1st Nordplus Seminar

Geochemical mapping and monitoringof trace elements and organic pollution

Vilnius 2007-03-05

The role of metrology in the interpretation of analytical data

Kaj HeydornDepartment of Chemistry

Definition of the Measurand

“Quantity intended to be measured”

VIM 3 (2004)

Metrology -

the science of measurement

The measurand, e.g.

time, length, mass

The object, i.e.

the particular specimen being measured

Metrology in Chemistry - MiC Determination of something, e.g.

pH, TOC, alcohol, insulin, gold, C-14

In something, e.g.

an archaelogical specimen, blood, lake water, soil, the universe

Definition of the Measurand I The determinand, i.e.

the chemical species to be determined

The specified amount of material

to which the measurement should apply

Specification of measurand

1) Should the result refer to a particular, specified sample or to a larger system

2) Shall the sample be subjected to a special pretreatment before analysis

3) Should the result refer to the time of analysis or be valid for a specified period

Specification of measurand

4) Shall the analysis be carried out as a test according to a precisely specified method

5) Should the result be corrected for bias associated with the analytical method used for its determination

6) Must the result be traceable to the SI- units or other stated references

Unless the complete history of a sample is known with certainty, the analyst should not spend his time analyzing it.

Thiers 1957

Validity of a sample

Sample analysed

SYSTEM

The sampling process

primary samplingrepresentativity versus

quantity

secondary sampling uniformity and sample size

Primary sample

Secondary sample

Test sample

SYSTEM

Analytical measurementsUntil a measurement operation…. has attained a state of statistical control, it cannot be regarded in any logical sense as measuring anything at all.

C.E. Eisenhart

Uncertainty of measurement

Parameter that characterizes the dispersion of the values that are being attributed to a measurand

VIM 3Draft April 2004

Uncertainty

A result without a statement of uncertainty is useless - because

No conclusions can be made from it

Definition of the Measurand II A result without corresponding

definition of the measurandis worthless

An uncertainty without corresponding specification of the measurand is misleading

Uncertainty evaluation

Type A statistical analysis of actual observations

Type B any other method

Uncertainty components 1

Testing = method-based result

• Repeatabiliy

• Intermediary precision

• Reproducibility

Propagation of uncertaintyxixi xjxj xkxk

y

++

u(y)

y = f(xi, xj, xk, .)

pp((y|xy|xii, , xxjj, , xxkk))

Reporting analytical results

• Definition of the measurand• Reported value of the measurand • ± its expanded uncertainty• The coverage factor used

The result of a measurement shall include

Uncertainty

A result with an incorrect statement of uncertainty is dangerous - because

Wrong conclusions can be made from it

Verification HOW?

By comparing predicted and actual variability of results

T-statistic

kj

j

ni

i ij

jijj

yu

yT

1 12

2

)(

)(

Expectation ValueµjBy calculating the weighted mean value

ni

i i

ni

i i

i

yu

yu

y

12

12

)(

1)(̂

k

j kn1

Verification of uncertainty

m is the number of duplicate results

A chi-square distribution with m degrees of freedom

Example:

Fall-out in Denmark

Determination of environmental radioactivity

in Denmark Average amount of 137Cs in the top

5 cm of uncultivated soil

expressed in Bq/m2 at a specified time and for a selected area

Determination of environmental radioactivity

in Denmark Without regard to

soil compositionsoil densitytemperature and humidityvegetation

Ishikawa diagram for 137Cs measurements

Measurement Definition

Sampling

137Cs Bq/m2

Time

Area

Topsoil

Counting statistics

Geometry

Calibration

Representativity

Reproducibility

Location

Uncertainty components, uD

Type AVariation with depth

Type B Sampling areaTime

3.2 %/cm

2 %negligible

Uncertainty components, uM

Type ACounting statistics

+ Counting geometry

Type B Calibration

1-2 %5 %

1.1 %

Uncertainty components, uS

Type AReproducibility

+ Location

Type B Representativity

15 %49 %

good

137Cs in Danish soils autumn 1987 Results for 10 random

locationsCs-137 Uncertainty Counting SampleBq/m2 Bq/m2 SD % kg

1441 232 1 1,811844 297 1 1,711242 200 1 2,543320 535 1 2,821269 204 1 2,311942 313 1 2,101177 189 1 2,17959 154 2 2,54817 132 1 1,69960 155 2 2,90

137Cs in Danish soils autumn 1989 Results for 10 selected

locationsData for 1989 Decay cor rected 1987 Value of TBq/m2 Uncertainty Bq/m2 Uncertainty per d.f.1200 188 1377 222 0,3711800 281 1762 284 0,0091130 177 1187 191 0,0472100 328 3172 511 3,1181350 211 1212 195 0,2291720 269 1855 299 0,1141020 159 1125 181 0,188490 77 916 148 6,576560 88 781 126 2,074770 120 917 148 0,597

10 d.f.T = 13,323

p> 0,21

Conclusions

The Null Hypothesis could not be rejected

More measurements must be made, before any conclusions are drawn

Thank youfor your attention

Verifikation

Type A løbende analytisk kvalitetskontrol

Type Brepræsentative dobbeltprøver