COMPENDIUM OF INTERNATIONAL METHODS OF ANALYSIS OIV

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1 Collaboratve Study Collaboratve Study The purpose of the collaboratve study s to gve a quantfed ndcaton of the precson of ethod of analyss, expressed as ts repeatablty r and reproducblty R. Repeatablty: the value below whch the absolute dfference between two sngle test results obtaned usng the sae ethod on dentcal test ateral, under the sae condtons (sae operator, sae apparatus, sae laboratory and a short perod of te) ay be expected to le wthn a specfed probablty. Reproducblty: the value below whch the absolute dfference between two sngle test results obtaned usng the sae ethod on dentcal test ateral, under dfferent condtons (dfferent operators, dfferent apparatus and/or dfferent laboratores and/or dfferent te) ay be expected to le wthn a specfed probablty. The ter "ndvdual result" s the value obtaned when the standardzed tral ethod s appled, once and fully, to a sngle saple. Unless otherwse stated, the probablty s 95%. General Prncples The ethod subjected to tral ust be standardzed, that s, chosen fro the exstng ethods as the ethod best suted for subsequent general use. The protocol ust be clear and precse. The nuber of laboratores partcpatng ust be at least ten. The saples used n the trals ust be taken fro hoogeneous batches of ateral. The levels of the analyte to be deterned ust cover the concentratons generally encountered. Those takng part ust have a good experence of the technque eployed. For each partcpant, all analyses ust be conducted wthn the sae laboratory by the sae analyst. The ethod ust be followed as strctly as possble. Any departure fro the ethod descrbed ust be docuented. The experental values ust be deterned under strctly dentcal condtons: on the sae type of apparatus, etc. They ust be deterned ndependently of each other and edately after each other. The results ust be expressed by all laboratores n the sae unts, to the sae nuber of decal places. Fve replcate experental values ust be deterned, free fro outlers. If an experental value s an outler accordng to the Grubbs test, three addtonal easureents ust be taken. OIV-MA-AS-07 : R000

2 Collaboratve Study Statstcal Model The statstcal ethods set out n ths docuent are gven for one level (concentraton, saple). If there are a nuber of levels, the statstcal evaluaton ust be ade separately for each. If a lnear relatonshp s found (y = bx or y = a + bx) as between the repeatablty (r) or reproducblty (R) and the concentraton (x ), a regresson of r (or R) ay be run as a functon of x The statstcal ethods gven below suppose norally-dstrbuted rando values. The steps to be followed are as follows: A/ Elnaton of outlers wthn a sngle laboratory by Grubbs test. Outlers are values whch depart so far fro the other experental values that these devatons cannot be regarded as rando, assung the causes of such devatons are not known. B/ Exane whether all laboratores are workng to the sae precson, by coparng varances by the Bartlett test and Cochran test. Elnate those laboratores for whch statstcally devant values are obtaned. C/ Track down the systeatc errors fro the reanng laboratores by a varance analyss and by a Dxon test dentfy the extree outler values. Elnate those laboratores for whch the outler values are sgnfcant. D/ Fro the reanng fgures, calculate standard devaton of repeatablty); Sr., and repeatablty r standard devaton of reproducblty S R and reproducblty R. Notaton: The followng desgnatons have been chosen: Nuber of laboratores ( =,... ) Index (No. of the laboratory) n Nuber of ndvdual values fro the th laboratory N Total nuber of ndvdual values n l x( =,... n ) Indvdual value of the th laboratory n x x Mean value of the th laboratory n = x N s = n- n = x n xx Total ean value Standard devaton of the th laboratory OIV-MA-AS-07 : R000

3 Collaboratve Study A/ Verfcaton of outler values wthn one laboratory After deternng fve ndvdual values x, a Grubbs test s perfored at the laboratory, to dentfy the outlers values. Test the null hypothess whereby the experental value wth the greatest absolute devaton fro the ean s not an outler observaton. x * x Calculate PG = s. x * = suspect value Copare PG wth the correspondng value shown n Table for P = 95%. If PG < value as read, value x * s not an outler and s can be calculated. If PG > value as read, value x * probably s an outler therefore ake a further three deternatons. Calculate the Grubbs test for x * wth the eght deternatons. If PG > correspondng value for P = 99%, regard x * as a devant value and calculate s wthout x *. B/ Coparson of varances aong laboratores - Bartlett Test The Bartlett test allows us to exane both ajor and nor varances. It serves to test the null hypothess of the equalty of varances n all laboratores, as aganst the alternatve hypothess whereby the varances are not equal n the case of soe laboratores. At least fve ndvdual values are requred per laboratory. Calculate the statstcs of the test: PB C C S r S r N ln f lns f N 3 f si N OIV-MA-AS-07 : R000 3

4 Collaboratve Study f = n - degrees of freedo of s. Copare PB wth the value x ndcated n table at - degrees of freedo. If PB > the value n the table, there are dfferences aong the varances. The Cochran test s used to confr that the varance fro one laboratory s greater than that fro other laboratores. Calculate the test statstcs: PC s ax s Copare PC wth the value shown n table 3 for and n at P = 99%. If PC > the table value, the varance s sgnfcantly greater than the others. If there s a sgnfcant result fro the Bartlett or Cochran tests, elnate the outler varance and calculate the statstcal test agan. In the absence of a statstcal ethod approprate to a sultaneous test of several outler values, the repeated applcaton of the tests s pertted, but should be used wth cauton. If the laboratores produce varances that dffer sharply fro each other, an nvestgaton ust be ade to fnd the causes and to decde whether the experental values found by those laboratores are to be elnated or not. If they are, the coordnator wll have to consder how representatve the reanng laboratores are. If statstcal analyss shows that there are dfferng varances, ths shows that the laboratores have operated the ethods at varyng precsons. Ths ay be due to nadequate practce or to lack of clarty or nadequate descrpton n the ethod. C/ Systeatc errors Systeatc errors ade by laboratores are dentfed usng ether Fscher's ethod or Dxon's test. R.A. Fscher varance analyss Ths test s appled to the reanng experental values fro the laboratores wth an dentcal varance. The test s used to dentfy whether the spread of the ean values fro the laboratores s very uch greater than that for the ndvdual values expressed by the varance aong the laboratores ( s ) or the varance wthn the laboratores ( s I ). OIV-MA-AS-07 : R000 4

5 Collaboratve Study Calculate the test statstcs: s PF si s s I - = N n = xx n = xx Copare PF wth the correspondng value shown n table 4 (dstrbuton of F) where f = f = - and f = f = N - degrees of freedo. If PF > the table value, t can be concluded that there are dfferences aong the eans, that s, there are systeatc errors. Dxon test Ths test enables us to confr that the ean fro one laboratory s greater or saller than that fro the other laboratores. Take a data seres (h), h =,,3...H, ranged n ncreasng order. Calculate the statstcs for the test: 3 to 7 Q 0 H or H H H 8 to 3 plus H Q or Q 3 H or H H H H H H 3 Copare the greatest value of Q wth the crtcal values shown n table 5. If the test statstc s > the table value at P = 95%, the ean n queston can be regarded as an outler. If there s a sgnfcant result n the R A Fscher varance analyss or the Dxon test, elnate one of the extree values and calculate the test statstcs agan wth the reanng values. As regards repeated applcaton of the tests, see the explanatons n paragraph (B). OIV-MA-AS-07 : R000 5

6 Collaboratve Study If the systeatc errors are found, the correspondng experental values concerned ust not be ncluded n subsequent coputatons; the cause of the systeatc error ust be nvestgated. D/Calculatng repeatablty (r) and reproducblty (R). Fro the results reanng after elnaton of outlers, calculate the standard devaton of repeatablty s r and repeatablty r, and the standard devaton of reproducblty s R and reproducblty R, whch are shown as characterstc values of the ethod of analyss. sr N f s r sr sr sa s I R s R a a N n N If there s no dfference between the eans fro the laboratores, then there s no dfference between s r and s R or between r and R. But, f we fnd dfferences aong the laboratory eans, although these ay be tolerated for practcal consderatons, we have to show s r and s R, and r and R. OIV-MA-AS-07 : R000 6

7 Collaboratve Study BIBLIOGRAPHY AFNOR, nore NFX0604, Fdéltè des éthodes d'essa. Déternaton de la répétablté et de la reproductblté par essas nterlaboratores. DAVIES O. L., GOLDSMITH P.l., Statstcal Methods n Research and Producton, Olver and Boyd, Ednburgh, 97. GOETSCH F. H., KRÖNERT W., OLSCHIMKE D., OTTO U., VIERKÖTTER S., Meth. An., 978, No 667. GOTTSCHALK G., KAISER K. E., Enführung n de Varanzanalyse und Rngversuche, B- Hoschultaschenbücher, Band 775, 976. GRAF, HENNING, WILRICH, Statstsche Methoden be textlen Untersuchungen, Sprnger Verlag, Berln, Hedelberg, New York, 974. GRUBBS F. E., Saple Crtera for Testng Outlyng Observatons, The Annals of Matheatcal Statstcs, 950, vol., p GRUBBS F. E., Procedures for Detectng Outlyng Observatons n Saples, Technoetrcs, 969, vol., No, p -. GRUBBS F. E. and BECK G., Extenson of Saple Szes and Percentage Ponts for Sgnfcance Tests of Outlyng Observatons, Technoetrcs, 97, vol. 4, No 4, p ISO, nore 575. KAISER R., GOTTSCHALK G., Eleentare Tests zur Beurtelung von Messdaten, B-I Hochschultaschenbücher, Band 774, 97. LIENERT G. A., Vertelungsfree Verfahren n der Bostatstk, Band I, Verlag Anton Hane, Mesenhe a Glan, 973. NALIMOV V. V., The Applcaton of Matheatcal Statstcs to Checal Analyss, Pergaon Press, Oxford, London, Pars, Frankfurt, 963. SACHS L., Statstsche Auswertungsethoden, Sprnger Verlag, Berln, Hedelberg, New York, 968. OIV-MA-AS-07 : R000 7

8 Collaboratve Study Table - Crtcal values for the Grubbs test n P = 95% P 99% ,55,48,75,887,00,6,5,90,355,4,55,496,764,973,39,74,387,48,564,636 Table Crtcal values for the Bartlett test (P = 95%) f( - ) X f( - ) X 3,84 5,99 3 7,8 4 9,49 5,07 6,59 7 4,07 8 5,5 9 6,9 0 8,3 9,68,03,36 3 3,69 4 5,00 5 6,30 6 7,59 7 8, ,4 9 3, ,7 33,9 35, 36,4 37,7 38,9 40, 4,3 4,6 43,8 49,8 55,8 67,5 79, 90,5 0,9 3, 4,3 OIV-MA-AS-07 : R000 8

9 Collaboratve Study Table 3 Crtcal values for the Cochran test n = n = 3 n = 4 n = 5 n = 6 99% 95% 99% 95% 99% 95% 99% 95% 99% 95% OIV-MA-AS-07 : R000 9

10 Collaboratve Study f f Table 4 Crtcal values for the F-Test (P=99%) OIV-MA-AS-07 : R000 0

11 Collaboratve Study f f Table 4 Crtcal values for the F-Test (P=99%) [Contnued] OIV-MA-AS-07 : R000

12 Collaboratve Study Table 5 Crtcal values for the Dxon test Q 0 = Q = Test crtera Crtcal values 95% 99% 3 0,970 0,994 () () ou (H) (H ) 4 0,89 0,96 (H) () (H) () 5 0,70 0,8 The greater of the two values 6 0,68 0, ,569 0, ,608 0,77 () () ou (H) (H ) 9 0,564 0,67 (H ) () (H) () 0 0,530 0,635 The greater of the two values 0,50 0,605 0,479 0,579 Q = 3 0,6 0,697 (3) () ou (H) (H ) 4 0,586 0,670 (H ) () (H) (3) 5 0,565 0,647 The greater of the two values 6 0,546 0,67 7 0,59 0,60 8 0,54 0, ,50 0, ,489 0,567 0,478 0,555 0,468 0, ,459 0, ,45 0,56 5 0,443 0,57 6 0,436 0,50 7 0,49 0,50 8 0,43 0, ,47 0, ,4 0, ,407 0, ,40 0, ,397 0, ,393 0, ,388 0, ,384 0, ,38 0, ,377 0, ,374 0, ,37 0,438 OIV-MA-AS-07 : R000

13 Collaboratve Study Table 6 Results of the collaboratve study Analyss Saple Lab nº Indvdual values x n x s s ,47 4, ,83 4,7 x, < x * ,5, ,6 7, ,89 34,7 - = ,9,6 s > s ,63 3, ,8 39, ,63 3, ,5 30, Statstcal Fgures: Bartlett Test: Wthn laboratory: s = ± 5.37 ƒ = 34 PB = 3.6 < 5.5 (95%; ƒ = 8) Between laboratory: s z = 3.97 ƒz = 7 Analyss of varance: s r = 5.37 r = 5 s R = 7.78 R = PF = 6.76 > 3. (99%; ƒ = 7; ƒ = 34) OIV-MA-AS-07 : R000 3