (yes/no answer) – “acceptance

sampling”


Sampling Strategies (2) Criteria?

attributes (x% of items must conform) variables (a specified average and sd)

Selective sampling OK? (eg fruit but not stone)? Overall strategy determined by

purpose: Client requirements Statutory requirements (legal obligations) Trade definitions (contractual)


Types of Sampling

100% sampling (all items monitored) Probability sampling (statistical

chance of being representative) Judgement (guided by the reason for

analysis) Quota (stratified judgement sampling) Convenience (as and when available)

Non-probability sampling (selective)


Sample size and number

Must be specified as part of the method.

Sample Size Enough for method Enough to be reflective (esp for trace

analysis) Sample number

enough to reduce uncertainty (esp that from sampling) to acceptable levels


Sampling Uncertainty

Overall uncertainty in analysis is composed of: Measurement uncertainty (quantifiable using standards) Sample uncertainty which is caused by

Population uncertainty (real wobble in the system) Sampling uncertainty (due to the process of collection)

Sampling uncertainty must be reduced until: it does not obscure population uncertainty the resource required outweighs the risk of an incorrect result

More samples and smaller particles reduce sampling uncertainty

See also CH250:1 Causes of uncertainty


How many samples are needed?

Number of samples needed can be estimated by rearranging the equation for confidence intervals:

n is the number of samples t is Student’s t (routinely approximated to 2 for 95%

confidence) s is the standard deviation for the method (measured using

reference standards, and inter-laboratory trials) E is the size of the effect that must be measurable (in the

same units as s).

n

tsIntervalConfidence

2

E

tsn


Number of samples - worked eg

Cadmium concentrations in soil were measured at a brownfield site during preliminary surveying. The mean ± standard deviation were (16 ± 4) ppm.

a) Calculate the number of samples required to obtain a total uncertainty of 20%.

b) How many samples would be required to reduce this uncertainty to 10%?


Number of samples - Answer

Cadmium concentrations in soil were measured at a brownfield site during preliminary surveying. The mean ± standard deviation were (16 ± 4) ppm.

a) Calculate the number of samples required to obtain a total uncertainty of 20%. Between 6 and 7, assuming t=2

b) How many samples would be required to reduce this uncertainty to 10%? 25, assuming t=2

25

6.1

42

6.1

161.0

16%10)

25.6

2.3

42

2.3

162.0

16%20)

2

2

n

ppm

ofEb

n

ppm

ofEa


There are various statistical calculations based on a) the proportion of analyte present and b) the particle size to approximate sample mass needed. The simplest of these is as follows:

Where Ks is the sampling constant, m is the mass in g and %CV is the Coefficient of Variation (which must be calculated from measurements on several test portions).

How big should the sample be?

mCVK s2%

x

sCV

100%


How big should the sample be?

Once Ks is known the equation can be rearranged to calculate:a) The test portion mass (m) required to achieve a specified %CV

b) The likely %CV from a given test portion mass

m

KCV s%

2)(%CV

Km s

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