ISO_8466-1_1990_PDF_version_(en)

ISO 8466-1

INTERNATIONAL STANDARD

First edition 1990-03-01

and evaluation Water quality - Calibration analytical methods and estimation of Performance characteristics Part 1: Statistical Qualith de l’ea des caractkes Partie 1: haha

evaluation rEtalonnage de Performance

tion s ta tistique

of the linear calibration et Evaluation de Ia fonction

des mhthodes

of

function

d’analyse et estimation

lin&aire d’h talonnage

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Reference number ISO 8466-1 : 1990 (EI

ISO 8466-1 : 1990 (EI

Contents

Page

Foreword

.. . Ill

............................................................

1

Scope ..............................................................

1

2

Definitions..

1

3

Symbols.........................................................~

4

Performance

5

........................................................ ..

3

........................................................

4.1

Choice of working

4.2

Calibration

4.3

Assessment

range ..........................................

and characteristics

of the method

........................

range ..........................................

5.2

Calibration

and characteristics

5.3

Evaluation

......................................................

Annex

A

Bibliography

of the method

.................................................

4

6

Example ............................................................ Choice of working

3

5

....................................................

5.1

2

........................

6 7 7 8

0 ISO 1990 All rights reserved. No patt of this publication may be reproduced or utilized in any form or by any means, electronie or mechanical, including photocopying and microfilm, without Permission in writing from the publisher. International Organization for Standardization Case postale 56 l CH-1211 Geneve 20 l Switzerland Printed in Switzerland Licensed to LAAM /MANUEL SOARES

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ISO 8466-1 : 1990 (E)

Foreword ISO (the International Organization for Standardization) is a worldwide federation of national Standards bodies (ISO member bedies). The work of preparing International Standards is normally carried out through ISO technical committees. Esch member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take patt in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Draft International Standards adopted by the technical committees are circulated to the member bodies for approval before their acceptance as International Standards by the ISO Council. They are approved in accordance with ISO procedures requiring at least 75 % approval by the member bodies voting. International Standard Water quaiity.

ISO 8466-1 was prepared

by Technical

Committee

ISO 8466 consists of the following Parts, under the general title Calibration and evaluation of analytical methods and estimation charac teris tics : -

Part 7: Statisticaf

evaluation

-

Part 2: Calibration

strategy

-

Part 3: Method

- Part 4: Estimation basis method. Annex

of Standard

of the linear calibration for non-linear

calibration

ISO/TC

147,

Water gua/ity of Performance

function functions

addition

of Limit of detection

and limit of determination

A of this part ISO 8466 is for information

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only.

of an analytical

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INTERNATIONAL

STANDARD

ISO 8466-1 : 1990 (E)

and evaluation of analytical Water quality - Calibration methods and estimation of Performance characteristics Part 1: Statistical 1

evaluation

of the linear calibration

Scope

This part of ISO 8466 describes the Steps to be taken in evaluating the statistical characteristics of the linear calibration function. lt is applicable to methods requiring a calibration. Further Parts of ttis lnternationa~ Standard will cover the determina$.i!! ok IGr%t of detection and FEmit of determination, the effect of Ln$erferences and other performante chara,cteristics

_

function

1

Originai

,

MeasUri!g

lt is intended especially for the evaluation of the pure analytical method and for the calculation of Performance characteristics of the calibration function.

Sample

1

;X~~nstructi;

1

measuring instructions

In Order to derive comparable analytical results and as a basis for analytical quality control the calibration and evaluation of analytical methods have to be performed uniformly.

1

Measur;

value

1

’

r-YG&q

calibrating and evaluating instructions

2

Definitions

For the purposes tions apply.

of this part of ISO 8466, the following

2.1

method:

analytical

of procedural, measuring, tions (see figure 1).

defini-

An analytical method is composed calibrating and evaluating instruc-

Figure 1 - The analytical

method

23

Whereas the procedural and measuring instructions depend on the method, and are therefore the Object of standardization of the respective method, the calibrating and evaluating instructions are valid for any analytical method requiring calibration.

2.2

calibrating instruction : Describes the approach to determine the calibration function from information values, yi, obtained by measuring given Standard concentrations, xi. The slope of the calibration function, b, as a measure of sensitivity of the analytical method and the Standard deviation of the which method, sXO, are figures of merit and characteristics result from the calibration experiment.

The Standard deviation, sXO, allows the comparison dent analytical methods.

of indepen-

evaluating instruction : A calculation guide for the computation of concentrations from the measured values by the use of the calibration function. Additionally, the confidence range permits an objective assessment of the imprecision of the analytical result[*J. 2.4

measured

values : The concentration-dependent

values (e.g. extinction)

of a measuring

initial

System.

NOTE - Information value and measured volume are synonymous.

25

residual Standard deviation, s : The residual Standard deviation describes the scatter of the information values about the calculated regression line. lt is a figure of merit, describing the precision of the calibration.

For the purpose of this Standard, the Standard deviation of the method means the Standard of deviation of the calibration proFor the user of the method, these characteristics present cedure. criteria for the internal laboratory quality control. Licensed to LAAM /MANUEL SOARES ISO Store order #:913756/Downloaded:2008-05-21 Single user licence only, copying and networking prohibited

1

ISO 8466-1 : 1990 (EI

Yi

Information value of the Standard concentration Xi calculated from the calibration function.

s2 i

Variante of the information analyses of Standard samples, centration Xi.

For the purpose of this Standard, the Standard deviation of the method means the Standard of deviation of the calibration procedure.

fi

Degrees of freedom for the calculation variance (f i = tli- 1).

2.7 coefficient

a

Calculated blank (Ordinate intercept bration straight line).

See also note to 2.5 and 2.6.

b

Sensitivity of the method (slope of the calibration line; coefficient of regression

x

Mean of the Standard concentrations resulting from the calibration experiment.

Y

Mean of the information values Yit resulting from the calibration experiment.

2.6 Standard deviation

of the method sXO: The ratio of the residual Standard deviation, s,,, to the sensitivity of the calibration function, b. lt is a figure of merit for the performance of the analytical method, and is valid within the working range (sec equation 13).

of Variation of the method, VXO: The ratio of the Standard deviation of the method sXOto the appertaining mean, F, which is the centre of the working range.

2.8 working

range (of an analytical method): The interval, being experimentally established and statistically proved by the calibration of the method, between the lowest and highest quantity or mass concentration. The lowest possible limit of a working range is the limit of detection of an analytical method.

2.9

homogeneity of variances: Homogeneity of variances of pooled data, such as those resulting from replicate analyses at different levels, is confirmed if these variances are not significantly correlated to their appertaining concentrations.

2.10

sensitivity

of the analytical

the calibration function of the complete clusive of all procedural Steps, within question.

The slope of analytical method, inthe working range in

measuring Sample (reaction Sample) : A Sample which tan be directly submitted to the measurement of the determinand. A measuring Sample is normally obtained by adding the required reagents to the analytical Sample. Obviously, measuring and analytical Sample are identical if no reagents have to be added to the analytical Sample.

Symbols

Xi

Concentration

i

Subscript

i= N

the

concentration

levels,

where

by linear

sY2

Residual Standard deviation linear regression calculation.

obtained

by non-

DS2

Differente

Y

Information

n

Number Sample.

P

Mean of information replicates.

x

Concentration sf the analytical Sample, calculated from the i nformation value Ym

2

Concentration of the analytical Sample, calculated from the mean of the information values 7.

of variances. value of an analysed of replicates

on the same analysed

values,

resulting

from

n

levels (for this part of tV;,

Concen tration of the Standard Sample at the lower level of the working range ( 1st Standard Sample).

XI0

Concentration of the Standard Sample at the upper level of the working range (10th Standard Sample).

Yi,j

jth information

j

Subscript

value for the concentration

value of the t-distribution with fl = and a confidence level of (1 - a) (f-factor of Student’s distribution).

Tabled

l-a)

N - 2 degrees of freedom

FV;,f2,1

-a)

Tabled value of the F-distribution (FisherSnedecor) with fl and f2 degrees of freedom and a confidence level of (1 - a).

Xi. %O

Standard

deviation

of the method.

VXO

Coefficient

of Variation

VB (x,

Confidence

interval for the concentration

of the replicate j of level i, where j = 1,

2, . . . . ni. of replicates

per level Xi.

Mean of the information values Yi,j of Standard Confidence interval Xi. samples, having the concentration centration. Licensed to LAAM /MANUEL SOARES ISO Store order #:913756/Downloaded:2008-05-21 Single user licence only, copying and networking prohibited

2

Sample.

h

Number of concentration ISO 8466, N = IO).

Number

deviation. obtained

1,2, . . . . N.

Xl

%

of the cali-

Residual Standard deviation regression calcula tion.

of the Ph Standard Sample. of

of the

sY1

method:

2.11

3

Residual Standard

sY

values for the having the con-

of the method. .?.

of the mean Z?of the con-

ISO 8466-1 :, 1990 IE)

4

Performance

4.1

Choice

4.1.2

of working

a)

range depends

the practice-related

with

the choice

10

of a

(Y i t j - El*

t: j=l

S*i =

on objective

of the variances

Both data sets of the concentrations x1 and xlo are used t~ calculate the variances sf and s$, as given in equation (1) :

range

Esch calibration experiment is started preliminary working rangeL3]. The working

Test for homogeneity

Ili -1

. . .

(11

. . .

(2)

differentes

at

of the calibration. with the mean

The working range shall cover, as far as possible, the application range for water, waste water, and sludge analysis. The most frequently expected Sample concentration should lie in the centre of the working range.

10

Y-‘,J *

c j=l

.-

Yj

fori

=

= 1 ori

= 10

yli b)

feasibilities

of technical

realizability.

The measured values obtained must be linearly correlated to the concentrations. This requires that the measured values obtained near the lower limit of the working range tan be distinguished from the blanks of the method. The lower limit of the working range should therefore be equal to or greater than the limit of detection of the method. Dilution and concentrating Steps should be feasible without the risk of bias. c) the variance of the information dent of the concentration.

values must be indepen-

The variances are tested (F-test) for significant the limits of the working rangeL5t 6]. The test value equation (3).

PG = 2

PG

forsyo

is

determined

for

the

> sf

F-test

.

from

. . (3)

1 S*

PG = --$

for s: > sf0

10

The independence linearity16t *l.

is verified

by a statistical

test on the

PG is compared

with the tabled values of the F-distribution[?

Decision :

4.1.1

Reparation

of the calibration a)

After establishing the preliminary working range, measured values of at least five (recommended N = 10) Standard samples are determined. The concentrations, xj, of these standard samples shall be distributed equidistantly over the working range. In Order to check for the homogeneity of the variances, ten replicates of each of the lowest and the highest concentrations (x, and x,~) of the working range are determined. Ten information values, )pi jl result from these series of measurements (see table 1). ’

Table 1 -

If PG

<

the Ffl. I f2. I 099 I

differente

between

the

between

the

variances sf and SS is not significant.

b) If PG > q, ; j-2;

0,99 the

differente

variances sf and s$ is significant. If the differente between the variances is significant, the preliminary working range should be made smaller until the difference between the variances is found to be random only.

Data sheet for the calibration

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3

lSO,8466-1 : 199O’E)

4.13

Test for linearity[*J

‘# *]

The easiest test for the linearity is the graphical representation of the calibration data with the calculated regression line. Any unlinearity is evident (see figure 2).

The measurement against a blank is not allowed, since thereby valuable information on the magnitude of the blank will be lost. The comparison medium for zeroing the instrument is always, if possible, a pure solvent (e.g. pure water).

. Table 2 -

5 B c

06 I

.-0

i

051 04 03

+E 8 z-

Data sheet for simple I j

xj

-vj

x;

lI I

linear regression -V2i

Xj’uj

--y-----------l----g:ppIIj 1

J

--

J

3

----

4

\

,

,

,

.,

,

;

.

t

----t---l----l

--L----1 t------t-m I

6 7

,)c

,

.-----j----~----~--q-----j

5 ~--

--L------

-t-

.--~~ --_.-

-----+------

I

---

12345-6789 Concentration

Figure 2 - Graphical

linearity

check

In the statistical linearity test the calibration data are used to calculate a linear calibration function as weil as a non-tin.ear calibration function, both with the residual Standard deviation Syl Or 52-

The differente

of the variances

(4) ..

OS’ = (N Degrees

OS* and the variance

: f = 1. of the non-linear

calibration

function

to a F-test in Order to examine for significant

The test value equation (5) PG =-

from equation

. . . (4)

2) s;, - (IV - 3) sy,

of freedom

are submitted ferences.

OS* is calculated

PG required

for the F-test

OS*

is calculated

sv2 dif-

from

. . . (5)

S* Y*

The ten data Sets, consisting of the va2ues of Xi and Yj, are submitted to a linear regression analysis to obtain the coefficients a and b of the calibration function whsich describe the linear correlation between the concentration x as an independent variable, and the measured value y as a dependent variable. The calibration function as well as the characteristics of the method should result from data obtained from a working range x1 to xIo, as received from the measurement and not corrected for blanks. Generally, no blank value (concentration x = 0) is to be included in the calibration experiment and, consequently, in the least-squares fit of the regression. The linear calibration

(6)

. . .

Y =U+bX

a) If PG 4 F: The non-linear calibration function does not lead to a significantly better adjustment, e.g. the calibration function is linear.

(6)

N c

b) If PG > F: The working range should be reduced as far as possible to receive a linear calibration function; otherwise the information values of analyzed samples must be evaluated using the non-linear calibration function.

Calibration

is given by equation

The coefficients are obtained from equations (7) for sensitivity (slope of the calibration function) and (8) for the Ordinate intercept (calculated blank)

Decision :

4.2

function

and characteristics

of the method

(Xj

-

XI

'

(Yj

i=l

b = p--_Ip--m_-

-

Y)

. . . (7)

N

(x; - XI* Y M’ . I=

a = r--b%

1

. . .

(8)

After the final working range is established, ten Standard The coefficients provide an estimate of the true function, which samples are analyzed in accordance with all the Steps of the is limited by the unavoidable procedural scatter. The precision analytical method in Order to obtain ten (IV = 10) measured of the estimate is quantified by the residual Standard deviation, values Yj (see table 2). Licensed to LAAM /MANUEL SOARES ISO Store order #:913756/Downloaded:2008-05-21 Single user licence only, copying and networking prohibited

4

ISO 8466-1 : 1990 (EI

sv, which is a measure of the scatter of the information values about the calibration line and is given by equation (9).

Fromsthe law of error propagation it follows that, for each value X, a confidence interval for the true value y exists whose limiting Points are on two hyperbolic paths bracketing the calibration line. Between these paths the true calibration function tan be expected with a significance level of a (fl : N - 2, confidence level = 1 - a), determined by Student’s t-factor.

N

c

[Y j - (a + bx,)l*

i=l

(9)

N-2 4.3

The confidence intervals for analytical results, calculated from the calibration function, are given by the intersections with the respective hyperbolic paths in figure 3. The estimation of the confidence intervals are given by equation (12) [71

Assessment

The concentration a)

of an analyzed

from the measured Y x =-

valuey,

Sample is obtained

7,,* = % + VB (.%,

to give ?

-a

. . .

b

.a Y -a .2,,2 = b

(IO)

(jf- Fl2

or b)

from the mean of a series of replicates,

the same original

7, petformed

on

N

Sample, to give ?

g=-

(Xi -

b*x

. Z=

\

7-a

. . .

b

(11)

(12)

1

/

A

NOTE - If i; = 1, F,,* =

As to the uncertainty of an analytical result, keep in mind that the analytical error is a combination of the uncertainty of the determination of the measured value, and the uncertainty of the estimation of the regression coeff icients[*!

Equation brackets statistical VB(g) is

X1,2-

(12) indicates that the confidence interval VB(?) the true analytical value with a range governed by the security of Student’s distribution. The magnitude of mainly determined by the number of replicates n^ and

0

7 0

a /’

/

/

1 I I I

-

- 44

vl3m

-

I I I I I I I I I I X

10

Working range

Figure 3 - Working

range x, to xlo, calibration line with confidence band and a Single analytical appertaining confidence interval Licensed to LAAM /MANUEL SOARES ISO Store order #:913756/Downloaded:2008-05-21 Single user licence only, copying and networking prohibited

result with its

5

ISO 8466-1 : 1990 (E)

5.1

their results, the mean of the information values 7, as weil as the characteristics of the method, the residual Standard deviation s,,, and the sensitivity b.

. . .

b

of working

range

For the analysis of drinking water and surface water, range of 0,05 mg to 0,5 mg (NO;)/1 is appropriate.

The quality of the analytical procedure increases therefore with increasing sensitivity and decreasing residual Standard deviation. The Standard deviation of the method sXO[see equation (1311 is the characteristic which allows the analyst to check the quality of his own work.

sXO =2

Choice

5.1.1

Testing

the hornogeneity

v xo = s~xloo

(13)

5

analytical expressed

(3)

= 2,9

4,67 x 10-6

1

F(9,9;

0,991 = 5,35

The comparison of the calculated value PC with the tabled one indicates a random differente between the variances under examination. As the variances are homogeneous a simple regression analysis may be petformed.

The photometric determination of nitrite is used to demonstrate the calibration and the subsequent estimation of the statistical characteristics of the method and their influence on the final results of the evaluation.

Table 3 - Data sheet for the calibration mgll

xi

Y*l,l

Yi,2

Yi,3

Y-1,4

Y-lt5

1

0,05

0,140

0,143

0,143

0,146

2

0,lO

0,281

3

0,15

0,405

4

0,20

0,535

5

0,25

0,662

6

0,30

0,789

7

0,35

0,916

8

0,40

1,058

9

0,45

1,173

0,50

1,303

1,302

1,300

1,304

10 =N

from equation

Consulting the F-tablesL5] forfi = f2 = YE- 1 = 9 degrees of freedom for the variances ST and S$ gives

(14)

Example

i

is calculated

13,54 x IO-6

S2

PG=s= . . .

sf the variancesl)

According to the approach outlined in 4.1 .l, the variances ~2 of the information values obtained from the Standard concen: trations at the lower or upper limit of the working range respectively, were determined (sec table 4). ’ The test value PG for the F-test

For the comparison of different standardized methods, the coefficient of Variation of the method, as a percentage, is given by equation (14)

a working

of NO;

Yfj i,

Y-1,7

i,

0,144

0,145

0,344

'

1,300

1,296

1,295

’

R,a

,

&,!3

j

Yi, 10

0,146

0,145

0,148

1,301

1,296

1,306

1 j I / I ) I 1 I 1 1

Table 4 -

Data sheet for the analysis

sf variance.

Object:

nitrite

I

i 1 I

10

1

xi

Y.

Yi,2

Yi,3

Yi, 10

Ext.*)

Ext.*)

Ext.*)

Ext. *)

Y* EX:,’ )

Yi, 9

Ex%

Y* Ex;.:)

yi,8

mgll

Ext.“,

Ext. *)

Ext. *)

mg& 12

0,05

0,140

0,143

0,143

0,146

0,144

0,145

0,144

0,146

0,145

0,148

4,67. IO-6

0,50

1 1,303

1,302

1 1,300

1 1,304

1 1,300

1,295

1 1,301

1 1,296

1 1,306

/

Yi, 5

yi,6

/

1,296

j

s?

11356 . lW6 1

I *c) Ext. : (extinction)

1) Forthe sake oftransparency, to the result.

I

alldimensions have intentionally been omitted in allequations, withoutambiguity.

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6

The dimensions are finallyadded

5.1.2

Testing

A non-linear

linearity

regression

The Standard equation ( 13) function

may be derived

s

0,005 sy b2,575

=

5.2

Calibration

xo

5.3

0,002o

as a

= 0,73

0,275

Single determination

The analysis of an unknown Sample, performed in the same way as the analysis of the Standards, gave an information value jk 0,641 (extinction). The analytical result was obtained using equation (12) with a confidence interva195 %, t(8; 0,951 = 2,31

0,641 - 0,018

Since the prerequisites for the Performance of a simple linear regression are fulfilled, the calibration function and the characteristics of the method tan be calculated using equations (71, (8) and (13). The results are shown in table 5.

%,2

=

+ is calculated

x 100

expressed

Evaluation

5.3.1

of the method

The slope, b, as a measure for the sensitivity, equation (7)

from

= 0,002 0

2

Sxo V xo = x x loo=

procedure)

are equal, the differente (411 does not need to be function does not lead to the calibration function is

and characteristics

is calculated

2

= 0,005 2 mg/l. sY* As both residual Standard deviations of the variances DS* [see equation calculated. The non-linear calibration a significantly better adjustment, e.g. linear.

method

The coefficient of Variation of the method, percentage, is given by equation (14)

The residual Standard deviations of the linear and the non-linear calibration function, sY, and su2, are compared: = 0,005 2 mg/1 (see 5.2 for calculation

of the

[*l as

Y = 0,013 5 + 2,62 x - 0,081 8 ~2, giving a residual standard deviation of sY2 = 0,005 2 mg/l.

sYl

deviation

2,575

+

0,002 0 x 2,31

-

+ -

(0,641 - 0,726 2)*

+

from

(2,575)*

x 0,206 25

= (0,242 + 0,005) mg/1 N

c

b =

-

(Xi

33

’ (yi

-

i=l

Thus the true value of the concentration within the range 0,237 < x < 0,247 mg/l, level of 0,95.

jd

= 2,575

tan be expected with a confidence

N

(X i-

c i=l

The Ordinate intercept, equation (8) a = v--

32

5.3.2

a, (calculated

For three replicate determinations, the analytical the information values 0,641; 0,631 and 0,633.

blank) is calculated

from

Replicate

Calculation

b X = 0,726 2 - 2 1575 2 x 0 1275 = 0 I 018 Ext .

The residual equation (9).

Standard

deviation,

sY, is

calculated

of the analytical 0,635

%,2

from

-

analysis

=

- 0,018

+

2,575 (0,635 - 0,726 2)*

+

(2,575)*

= 0,005 2 [Ext.l

N-2

The equation

for the straight

Y = 0,018

gave

result:

(Y i - yi)*

sy =

method

x 0,206 25

= (0,240 + 0,003) mg/l

line is given by equation

Thus the true value of the concentration within the range 0,237 < x < 0,243 mg/I, level of 0,95.

(4)

+ 2,575 2 x

Table 5 -

tan be expected with a confidence

Data sheet for the regression 4

1 1 1 $i 1 ,66,

4

I

X = 0,275 mg /I

0,20

1

0,535

7 = 0,726 (Extinction)

6

0,30

0,789

7

0,35

0,916

8

0,40

1,058

-

dV*1

mg0

T--t-/ r 9

0,45

1,173

10

0,50

1,303

--

I

xi

i

c I 2f75l

i=l

I

I

7,262

I l

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7

rSO8466-1 : 1990 (El

Annex A (informative) Bibliography

111 VONDERHEID, C., DAMMAN, V. , DÜRR, w., FUNK, W. and KRUTZ, H., Statistical assessment

and comparison

of analytical

procedures.

141 FRANKE, J.P., dE tion spectrometry

of quantitative

ZEEW,

analytical

procedures,

BI

SACHS, L., Methods

for statistkaI

DOERFFEL, K., Statistics

2nd Edition,

theory and methodology

in Chemical analysis,

a I’energie

atomique,

in science and enghering,

water,

VEB- Verlag für die Grundstoffindustrie,

series -

Presentation

of a Computer

Statistique appliquee & l’exploitation

program,

(1966), Leipzig.

Vom Wasser 58, (1982), pp. 231-255.

des mesures, tome 2, Masson,

quality,

tests, Chemical analysis, calibration,

statistical analysis.

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Springer Verlag, (1966),

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