Biologically Related National Institute of Standards and Technology

Chapter 5

Biologically Related National Institute of Standards and Technology Standard Reference Materials Downloaded by UNIV MASSACHUSETTS AMHERST on August 1, 2012 | http://pubs.acs.org Publication Date: December 26, 1991 | doi: 10.1021/bk-1991-0445.ch005

Variability in Concentration Estimates William Horwitz and Richard Albert U.S. Food and Drug Administration, HFF-7, Washington, DC 20204

The extensive compilation of data on SRMs by Gladney et al. (Standard Reference Materials: Compilation of Elemental Concentration Data for NBS Clinical, Biological, Geological, and Environmental Standard Reference Materials, NBS Special Publication 260-111 (1987)) provides a remarkable opportunity to check the statistical distribution of analytical results for SRMs reported under unusually favorable circumstances. The precision estimates obtained for 11 biologically related SRMs by the compilers, who exercised subjective, critical analytical judgment to eliminate data "clearly beyond the limit of acceptability" by removing values beyond 2 standard deviations from the mean, provided published consensus values that are compared to the results predicted by the Horwitz equation: relative standard deviation between-laboratories (RSD , %) = 2 exp (1 - 0.5 log C), where C is the concentration expressed as a decimal fraction. The compilers removed 14% of the reported values from the 117 certified analyte-matrix combinations, when at least 8 values were available, for 28 elements over a certified concentration range from 5 ng/g to 40 mg/g. Only 2 of the resulting RSDR values are outside the acceptable maximum of twice the RSD value calculated from the Horwitz equation. However, removal of 14% of the data as nonconforming is regarded as excessive. This finding suggests that many laboratories lack a quality assurance program to investigate the occurrence of gross deviations from certified values. R

R

Very little information exists in the literature as to the magnitude of the underlying error structure of analytical chemistry. One of the best and most understandable expositions is that of Currie (1). One particularly practical statement by Currie is that the This chapter not subject to U.S. copyright Published 1991 American Chemical Society In Biological Trace Element Research; Subramanian, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

Downloaded by UNIV MASSACHUSETTS AMHERST on August 1, 2012 | http://pubs.acs.org Publication Date: December 26, 1991 | doi: 10.1021/bk-1991-0445.ch005

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v a r i a b i l i t y s h o u l d n o t exceed about 10% f o r a p p l i c a t i o n t o t h e t r a c e concentration l e v e l . A number o f p r o f e s s i o n a l and commodityo r i e n t e d o r g a n i z a t i o n s c o n d u c t programs t o c o n t r o l p o t e n t i a l s o u r c e s of a n a l y t i c a l e r r o r . F o r example, t h e A s s o c i a t i o n o f O f f i c i a l A n a l y t i c a l C h e m i s t s (AOAC) c o n t r o l s t h e method v a r i a b l e by p r o v i d i n g a mechanism t o v a l i d a t e methods o f a n a l y s i s a p p l i e d t o s p e c i f i c commodities b u t on a c a s e - b y - c a s e b a s i s . S i m i l a r l y , t h e American O i l C h e m i s t s ' S o c i e t y (AOCS) and t h e American A s s o c i a t i o n o f C e r e a l C h e m i s t s (AACS) n o t o n l y v a l i d a t e methods b u t a l s o f u r n i s h laboratory (analyst) p r o f i c i e n c y evaluation s e r v i c e s f o r o i l s e e d s , g r a i n s , and r e l a t e d commodities. The American A s s o c i a t i o n o f Feed C o n t r o l O f f i c i a l s (AAFCO) p r o v i d e s g u i d e l i n e s f o r a l l o w a n c e s f o r s a m p l i n g and a n a l y t i c a l e r r o r i n c o n s t i t u e n t d e c l a r a t i o n s p l a c e d on f e e d l a b e l s . I n r e c e n t y e a r s , many i n t e r n a t i o n a l s t a n d a r d s o r g a n i z a t i o n s , such as I n t e r n a t i o n a l O r g a n i z a t i o n f o r S t a n d a r d i z a t i o n (ISO), I n t e r n a t i o n a l Union f o r Pure and A p p l i e d C h e m i s t r y (IUPAC), and I n t e r n a t i o n a l D a i r y F e d e r a t i o n (IDF), have i n i t i a t e d r o u t i n e programs f o r o b t a i n i n g a c c u r a c y and p r e c i s i o n p a r a m e t e r s from method-performance ( c o l l a b o r a t i v e ) s t u d i e s . The N a t i o n a l I n s t i t u t e o f S t a n d a r d s and T e c h n o l o g y (NIST, f o r m e r l y N a t i o n a l Bureau o f S t a n d a r d s ) and numerous o t h e r intergovernmental, g o v e r n m e n t a l , and p r i v a t e i n s t i t u t i o n s p r o v i d e c e r t i f i e d r e f e r e n c e m a t e r i a l s a g a i n s t which a c c u r a c y o r " t r u e n e s s " (the c u r r e n t l y ISO-recommended (2) s u b s t i t u t e term f o r a c c u r a c y ) can be e v a l u a t e d . An e x t e n s i v e c o m p i l a t i o n o f s o u r c e s f o r b i o l o g i c a l r e f e r e n c e m a t e r i a l s can be found i n t h e r e c e n t book by Iyengar (3). As a r e s u l t o f r e v i e w i n g numerous AOAC c o m m o d i t y - o r i e n t e d c o l l a b o r a t i v e s t u d i e s , H o r w i t z and h i s c o l l a b o r a t o r s (4) e l a b o r a t e d an e q u a t i o n which c h a r a c t e r i z e s t h e b e t w e e n - l a b o r a t o r i e s p r e c i s i o n o f chemical a n a l y s i s f a i r l y w e l l . This equation r e l a t e s r e l a t i v e s t a n d a r d d e v i a t i o n b e t w e e n - l a b o r a t o r i e s i n p e r c e n t (RSD ) t o c o n c e n t r a t i o n e x p r e s s e d as a d e c i m a l f r a c t i o n (e.g., f o r 1$, C = 0.01): RSD

R

(%) = 2 exp (1 - 0.5 l o g

1 Q

C).

(1)

T h i s e q u a t i o n s t a t e s t h a t b e g i n n i n g w i t h 2% f o r p u r e m a t e r i a l s (C = 1 ) , RSD d o u b l e s f o r e v e r y 0 . 0 1 - f o l d d e c r e a s e i n c o n c e n t r a t i o n , as shown i n T a b l e I , which p r o v i d e s some c a l c u l a t e d RSD v a l u e s f o r t h e range o f c o n c e n t r a t i o n s o f i n t e r e s t h e r e . R

Table I . R e l a t i v e Standard D e v i a t i o n Between-Laboratories, RSD (%), f o r Some Benchmark C o n c e n t r a t i o n s , C, as C a l c u l a t e d from E q u a t i o n (1) R

Concentration Fractional Log C 1.0 0 0.01 -2 0.0001 -4 0.000001 -6 (1 ppm) 0.00000001 (10 ppb) -8

RSD , % R

% 100 1 0.01 0.0001 0.000001

2 4 8 16 32

In g e n e r a l , RSD appears t o be a f u n c t i o n o f c o n c e n t r a t i o n independent o f a n a l y t e , m a t r i x , and method. This R

only,

In Biological Trace Element Research; Subramanian, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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a p p r o x i m a t i o n has been t e s t e d f o r numerous a n a l y t e s and m a t r i c e s o f r e g u l a t o r y i n t e r e s t , such as p h a r m a c e u t i c a l s , p e s t i c i d e f o r m u l a t i o n s and r e s i d u e s , c o n t a m i n a n t s , m y c o t o x i n s , t r a c e e l e m e n t s , f e r t i l i z e r s , feeds, d a i r y products, and other foods, over a c o n c e n t r a t i o n range o f C = 1 t o 10~ . W i t h some methods, i . e . , t h o s e i n which t h e a n a l y t e c o n c e n t r a t i o n i s commonly a d j u s t e d t o the p o i n t c o r r e s p o n d i n g t o maximum s e n s i t i v i t y o f t h e m e a s u r i n g i n s t r u m e n t , e.g., t h o s e u s i n g s p e c t r o p h o t o m e t r y , S (absolute standard d e v i a t i o n between-laboratories) i s a c o n s t a n t , even i n d e p e n d e n t o f c o n c e n t r a t i o n , s i n c e an attempt i s made always t o measure a t about t h e same c o n c e n t r a t i o n . The a v a i l a b i l i t y o f t h e e x t e n s i v e c o m p i l a t i o n o f p u b l i s h e d d a t a on S t a n d a r d R e f e r e n c e M a t e r i a l s (SRMs) by Gladney e t a l . (5) p r o v i d e d a r e m a r k a b l e o p p o r t u n i t y t o check t h e s t a t i s t i c a l d i s t r i b u t i o n o f a n a l y t i c a l r e s u l t s r e p o r t e d under u n u s u a l l y favorable circumstances. T h i s c o m p i l a t i o n i n c l u d e d o r i g i n a l d a t a on SRMs from 67 major j o u r n a l s i n a n a l y t i c a l c h e m i s t r y , g e o l o g y , g e o c h e m i s t r y , and e n v i r o n m e n t a l s c i e n c e , as w e l l as books and i n s t i t u t i o n a l r e p o r t s f o r t h e p e r i o d 1972-1985. A l t h o u g h many o f the p a p e r s a r e r e s e a r c h r e p o r t s o f methods development and a p p l i c a t i o n , q u a l i t y c o n t r o l d a t a a l s o may be i n c l u d e d . For the p r e s e n t p u r p o s e , t h e o r i g i n a l documents were not c o n s u l t e d t o c l a s s i f y the source or q u a l i t y of the data. I t i s assumed t h a t t h e c o m p i l a t i o n c o n t a i n s p r a c t i c a l d a t a r e s u l t i n g from a c o n s c i o u s d e c i s i o n on t h e p a r t o f t h o s e members o f t h e a n a l y t i c a l c h e m i s t r y community who were w i l l i n g t o e x h i b i t t h e i r p e r f o r m a n c e on a n a l y s i s o f homogeneous m a t e r i a l s o f known o r a s s i g n e d c o m p o s i t i o n t o p u b l i c scrutiny. Under s u c h c o n d i t i o n s , i t would be e x p e c t e d t h a t t h i s c o l l e c t i o n o f p u b l i s h e d v a l u e s would show t h e b e s t p e r f o r m a n c e t h a t the a n a l y t i c a l p r o f e s s i o n has t o o f f e r . The p r e s e n t p a p e r compares t h e s e d a t a w i t h t h e betweenl a b o r a t o r i e s v a r i a b i l i t y p r o d u c e d under method-performance ( c o l l a b o r a t i v e ) s t u d y c o n d i t i o n s . A method-performance study s u b j e c t s a number o f homogeneous t e s t samples t o a n a l y s i s as unknowns by a number o f l a b o r a t o r i e s , a l l u t i l i z i n g t h e same method. A n a l y s t s g e n e r a l l y work v e r y c a r e f u l l y d u r i n g t h e a n a l y s i s o f such t e s t samples. The c o m p i l a t i o n by Gladney e t a l . (5) c o n t a i n s d a t a from what can be c o n s i d e r e d s u p p l e m e n t a r y - t o - c e r t i f i c a t i o n (material-performance) s t u d i e s o f s p e c i f i c , homogeneous t e s t m a t e r i a l s by any v a l i d method t h a t p r o v i d e s u b s t a n t i a t e d o r a s s i g n e d v a l u e s w i t h s t a t e d u n c e r t a i n t i e s a g a i n s t which o t h e r measured v a l u e s can be compared. A n a l y s t s who p r o v i d e d t h e s e l i t e r a t u r e v a l u e s were aware o f t h e c e r t i f i e d , i n f o r m a t i o n , o r p u b l i s h e d c o n c e n t r a t i o n value a s s o c i a t e d w i t h the a n a l y t e of i n t e r e s t . Interpreters of a n a l y t i c a l d a t a g e n e r a l l y e x p e c t b e t t e r p r e c i s i o n when a n a l y s t s know t h e v a l u e e x p e c t e d t h a n when t h e a n a l y s e s a r e c o n d u c t e d " b l i n d " (6, 7). The c o m p i l e r s o f t h e SRM document (5) r e c o g n i z e d t h e many u s e s t o w h i c h t h e i r c o l l e c t i o n would be p u t and i n v i t e d r e c a l c u l a t i o n s t o r e f l e c t s p e c i f i c purposes.


g

Method To l i m i t t h e work t o a manageable e x t e n t , t h i s i n i t i a l e x a m i n a t i o n was c o n f i n e d t o t h e 11 b i o l o g i c a l SRMs numbered 1566 t o 1577a. I t



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was f u r t h e r r e s t r i c t e d t o t h o s e a n a l y t e s w i t h 8 o r more q u a n t i t a t i v e entries. The d a t a were e n t e r e d i n t o an APL computer language workspace, and o u t l i e r s were examined by t h e IUPAC-1987 p r o t o c o l (8), which r e q u i r e s a minimum o f 8 l a b o r a t o r i e s ( e n t r i e s ) . F o r f u r t h e r s i m p l i f i c a t i o n , each p u b l i s h e d e n t r y was c o n s i d e r e d as a s i n g l e value with a uniform weight. T h e r e f o r e , the Cochran t e s t f o r r e p l i c a t e o u t l i e r s c o u l d n o t be a p p l i e d . O n l y t h e Grubbs and t h e p a i r e d Grubbs o u t l i e r t e s t s were a p p l i e d t o t h e d a t a , and a b e r r a n t i n d i v i d u a l v a l u e s were removed o n l y i f t h e y exceeded t h e v e r y c o n s e r v a t i v e c r i t i c a l v a l u e e q u i v a l e n t t o a p r o b a b i l i t y (P) o f f a l s e r e j e c t i o n = 0.01. The r e a d i l y a v a i l a b l e Grubbs t a b l e s f o r a s i n g l e t e r m i n a l o u t l i e r extended o n l y t o 40 v a l u e s . S i n c e as many as 212 v a l u e s were p r e s e n t i n a d a t a s e t o f t h i s d a t a b a s e , t h e c r i t i c a l v a l u e t a b l e f o r a s i n g l e extreme v a l u e was expanded t o 325 v a l u e s by s i m u l a t i o n and smoothing. F o r t h e p a i r e d Grubbs t e s t s ( h i g h - h i g h , low-low, and h i g h - l o w , s i m u l t a n e o u s l y ) , we adapted t h e v a l u e s g i v e n by K e l l y ( 9 ) . The extended t a b l e s f o r t h e s i n g l e Grubbs t e s t and f o r t h e p a i r e d Grubbs t e s t s were added t o t h e APL program t h a t e x e c u t e d t h e IUPAC-1987 p r o t o c o l f o r t h e s t a t i s t i c a l a n a l y s i s . The IUPAC-1987 p r o t o c o l i s s i l e n t w i t h r e s p e c t t o r e c y c l i n g outlier tests. S t a t i s t i c i a n s hesitate to reapply o u t l i e r tests a f t e r an i n i t i a l removal o f a v a l u e because " t h e p r o b a b i l i t i e s change." However, w i t h some o f t h e d a t a s e t s , i t was o b v i o u s t h a t o u t l i e r t e s t s had t o be a p p l i e d c o n s e c u t i v e l y , i f o n l y f o r c o n s i s t e n c y i n removal o f v a l u e s i n a t i g h t c l u s t e r some d i s t a n c e from t h e main c l u s t e r . The o u t l i e r r e m o v a l o p e r a t i o n used h e r e was t h a t c a l l e d f o r by t h e IUPAC-1987 p r o t o c o l as i n t e r p r e t e d by us f o r multiple outliers. The p r o c e d u r e c o n s i s t e d o f f i r s t t e s t i n g f o r a s i n g l e Grubbs o u t l i e r ; i f p r e s e n t , t h e v a l u e was removed and t h e s e t was r e t e s t e d f o r a f u r t h e r s i n g l e Grubbs o u t l i e r ; when no s i n g l e Grubbs o u t l i e r was removed d u r i n g a c y c l e , t h e s e t o f v a l u e s was t e s t e d f o r a p a i r e d Grubbs o u t l i e r . I f found, t h e p a i r was removed and t h e s e t was r e c y c l e d t o b e g i n a g a i n w i t h t h e s i n g l e and t h e n t h e p a i r e d Grubbs t e s t s u n t i l no f u r t h e r v a l u e s were removed. The IUPAC-1987 o u t l i e r p r o c e d u r e b l i n d l y a p p l i e d t o t h e o r i g i n a l d a t a r e t a i n e d c o n s i d e r a b l y more v a l u e s t h a n were k e p t by t h e c o m p i l e r s (5) who r i g h t l y e x h i b i t e d s u b j e c t i v e , c r i t i c a l a n a l y t i c a l c h e m i c a l judgment " t o e l i m i n a t e d a t a on e i t h e r end o f t h e c o n c e n t r a t i o n spectrum t h a t we judged t o be c l e a r l y beyond t h e l i m i t of a c c e p t a b i l i t y . " T h i s i n i t i a l s c r e e n i n g by t h e d a t a c o m p i l e r s u s u a l l y removed l e s s t h a n 1% o f t h e t o t a l d a t a . Then t h e y c a l c u l a t e d a p r e l i m i n a r y mean and s t a n d a r d d e v i a t i o n , S, and removed p o i n t s o u t s i d e 2S from t h e mean. Then a r e c a l c u l a t e d mean and an S were r e p o r t e d as t h e "consensus v a l u e and a s s o c i a t e d s t a n d a r d deviation." U n q u a n t i t a t e d v a l u e s r e p o r t e d as " l e s s t h a n " o r " g r e a t e r t h a n " were n o t c o n s i d e r e d i n t h e s c r e e n i n g o r c a l c u l a t i o n s . In o n l y 1 c a s e o f t h e 206 d a t a s e t s (Mn i n P i n e Needles) d i d t h e IUPAC-1987 r u l e s , as e l a b o r a t e d h e r e , remove more o u t l i e r s t h a n d i d the c o m p i l e r s . F o r t h e p r e s e n t p a p e r , t h e p u b l i s h e d d a t a under each SRM f o r each element, i f 8 o r more v a l u e s were t a b u l a t e d , were r e a n a l y z e d by t h e IUPAC-1987 p r o t o c o l , u s i n g t h e a p p r o p r i a t e o u t l i e r c r i t i c a l v a l u e s , and t h e r e s u l t s were p r e s e n t e d as r e l a t i v e s t a n d a r d d e v i a t i o n s b e t w e e n - l a b o r a t o r i e s (RSD ) . The u s e o f t h i s parameter


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p e r m i t s c o n s i s t e n t comparison o f p r e c i s i o n a c r o s s m a t e r i a l s , a n a l y t e s , and c o n c e n t r a t i o n s , u n a d j u s t e d f o r a n a l y t i c a l c h e m i s t r y judgment, which may d i f f e r from r e v i e w e r t o r e v i e w e r . These RSD v a l u e s were t h e n u s e d as numerators i n r a t i o s c o n t a i n i n g , as d e n o m i n a t o r s , t h e RSD v a l u e s based on c o n c e n t r a t i o n , C, as a d e c i m a l f r a c t i o n (e.g., C = 0.002 f o r a 0.2% l e v e l ) , as c a l c u l a t e d from t h e H o r w i t z e q u a t i o n ( 4 ) . The r e s u l t i n g r a t i o , d e s i g n a t e d as the HORWITZ RATIO o r HORRAT i n t h e t a b l e s and g r a p h s , has been found t o be i n f o r m a t i v e as t o t h e a c c e p t a b i l i t y o f t h e u n d e r l y i n g d a t a . C o l l a b o r a t i v e a s s a y s t h a t g i v e a HORRAT g r e a t e r t h a n 2.0 have been c o n s i d e r e d as s u s p e c t i n method p e r f o r m a n c e s t u d i e s (10). R


R

Results The NIST v a l u e s , t h e consensus r e s u l t s from t h e c o m p i l a t i o n by Gladney e t a l . ( 5 ) , and t h e d a t a from t h e p r e s e n t IUPAC r e c a l c u l a t i o n a r e g i v e n i n the computer p r i n t o u t , T a b l e I I , a r r a n g e d a l p h a b e t i c a l l y by a n a l y t e . The f i r s t column c o n t a i n s a c o n s e c u t i v e number a s s i g n e d by the computer. Columns 2 and 3 g i v e t h e a n a l y t e and t h e NIST SRM m a t r i x numbered 1566 t o 1577a. Two SRMs e x i s t f o r B o v i n e L i v e r . The o r i g i n a l SRM 1577 i s d e s i g n a t e d " L i v e r l - B o v i n e " and t h e second one, " L i v e r 2 - B o v i n e . " The n e x t 3 columns r e f e r t o NIST v a l u e s : The f o u r t h (NIST VALUE) i s t h e c e r t i f i e d o r i n f o r m a t i o n a l v a l u e ; t h e f i f t h (UN) i s u n i t s i n p a r t s p e r 100 (%) as H, i n p a r t s p e r m i l l i o n (ug/g) as M, and i n p a r t s p e r b i l l i o n (ng/g) as B; and t h e s i x t h column (NIST RSDR) r e f e r s t o the NIST u n c e r t a i n t y v a l u e s , when g i v e n , r e c a l c u l a t e d t o RSD (= S x 100/NIST v a l u e ) . The NIST u n c e r t a i n t y v a l u e i n t h e c o m p i l a t i o n may n o t n e c e s s a r i l y be g i v e n as a s t a n d a r d d e v i a t i o n , S, b u t i t i s t r e a t e d as s u c h . As a m a t t e r o f f a c t , t h e c e r t i f i c a t e s o f d i f f e r e n t SRMs g i v e d i f f e r e n t d e f i n i t i o n s f o r t h e NIST u n c e r t a i n t y . This p o i n t i s not i m p o r t a n t i n t h e p r e s e n t c o n t e x t . I f t h e NIST v a l u e i s " f o r i n f o r m a t i o n " ( i . e . , no u n c e r t a i n t y i s i n d i c a t e d ) , t h e NIST RSDR column i s b l a n k ; i f no NIST v a l u e i s a v a i l a b l e , b o t h columns 4 and 6 are blank. Columns 7-10 r e f e r t o t h e c o m p i l e r s ' consensus v a l u e s g i v e n i n t h e p u b l i c a t i o n , c o m p i l e d t o 3/1/1986 ( 5 ) . Column 7 i s t h e mean, column 8 i s i t s S r e c a l c u l a t e d t o an RSD ; column 9 g i v e s t h e range o f v a l u e s i n c l u d e d i n t h e consensus d a t a ; and column 10 i n d i c a t e s t h e number o f v a l u e s ( c o n s i d e r e d as l a b o r a t o r i e s ) removed by t h e c o m p i l e r s / t o t a l number l i s t e d w i t h q u a n t i t a t i v e v a l u e s . The l a s t 4 columns r e f e r t o v a l u e s c a l c u l a t e d by t h e IUPAC-1987 r u l e s (8) as extended h e r e . The IUPAC VALUE i s t h e mean; IUPAC RSD i s t h e S o f t h e c o n c e n t r a t i o n e s t i m a t e s o b t a i n e d by t h e IUPAC r u l e s , r e c a l c u l a t e d t o an S D ; t h e IUPAC OMIT/LABS column, which f o l l o w s , c o n t a i n s t h e number o f l a b o r a t o r i e s removed as o u t l i e r s by t h e IUPAC-1987 r u l e s / t o t a l number l i s t e d . The f i n a l column g i v e s t h e HORRAT v a l u e as c a l c u l a t e d from t h e IUPAC RSD v a l u e u s e d as t h e numerator i n a r a t i o c o n t a i n i n g , as t h e denominator, t h e RSD c a l c u l a t e d from t h e NIST c e r t i f i e d o r i n f o r m a t i o n v a l u e , i f g i v e n ; o t h e r w i s e the consensus mean was u s e d as t h e denominator i n t h e calculation. The NIST SRM v a l u e s a r e g i v e n i n 3 c a t e g o r i e s : (a) a c e r t i f i e d v a l u e w i t h an a s s o c i a t e d u n c e r t a i n t y ; (b) a v a l u e w i t h o u t an R

R

R

R

R

R

R

R



5.

HORWITZ & ALBERT


55

u n c e r t a i n t y f o r i n f o r m a t i o n ( u n c e r t i f i e d ) ; and (c) no v a l u e provided. I n t h e c o m p i l a t i o n , some o f t h e i n d i v i d u a l p u b l i s h e d v a l u e s f o r a s p e c i f i c a n a l y t e f o r a g i v e n SRM a l s o had an a s s o c i a t e d w i t h i n - l a b o r a t o r y u n c e r t a i n t y . These v a l u e s were n o t i n c l u d e d h e r e n o t o n l y because t h e d a t a were i n c o m p l e t e b u t a l s o because o f t h e c o m p l i c a t i o n o f i n t e r p r e t a t i o n t h a t would have been i n t r o d u c e d by any k i n d o f w e i g h t i n g . We do n o t b e l i e v e t h a t t h i s s i m p l i f i c a t i o n a f f e c t e d t h e conclusions reached. A l t h o u g h t h e raw d a t a were a l s o c a t e g o r i z e d by method, t h a t i n f o r m a t i o n was n o t i n c o r p o r a t e d i n t o the database. The method t y p e and r e f e r e n c e s p r o v i d e d i n t h e c o m p i l a t i o n w i t h each v a l u e were used o n l y i n c i d e n t a l l y t o d e t e r m i n e d a t a p a t t e r n s c o n s i s t e n t l y r e s p o n s i b l e f o r extreme v a l u e s a c r o s s a n a l y t e s and m a t r i c e s . F o r t h e a n a l y t e s and m a t r i c e s we have examined t o d a t e ( f e e d s , f e r t i l i z e r s , f o o d s , m y c o t o x i n s and c o n t a m i n a n t s , n u t r i e n t s , p e s t i c i d e r e s i d u e s and f o r m u l a t i o n s , p h a r m a c e u t i c a l s , t r a c e e l e m e n t s ) , we have found t h a t g e n e r a l l y p r e c i s i o n i s i n d e p e n d e n t o f method. I n t h i s c o m p i l a t i o n , however, some s t u d i e s o r methods, such as X-ray f l u o r e s c e n c e and o p t i c a l e m i s s i o n s p e c t r o s c o p y , seem t o c o n s i s t e n t l y p r o v i d e extreme v a l u e s . A s p e c i f i c s t u d y o f t h e r e l a t i o n s h i p o f "removed v a l u e s " o f t h i s c o m p i l a t i o n t o a n a l y t e , m a t r i x , method, and c o n c e n t r a t i o n may provide interesting correlations. T a b l e I I I p r e s e n t s t h e d i f f e r e n c e s between t h e consensus v a l u e s and t h e NIST v a l u e s and between t h e IUPAC v a l u e s and t h e NIST v a l u e s f o r t h e 117 c e r t i f i e d c o n c e n t r a t i o n s o n l y . O t h e r columns g i v e t h e p e r c e n t o u t l i e r s removed by b o t h p r o t o c o l s and t h e c o r r e s p o n d i n g HORWITZ RATIOS. The "N" o f t h i s t a b l e i s t h e o r i g i n a l number o f q u a n t i t a t i v e v a l u e s r e p o r t e d by t h e c o m p i l e r s b e f o r e o u t l i e r removal, f o r use i n c a l c u l a t i n g confidence l i m i t s o r standard errors. I n t h i s t a b l e t h e o r i g i n a l B o v i n e L i v e r SRM-1577 i s d e s i g n a t e d as "Bovn L i " ; t h e new l o t SRM-1577a, "Bovn L i A " . R e s u l t s by Element The i d e n t i f i c a t i o n i n f o r m a t i o n and t h e c e r t i f i c a t i o n , c o n s e n s u s , and I U P A C - r e c a l c u l a t e d d a t a f o r 206 a n a l y t e - m a t r i x c o m b i n a t i o n s a v a i l a b l e i n t h e c o m p i l a t i o n (5) a r e a c c u m u l a t e d i n t h e d a t a b a s e ( T a b l e I I ) . The c e r t i f i e d a n a l y t e component c o n t a i n s 117 i t e m s ; t h e i n f o r m a t i o n a l component, 37; and no NIST v a l u e , 52. To keep t h e d i s c u s s i o n w i t h i n r e a s o n a b l e bounds, f u r t h e r remarks a r e c o n f i n e d t o the c e r t i f i e d v a l u e s . Table I I I presents the r e l a t i v e d i f f e r e n c e s , with sign ignored, o f t h e consensus v a l u e s from t h e NIST c e r t i f i e d v a l u e s , t h e c o r r e s p o n d i n g d i f f e r e n c e s f o r t h e IUPAC-1987 p r o t o c o l means, and t h e number o f extreme v a l u e s t h a t were removed t o a c h i e v e t h e r e c o r d e d values. These d i f f e r e n c e s p r o v i d e a measure o f s y s t e m a t i c e r r o r . The NIST u n c e r t a i n t i e s and t h e RSD v a l u e s from consensus and IUPAC-1987 c a l c u l a t i o n s t r a n s f o r m e d t o H o r w i t z r a t i o s a r e g i v e n under t h e HORRAT column head. The numbers o f HORRAT v a l u e s e x c e e d i n g 2.0 a r e NIST, 4; c o n s e n s u s , 2; and IUPAC-1987, 30. These d a t a a r e f u r t h e r summarized i n T a b l e IV f o r t h o s e elements c e r t i f i e d in at least 3 matrices. The average d i f f e r e n c e o f t h e consensus v a l u e from t h e NIST c e r t i f i e d v a l u e i s 3.5%, w i t h a minimum o f 0.5% f o r z i n c and a maximum o f 8.7% f o r chromium. The a v e r a g e HORRAT



ANALYTE

ALUMINUM ALUMINUM ALUMINUM ALUMINUM ALUMINUM ANTIMONY ANTIMONY ANTIMONY ANTIMONY ARSENIC ARSENIC ARSENIC ARSENIC ARSENIC ARSENIC ARSENIC ARSENIC BARIUM BARIUM BARIUM BERYLIUM BISMUTH BORON BORON BORON BROMINE BROMINE BROMINE BROMINE CADMIUM CADMIUM CADMIUM CADMIUM CADMIUM CADMIUM CADMIUM CADMIUM CALCIUM CALCIUM CALCIUM CALCIUM CALCIUM CALCIUM CALCIUM CALCIUM CALCIUM CERIUM CESIUM CESIUM CESIUM CHLORINE CHLORINE CHROMIUM CHROMIUM

OBS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 ORCHARD-L PINE-NEED LIVER1-BO SPINACH-1 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 ORCHARD-L TOMATO-LE PINE-NEED ORCHARD-L ORCHARD-L ORCHARD-L TOMATO-LE PINE-NEED ORCHARD-L TOMATO-LE LIVER1-BO SPINACH-1 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO LIVER2-BO SPINACH-1 ORCHARD-L ORCHARD-L TOMATO-LE LIVER1-BO ORCHARD-L LIVER1-BO OYSTER-TI BREWERS-Y

REFERENCE MATERIAL

H M B

H H

B M

UN

690.00 M 2700.00 M 690.00 B 2.12 M

40.00

270. 00 1.50 1500. 190. 140. 2.09 3. 00 4100. 124. 120. 1.35

54! 00 3.50 32.00 29.00 110.00 3.00

10 loo 26.00

27.00 100.00 33.00 30.00

870!00 2.90 200.00 5.00 40.00 13.40 6.00 410.00 10.00 270.00 210.00 55.00 150.00 44.00

1200.00 545.00

NIST VALUE

39.1 2.4

13.*3 5.3 14.3 1.4 1.0 4.9 4.8 5.8 2.2

14.8

11.4 21.9 13.8 9.1

9!l

37.0

12:2 20.0 18.5 19.0 9.1 33.3

14.2

5.7 10.3

5.5

NIST RSDR

CONSENSUS OMIT/LABS 4/ 57 12/ 22 5/ 29 1/ 26 6/ 19 6/ 85 1/ 13 8/ 31 2/ 9 4/ 21 1/ 11 3/ 27 17/199 2/ 26 2/ 20 11/ 64 1/ 19 10/ 55 0/ 10 1/ 9 2/ 9 1/ 10 4/ 40 1/ 19 0/ 18 7/ 62 2/ 13 6/ 52 1/ 15 1/ 18 1/ 11 2/ 9 11/ 98 3/ 32 0/ 21 10/123 4/ 34 3/ 17 2/ 19 2/ 16 13/105 5/ 36 4/ 32 7/ 66 4/ 30 7/ 28 4/ 21 3/ 23 1/ 8 4/ 23 7/ 42 5/ 38 3/ 15 5/ 21

CONSENSUS RANGE 123.0- 520.0 628.0- 1300 399.0- 620.0 0.7- 45.6 609.0- 909.0 2.3- 3.5 180.0- 220.0 4.0- 26.0 27.0- 50.0 11.1- 15.5 5.4- 6.3 370.0- 464.0 8.0- 14.3 170.0- 310.0 180.0- 240.0 40.0- 70.0 114.0- 180.0 35.0- 52.0 40.0- 69.0 6.0- 8.4 13.7- 36.0 30.0- 160.0 25.1- 40.0 25.5- 38.0 13.0- 20.0 7.1- 12.0 19.0- 25.3 7.3- 11.1 42.4- 55.3 3.2- 3.7 20.0- 40.0 20.0- 30.0 70.0- 190.0 3.0 2.1140.0- 340.0 230.0- 337.0 1.2- 1.7 1200- 1549 170.0- 208.0 135.0- 162.0 1.7- 2.3 2.4- 3.3 3600- 5000 87.0- 151.0 111.3- 129.7 1.2- 1.5 1.3 0.8 20.0- 50.0 43.0 70.0 9.0- 35.0 630.0 810.0 2410- 3000 540.0- 750.0 1.2 2.2

CONS RSDR 34.7 30.0 11.8 87.5 11.1 10.3 8.6 49.0 22.5 9.2 5.3 6.3 12.1 14.2 8.7 10.9 13.1 9.3 15.8 11.1 33.3 44.4 9.1 12.1 11.8 11.6 9.5 9.9 8.3 4.7 16.7 14.8 18.5 8.0 26.4 7.5 9.8 8.6 5.8 5.4 5.9 8.1 8.6 11.5 4.1 6.0 12.1 23.7 14.0 41.2 5.5 5.2 12.3 13.0

323.00 1000.00 510.00 16.00 810.00 2.90 198.00 9.60 40.00 13.00 5.70 414.00 10.70 253.00 207.00 55.00 153.00 43.00 57.00 7.20 24.00 90.00 33.00 33.00 17.00 9.50 21.00 9.10 48.00 3.43 30.00 27.00 119.00 2.50 227.00 281.00 1.43 1400.00 190.00 148.00 2.04 2 83 4200!00 122.00 121.00 1.33 0.99 38.00 57.00 17.00 730.00 2680.00 650.00 2.00

IUPAC OMIT/LABS 1/ 57 0/ 22 1/ 29 0/ 26 0/ 19 2/ 85 1/ 13 1/ 31 1/ 9 0/ 20 1/ 11 2/ 27 5/199 0/ 26 0/ 24 10/ 64 1/ 19 3/ 55 0/ 10 0/ 9 0/ 9 0/ 10 1/ 40 0/ 19 0/ 18 1/ 62 1/ 13 1/ 52 1/ 15 1/ 18 0/ 11 1/ 9 6/ 98 0/ 31 0/ 21 3/123 1/ 35 1/ 17 1/ 19 1/ 16 3/105 1/ 36 1/ 32 3/ 66 4/ 30 1/ 28 1/ 21 3/ 23 1/ 8 2/ 23 1/ 42 3/ 38 1/ 15 0/ 21

IUPAC RSDR 37.8 61.6 20.9 89.3 29.5 11.2 8.6 128.4 33.5 13.2 5.4 7.6 15.7 18.4 11.4 13.2 13.0 15.4 16.1 23.9 82.4 57.1 12.2 12.9 13.8 16.0 13.0 17.0 8.1 4.7 23.4 19.8 26.3 12.4 26.3 10.2 16.0 14.2 6.6 7.2 8.8 10.8 11.4 15.1 4.5 15.4 123.0 23.0 14.7 50.0 14.0 7.0 24.9 35.9

312.2 646.3 511.9 18.8 733.3 2.9 197.8 26.3 36.8 12.8 5.7 410.0 11.0 251.1 202.7 54.2 152.7 43.3 57.1 6.7 38.1 82.7 32.4 33.3 16.9 9.3 22.1 9.0 47.8 3.4 32.1 28.6 124.6 2.5 227.5 282.1 1.5 1392.8 191.9 146.0 2.0 2.9 4172.2 119.4 121.3 1.3 1.4 37.7 57.3 19.6 711.1 2673.4 667.9 1.7

Reference

IUPAC VALUE

d a t a o f NIST b i o l o g i c a l S t a n d a r d

CONSEN VALUE

T a b l e I I . Database o f e l e m e n t a l c o m p o s i t i o n


5.6 11.2 3.4 8.5 5.1 0.8 0.4 3.6 1.3 1.2 0.2 0.4 1.4 0.9 0.6 0.5 0.6 1.7 1.8 2.0 3.0 2.5 1.3 1.3 1.3 1.4 1.3 1.5 0.9 0.4 0.9 0.7 1.2 0.9 1.3 0.5 1.1 2.7 0.9 0.9 2.5 3.2 2.5 2.0 0.6 4.0 7.7 0.9 0.6 1.7 2.3 1.4 1.5 2.5

IUPAC HORRAT

Materia]


55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108

CHROMIUM CHROMIUM CHROMIUM CHROMIUM CHROMIUM COBALT COBALT COBALT COBALT COBALT COPPER COPPER COPPER COPPER COPPER COPPER COPPER COPPER COPPER EUROPIUM FLUORINE 60L0 GOLD HAHNIUM IODINE IODINE IRON IRON IRON IRON IRON IRON IRON IRON IRON LANTHANU LANTHANU LEAD LEAD LEAD LEAD LEAD LEAD LITHIUM LUTECIUM MAGNESIU MAGNESIU MAGNESIU MAGNESIU MAGNESIU MAGNESIU MAGNESIU MANGANES MANGANES

ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 SPINACH-1 OYSTER-TI ORCHARD-L TOMATO-LE LIVER1-B0 SPINACH-1 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 LIVER2-B0 SPINACH-1 ORCHARD-L ORCHARD-L ORCHARD-L LIVER1-B0 ORCHARD-L ORCHARD-L LIVER1-B0 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 LIVER2-B0 SPINACH-1 ORCHARD-L LIVER1-B0 OYSTER-TI ORCHARO-L TOMATO-LE PINE-NEED LIVER1-B0 SPINACH-1 ORCHARD-L ORCHARD-L OYSTER-TI WHEAT-FLO ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 SPINACH-1 OYSTER-TI WHEAT-FLO 7.0 3.2 1*5 6*9 5.9

1280!00

604*. 00

17! 50 8.50

8.3 6.7 4.8 4.6 23.5 16.7

17.4 5.5 6.9 6.7 3.6 5.0 3.0 10.3 3.6

5.6 15.0 13.6 8.3 9.1 10.0 5.2 4.4 16.7

11.5 11.1 7.7 13.6 6.5

6200'.00 7000.00

480.00 45.00 6.30 10.80 340.00 1.20 600.00

170.00 180.00 195.00 18.30 8.70 300.00 690.00 200.00 268.00 194.00 550.00

4:00

2.60 4.50 2.60 88.00 4.60 400.00 200.00 600.00 180.00 1.50 63.00 2.00 2.20 12.00 11.00 3.00 193.00 158.00 12.00

2.60 4.00 2.60 116.00 4.30 370.00 160.00 525.00 230.00 1.56 63.00 1.96 2.08 12.00 11.00 3.00 190.00 149.00 11.80 24.00 3.90 1.40 2.80 30.00 186.00 234.00 195.00 17.80 8.00 286.00 580.00 185.00 265.00 155.00 540.00 1.17 16.00 480.00 44.00 5.90 10.70 350.00 1.19 700.00 5.10 1330.00 400.00 6050.00 6850.00 1220.00 608.00 8650.00 17.00 8.60

11.5 12.5 7.7 44.8 11.6 10.8 23.1 8.8 17.4 7.7 3.2 5.1 7.7 11.7 18.2 13.3 4.7 9.4 5.9 12.5 12.8 28.6 107 16.7 9.7 13.2 5.6 6.7 15.0 9.8 19.0 14.1 6.8 11.0 5.6 9.4 25.0 6.3 6.8 13.6 4.7 14.3 21.0 21.4 49.2 7.5 5.3 6.3 4.8 13.1 6.7 3.6 7.1 7.0

1.9- 3.3 3.0- 4.6 2.2- 3.1 22.0- 280.0 3.3- 5.2 310.0- 440.0 100.0- 260.0 467.0- 610.0 160.0- 310.0 1.4- 1.8 60.0- 69.0 1.8- 2.1 1.9- 2.4 8.9- 16.0 6.9- 15.0 2.0- 4.5 161.0- 216.0 114.2- 164.0 10.2- 13.2 20.0- 31.0 3.1- 4.8 0.7- 2.0 0.1- 7.0 23.0- 37.0 160.0- 220.0 180.0- 280.0 177.0- 212.5 15.2- 19.6 5.6- 9.7 213.0- 348.0 340.0- 706.0 118.0- 254.0 205.0- 315.0 116.1- 181.0 478.0- 601.0 0.9- 1.4 10.0- 24.5 420.0- 540.0 37.0- 54.0 4.0- 8.1 9.6- 11.9 240.0- 490.0 0.8- 2.0 500.0- 830.0 2.9- 8.5 1150- 1451 370.0- 429.0 5140- 6800 6100- 7400 900.0 1600 516.0- 700.0 7800 9200 14.5 19.3 7.2 9.9

15/108 6/ 25 5/ 21 20/ 71 15/ 40 2/ 14 9/ 59 2/ 9 6/ 75 2/ 14 4/ 25 4/ 24 2/ 20 14/182 6/ 58 9/ 49 18/183 4/ 34 4/ 50 5/ 25 1/ 11 2/ 20 1/ 8 2/ 8 2/ 11 0/ 15 4/ 26 3/ 21 1/ 15 18/165 10/ 53 7/ 44 16/152 6/ 31 7/ 43 9/ 39 4/ 14 2/ 21 18/144 5/ 46 5/ 35 9/ 79 5/ 33 3/ 8 3/ . 1/ 13 1/ 11 9/ 80 4/ 29 2/ 26 8/ 58 4/ 23 4/ 26 2/ 23

2.6 3.9 2.6 408.4 7.6 354.8 179.4 528.8 240.5 1.6 62.5 2.0 2.1 12.2 11.1 3.5 189.3 142.0 11.7 24.8 3.9 1.5 2.9 29.9 170.3 234.3 194.0 17.6 8.2 282.8 556.1 182.1 266.9 149.6 541.8 1.1 28.6 485.5 44.4 6.0 10.8 361.0 1.4 3960.0 4.6 1307.5 405.8 6065.7 6769.7 1237.0 609.5 8496.2 17.1 8.4

2/108 0/ 25 0/ 21 1/ 71 0/ 40 1/ 14 3/ 59 0/ 9 0/ 75 2/ 14 2/ 25 0/ 24 0/ 20 6/182 1/ 58 2/ 49 6/183 0/ 34 2/ 50 3/ 25 1/ 11 1/ 20 1/ 8 0/ 8 0/ 11 0/ 15 1/ 26 2/ 21 0/ 15 7/165 0/ 53 2/ 44 8/152 0/ 31 4/ 43 1/ 39 0/ 14 1/ 21 7/144 1/ 46 1/ 35 3/ 79 1/ 33 0/ 8 0/ 11 0/ 13 0/ 11 2/ 80 0/ 29 1/ 26 5/ 58 0/ 23 2/ 26 0/ 23

1.3 1.9 2.0 6.0 7.4 0.9 1.7 0.9 1.2 0.5 0.7 0.8 0.8 1.3 2.3 3.3 1.0 2.4 0.7 0.6 0.9 0.9 2.7 1.2 1.1 0.6 1.0 0.7 1.5 1.8 5.7 3.2 1.4 2.9 1.1 1.0 2.6 0.4 1.2 1.4 1.0 1.0 2.8 8.9 1.9 1.9 1.1 2.0 1.8 2.7 1.3 2.0 0.9 0.9

Continued on next page

17.8 23.9 27.1 139.2 93.9 16.8 35.4 15.3 24.0 7.5 5.8 11.0 11.2 14.6 25.7 45.1 7.6 17.7 7.4 16.3 11.9 40.5 106.1 32.8 22.5 13.2 7.4 7.6 17.7 12.5 33.9 22.9 9.6 20.9 6.8 16.4 77.0 7.1 11.1 17.4 11.5 18.4 44.0 154.2 68.4 10.5 6.9 8.4 7.4 14.9 8.2 8.0 9.3 11.0


Co

3


MANGANES MANGANES MANGANES MANGANES MANGANES MANGANES MANGANES MERCURY MERCURY MOLYBOEN MOLYBOEN MOLYBOEN MOLYBOEN MOLYBOEN NEODYMIU NICKEL NICKEL NICKEL NICKEL NICKEL NICKEL NITROGEN PHOSPHOR PHOSPHOR PHOSPHOR PHOSPHOR PHOSPHOR PHOSPHOR PHOSPHOR POTASSIU POTASSIU POTASSIU POTASSIU POTASSIU POTASSIU POTASSIU POTASSIU RUBIDIUM RUBIDIUM RUBIDIUM RUBIDIUM RUBIDIUM SAMARIUM SCANDIUM SCANDIUM SCANDIUM SELENIUM SELENIUM SELENIUM SELENIUM SELENIUM SELENIUM SILICON SILVER

ANALYTE

109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162

OBS

RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 LIVER2-B0 SPINACH-1 ORCHARD-L LIVER1-B0 WHEAT-FLO ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 ORCHARD-L OYSTER-TI ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 SPINACH-1 ORCHARD-L OYSTER-TI WHEAT-FLO ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 SPINACH-1 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L TOMATO-LE PINE-NEED LIVER1-B0 SPINACH-1 OYSTER-TI ORCHARD-L TOMATO-LE LIVER1-B0 SPINACH-1 ORCHARD-L TOMATO-LE LIVER1-B0 SPINACH-1 OYSTER-TI WHEAT-FLO RICE-FLOU ORCHARD-L LIVER1-B0 SPINACH-1 ORCHARD-L LIVER1-B0

REFERENCE MATERIAL

60.00

160. 2. 1. 400. 80. 1.

130.00

2100 00 3400, 00 1200 00 1 10 5500 00 0 97 1360 1120 1 47 4 46 3700 00 0 97 3 56 4 45 12 16 18 12

6 00 2 76 8100 00

3.50

3.40

20.10 91.00 238.00 675.00 10.30 9.90 165.00 155.00 16.00 400.00 300.00

NIST VALUE

H H M H H M

M M M M B M H M M M M M H M H

UN

CONSENSUS OMIT/LABS 1/ 17 20/162 6/ 50 3/ 39 12/150 1/ 35 10/ 50 13/100 7/ 50 1/ 9 9/ 34 6/ 12 5/ 10 7/ 65 0/ 10 3/ 12 10/ 70 2/ 9 3/ 17 8/ 20 4/ 28 1/ 17 2/ 16 1/ 8 7/ 63 3/ 31 4/ 29 3/ 25 3/ 27 2/ 14 3/ 15 2/ 11 14/ 97 8/ 36 3/ 26 13/ 75 6/ 31 1/ 8 6/ 74 1/ 8 9/ 67 2/ 8 6/ 27 0/ 9 1/ 9 1/ 10 2/ 21 3/ 38 0/ 34 11/107 15/187 3/ 12 4/ 10 5/ 22

CONSENSUS RANGE 19.1 - 22.4 76.0 •103.0 197.0 -252.0 430.0 •738.0 8.4 - 12.0 9.1 - 10.8 155.0 -178.0 122.0 •190.0 13.7 - 20.0 380.0 -470.0 200.0 -410.0 0.4 - 0.6 0.1 - 0.2 2.3 • 4.1 320.0 •765.0 0.9 • 1.1 0.9 • 1.8 1.1 • 1.7 2.2 - 3.3 50.0 -270.0 4.1 • 7.5 2.6 - 2.8 6530 • 8200 1350 • 1450 1560 - 2400 2800 • 3900 1000 - 1410 0.9 • 1.3 4530 - 5700 0.8 - 1.0 1130 • 1500 900.0 - 1150 1.3 - 1.6 3.8 • 4.8 2700 - 5100 0.8 - 1.1 3.3 • 3.9 3.8 - 5.3 8.5 - 14.8 15.2 - 22.0 15.1 - 21.2 10.0 • 12.7 88.0 •150.0 138.0 •220.0 0.4 • 1.2 150.0 •180.0 1.7 - 2.4 0.9 - 1.2 280.0 -480.0 55.0 •110.0 0.9 - 1.3 24.0 - 66.0 475.8 •750.0 40.0 •100.0

CONS RSDR 4.9 5.6 5.8 10.8 6.9 4.0 3.7 9.0 9.8 7.1 24.1 17.0 33.3 12.5 25.5 8.9 15.4 15.4 12.0 50.0 12.5 1.5 6.6 2.2 9.0 6.5 9.2 10.6 5.9 7.5 6.9 8.6 4.9 5.4 8.4 6.1 4.2 11.1 10.5 14.5 6.5 7.8 17.5 15.0 33.3 6.6 9.6 7.8 13.2 12.3 7.3 35.0 20.0 21.0

20.50 89.00 224.00 650.00 10.20 9.90 164.00 155.00 16.40 420.00 290.00 0.53 0.15 3.20 510.00 1.01 1.30 1.30 2.50 160.00 5.60 2.72 7600.00 1390.00 2000.00 3370.00 1190.00 1.13 5240.00 0.93 1300.00 1050.00 1.44 4.44 3670.00 0.98 3.56 4.50 11.40 17.30 18.40 11.50 114.00 173.00 0.90 166.00 2.08 1.03 380.00 81.00 1.09 40.00 550.00 62.00

2.0 4.4 2.9 2.2 9.7 8.1 3.6 9.7 12.5

23.8 18.2 25.0 12.5 9.1

3*6 0.5 2.9 1.8 2.0 0.7 5.4 0.5 0.8 2.0 8.3 0.6 5.5 1.7

4.8 5.9 16.7

1.8

18.4 15.4

33*3

NIST RSDR

CONSEN VALUE

Table II. Continued

20.5 89.2 224.8 663.4 10.2 9.8 165.4 156.3 16.8 404.4 768.3 4.9 1.1 3.2 1.0 1.1 1.4 1.2 2.6 368.6 5.5 2.7 7392.1 1392.9 2012.0 3313.7 1220.0 1.1 5211.4 0.9 1306.1 1093.1 1.4 4.3 3946.8 0.9 3.6 4.5 11.5 17.3 18.4 12.3 107.2 173.4 0.9 165.8 2.1 1.0 383.4 81.7 1.1 135.9 1110.2 81.4

IUPAC VALUE 4.9 8.5 7.5 6.3 8.5 5.2 5.1 12.5 12.4 10.9 154.7 127.3 115.6 16.3 0.0 21.6 18.9 35.1 21.2 96.8 25.6 2.1 9.6 2.4 11.8 9.0 15.1 14.6 8.1 7.7 10.1 12.2 8.5 13.5 21.6 13.2 5.8 11.6 11.0 14.2 9.1 18.4 31.8 15.0 30.1 6.6 11.9 10.9 13.6 19.3 8.7 130.1 74.1 77.2 1/ 17 7/162 2/ 50 5/ 39 6/150 0/ 35 6/ 50 2/100 4/ 50 0/ 9 3/ 34 0/ 12 1/ 10 1/ 65 0/ 17 0/ 12 6/ 70 1/ 9 0/ 17 0/ 20 0/ 28 0/ 17 0/ 16 1/ 8 2/ 63 1/ 31 1/ 29 1/ 25 1/ 27 2/ 14 1/ 15 0/ 11 1/ 97 1/ 36 1/ 26 0/ 75 3/ 31 1/ 8 5/ 74 1/ 8 4/ 67 1/ 8 1/ 27 0/ 9 1/ 9 1/ 10 0/ 21 0/ 38 0/ 34 3/107 9/187 0/ 12 0/ 10 2/ 22

IUPAC IUPAC RSDR OMIT/LABS


0.5 1.1 1.1 1.1 0.8 0.5 0.7 0.6 0.4 0.6 8.1 7.2 5.4 1.2 0.0 1.4 1.2 2.3 1.6 4.6 2.1 0.6 2.3 0.5 2.3 1.9 2.7 3.7 1.9 1.9 1.9 2.2 2.3 4.2 4.7 3.3 1.8 0.9 1.0 1.4 0.9 1.7 1.4 0.7 0.7 0.3 0.8 0.7 0.7 0.8 0.6 5.0 12.0 3.2

IUPAC HORRAT

00


SODIUM SODIUM SODIUM SODIUM SODIUM SODIUM STRONTIU STRONTIU STRONTIU STRONTIU STRONTIU STRONTIU SULFUR SULFUR SULFUR SULFUR SULFUR SULFUR SULFUR SULFUR TERBIUM THORIUM TIN TITANIUM URANIUM URANIUM VANADIUM VANADIUM VANADIUM VANADIUM VANADIUM VANADIUM YTTERBIU ZINC ZINC ZINC ZINC ZINC ZINC ZINC ZINC ZINC ZINC ZIRCONIU

OYSTER-TI ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 OYSTER-TI ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 WHEAT-FLO RICE-FLOU ORCHARD-L CITRUS-LE TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 ORCHARD-L ORCHARD-L ORCHARD-L ORCHARD-L BREWERS-Y ORCHARD-L OYSTER-TI ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO SPINACH-1 ORCHARD-L OYSTER-TI WHEAT-FLO RICE-FLOU BREWERS-Y ORCHARD-L TOMATO-LE PINE-NEED LIVER1-BO LIVER2-BO SPINACH-1 ORCHARD-L

130! 123. 50.

25! 62.

852. 10. 19.

29. 2.

64.00

1900. 4070.

M ~ M M M M M M M M M B B B M B B M B M B B M B M M M M M M M M M M M 6.5 4.0

io!o

12i0 9.7

1.6 9.4 5.2

17.2 4.3

9.4

2.2

2'.3

2.7 0.7 4.2

5*. A

5.3

2430.00

10. 37. 44. 4.80 140. 00 87. 00

5.9 7.3

5100. 82.

4950.00 89.00 470.00 50.00 2395.00 1.42 10.10 36.00 42.00 5.00 170.00 80.00 1810.00 1350.00 2040.00 4080.00 6200.00 1320.00 7900.00 4350.00 13.00 58.00 290.00 20.00 470.00 29.00 2.70 500.00 1.20 390.00 58.00 1.20 25.00 854.00 10.60 19.70 65.00 25.00 61.00 67.00 130.00 122.00 50.00 2.00

4.4 16.9 23.4 60.0 8.4 7.0 6.9 8.3 11.9 8.0 41.2 6.3 6.1 4.4 11.8 4.4 6.5 8.3 12.7 10.8 23.1 20.7 20.7 35.0 3.4 10.3 7.4 22.0 16.7 17.9 13.8 13.3 20.0 2.8 3.8 3.0 4.6 8.0 6.6 13.4 5.4 3.3 8.0 55.0

4600- 5300 74.0- 140.0 326.0- 650.0 18.0- 105.0 1940- 3010 1.6 1.28.6 11.0 28.0- 44.2 35.6- 54.0 4.4- 5.5 100.0- 300.0 72.5- 87.0 1623- 1980 1256- 1400 1660- 2600 3822- 4400 5500- 6900 1200- 1500 6300- 9500 3600- 4860 9.0- 18.0 40.0- 85.0 180.0- 375.0 6.6- 30.0 441.0- 490.0 25.0- 34.3 2.3- 3.1 300.0- 700.0 1.5 0.9248.0- 470.0 33.0- 66.2 1.01.5 20.0- 34.0 805.0- 887.6 9.9- 11.3 18.7- 21.3 59.0- 70.0 19.0- 32.0 52.0- 71.0 51.0- 87.0 112.0- 150.0 111.6- 130.1 42.0- 60.1 0.4- 3.8

2/ 12 16/ 65 5/ 24 1/ 18 5/ 64 1/ 18 1/ 9 12/ 65 2/ 14 2/ 9 3/ 8 1/ 8 0/ 9 4/ 10 5/ 38 4/ 11 2/ 10 1/ 12 2/ 13 3/ 10 4/ 13 3/ 16 2/ 9 5/ 23 0/ 8 2/ 23 1/ 9 8/ 46 1/ 9 1/ 9 8/ 21 2/ 14 3/ 13 5/ 26 4/ 21 3/ 19 1/ 10 24/212 11/ 56 6/ 40 19/210 2/ 29 4/ 47 1/ 8

4882.0 95.9 549.7 49.6 2401.9 1.4 10.1 36.0 44.2 5.6 274.3 80.4 1810.0 1347.5 1996.2 4097.1 6204.8 1310.0 7541.9 4213.4 21.6 53.6 469.1 19.8 470.1 28.8 2.6 505.6 1.1 354.8 167.0 1.2 24.9 834.9 11.0 19.7 65.1 25.6 62.2 71.5 130.4 121.7 51.3 2.0

SOURCE:

Compiled from ref. 5: identification information, concentration estimates, and variability parameters as calculated from the N I S T certification data, the consensus procedure, and the IUPAC-1987 protocol. Only analytes with 8 or more quantitative literature values given were used.

163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206

6.4 33.9 37.2 63.2 10.4 8.7 7.4 13.7 18.2 32.5 66.5 6.4 1.5 9.0 15.9 6.4 6.7 8.1 21.8 18.1 113.3 42.6 111.1 44.4 3.3 12.7 16.4 29.2 33.2 33.4 111.1 16.9 29.9 5.9 11.7 4.9 5.2 12.6 11.0 20.4 8.0 4.4 12.2 56.5


1/ 12 3/ 65 1/ 24 1/ 18 2/ 64 0/ 18 1/ 9 4/ 65 1/ 14 1/ 9 1/ 8 1/ 8 2/ 9 0/ 10 1/ 38 0/ 11 0/ 10 1/ 12 1/ 13 0/ 10 0/ 13 0/ 16 1/ 9 3/ 23 0/ 8 1/ 23 0/ 9 1/ 46 0/ 9 0/ 9 0/ 21 0/ 14 0/ 13 1/ 26 0/ 21 1/ 19 1/ 10 8/212 3/ 56 2/ 40 5/210 0/ 29 1/ 49 1/ 8

1.4 4.1 5.9 7.1 2.1 2.3 0.7 1.5 2.0 2.6 3.1 0.8 0.3 1.7 3.1 1.4 1.6 1.5 5.3 4.0 3.7 1.8 5.8 4.4 0.2 0.5 1.2 1.6 2.1 1.8 4.5 1.1 1.1 1.0 1.0 0.5 0.6 1.3 1.3 2.4 1.0 0.6 1.4 3.9

60

BIOLOGICAL TRACE ELEMENT RESEARCH


Table I I I . Percent D i f f e r e n c e s o f Consensus (CONS) and IUPAC Mean Values from C e r t i f i e d Concentrations o f Analytes i n B i o l o g i c a l NIST Standard Reference M a t e r i a l s ; Percent O u t l i e r s Removed by Compilers and by Applying IUPAC P r o t o c o l t o O r i g i n a l Data; and HORRAT Values o f R e l a t i v e Standard D e v i a t i o n s f o r U n c e r t a i n t i e s Analyte Aluminum Antimony Arsenic

Berylium Boron Cadmium

Calcium

Chromium

Copper

SRM Spinach Pine Nd Orchard Oyster Rice F l

NIST concn 870 545 2.9 13.4 410

M M M M M

19 29 85 21 27

Spinach Orchard Tomato Pine Nd Bovn L i

150 10 270 210 55

M M B B B

19 199 26 20 64

2.0 7.0 6.3 1.4 0.0

2.0 10 7.0 3.3 1.8

Orchard Orchard Oyster Wheat F Rice F l

27 B 33 B 3.50M 32 B 29 B

9 40 18 11 9

11.0 0.0 2.0 6.2 6.9

29 1.8 2.0 0.0 0.0

Orchard Bovn L i Oyster Wheat F Spinach

110 B 270 B 1500 M 190 M 1.35H

98 123 17 19 28

8.2 4.1 6.7 0.0 1.5

Orchard Tomato Rice F l Pine Nd Bovn L i

2.09H 3.00H 140 M 4100 M 124 M

105 36 16 32 66

Bovn L i A Oyster Brewr Y Spinach Orchard

120 M 690 B 2.12M 4.6 M 2.6 M

N

U

Difference, % CONS IUPAC 6.9 16 6.4 6.1 0.0 0.0 3.0 4.5 1.0 0.0

Outliers, % CONS IUPAC 32 0 17 3 11 2 20 0 7 11 5 9 8 8 17

NIST 1.0 0.9 0.7 1.3 0.7

HORRAT CONS IUPAC 1.9 5.1 3.4 1.9 0.7 0.8 0.8 1.2 0.4 0.3

5 3 0 0 16

1.6 1.8 1.1 0.9 0.4

0.6 1.1 0.8 0.4 0.4

0.6 1.4 1.0 0.5 0.5

22 10 6 9 22

0 2 6 0 11

1.3 1.1 0.8 0.8 0.5

1.2 1.0 0.4 0.6 0.5

3.0 1.3 0.4 0.9 0.7

14 4.4 7.3 1.1 2.2

11 8 18 11 25

6 2 6 5 4

0.4 0.6 2.4 0.7 0.6

0.8 0.3 1.6 0.8 1.6

1.2 5.2 2.7 0.9 4.0

2.4 5.7 5.7 2.4 1.6

2.4 4.3 4.3 1.7 4.0

12 14 12 14 11

3 3 6 3 5

0.4 0.3 1.8 1.1 0.6

1.6 2.4 0.7 1.9 1.5

2.5 3.2 1.0 2.5 1.9

30 15 21 40 108

0.8 5.8 5.7 6.5 0.0

0.8 3.2 19 64 0.0

13 20 24 38 14

13 7 0 0 2

0.8 2.3 0.2 0.5 0.8

0.5 0.7 0.9 0.9 0.8

0.5 1.5 2.4 7.4 1.3

Tomato Pine Nd Bovn L i Oyster Wheat F

4.5 2.6 88 63 2.0

M M B M M

25 21 71 25 24

11 0.0 32 0.0 2.0

13 1.2 364 0.8 0.5

24 24 28 16 17

0 0 1 8 0

0.9 0.6 0.6 0.6 1.0

1.0 0.6 1.9 0.4 0.4

1.8 2.0 6.0 0.7 0.8

Rice F l Spinach Orchard

2.2 M 12 M 12 M

20 50 182

5.5 1.7 0.0

4.5 2.5 1.7

10 8 8

0 4 3

1.0 1.5 0.8

0.5 0.5 1.1

0.8 0.7 1.3



5.

HORWITZ & ALBERT


61

Table III. Continued Analyte Copper

Lead

Magnesium

Manganese

NIST concn Tomato 11 Pine Nd 3.0 Bovn L i 193 Bovn L i A 158 Oyster 195

M M M M M

58 49 183 34 26

Difference , % CONS IUPAC 0 .0 0 .9 0 .0 17 2 .1 1 .6 10 5 .7 0 .0 0 .5

Wheat F Spinach Orchard Tomato Pine Nd

18.3 550 300 690 200

M M M M M

21 43 165 53 44

2 .7 1 .8 4 .7 16 7 .5

3 .8 1 .5 5 .7 19 9 .0

17 16 11 19 16

10 9 4 0 5

0.,5 0. 6 1.,0 0.,6 0.,7

0.,6 0.9 1.,4 3.,2 2.,0

0.7 1.1 1.8 5.7 3.2

Bovn L i Rice F l Bovn L i A Oyster Spinach

268 8.7 194 480 1.2

M M M B M

152 15 31 21 33

1 .1 8 .0 20 0 .0 0 .8

0 .4 5 .7 23 1 .1 16

11 7 19 10 15

5 0 0 5 3

0. 4 0.6 1.4 0. 5 1.1

1.,0 1. 3 1.,5 0.4 1.4

1.4 1.5 2.9 0.4 2.8

Orchard Tomato Pine Nd Bovn L i Oyster

45 6.3 10.8 340 1280

M M M B M

144 46 35 79 13

2 .2 6 .3 0 .9 2 .9 3 .9

2 .2 4 .8 0 .0 6 .2 2 .3

12 11 14 11 8

5 2 3 1 0

0. 7 0.4 0.4 1.2 1. 3

0.8 1.1 0.4 0.8 1.4

1.2 1.4 1.0 1.0 1.9

Orchard Bovn L i Oyster Wheat F Rice F l

6200 604 17.5 8.5 20.1

M M M M M

80 58 26 23 17

2 .4 0 .7 2 .9 1 .2 2 .0

2 .2 1 .0 2 .3 1 .2 2 .0

11 14 15 9 6

2 9 8 0 6

0. 7 0. 2 0.7 0. 5 0. 2

1.5 1.2 1.0 0.6 0. 5

1.95 1.3 1.4 1.0 0.5

Spinach Orchard Tomato Pine Nd Bovn L i

165 91 238 675 10.3

M M M M M

50 162 50 39 150

0 .6 2 .2 5.9 3 .7 1 .0

0,.0 2 .2 5,.5 1 .0

22 14 12 8 8

12 4 4 13 4

0. 5 0.5 0.4 0.4 0.9

0.5 0.7 0.8 1.5 0.6

0.7 1.0 1.1 1.0 1.2

9.9 M B 155 16 P 300 B 1.03M

35 100 50 34 12

0 .0 0 .0 2 .5 3 .3 1 .9

1 .0 0,.6 5,.0 156 9,.7

3 13 14 26 25

0 2 8 9 0

0.7 0. 5 0.4 1.7 1.2

0.4 0.4 0. 3 1.3 0.6

0.5 0.6 0.4 8 1.4

1.0 0. 5 0.8 1.0 1.2

1.0 0.4 1.4 1.8 1.4

1.2 0.6 1.8 2.5 1.9

3.0

1.7

2.7

Bovn L i A Orchard Bovn L i Molybdenum Orchard Nickel Oyster Mercury

N

U

CO


Iron

SRM

Outliers, % CONS IUPAC 12 2 18 4 10 3 12 1 15 4

Orchard Nitrogen Orchard Phosphorus Spinach Orchard Tomato

1.3 M 2.76H 0.550H 0.210H 0.340H

70 17 27 63 31

0 .0 1 .4 6 .2 4 .8 0 .9

7,.7 1,.8 8,.7 4,.2 2,.5

14 6 11 11 10

9 0 4 3 3

Pine Nd

0.120H

29

0 .8

1,.7

14

3

NIST 0.,8 0.,7 0.,7 0. 6 2.,3

HORRAT CONS IUPAC 2.3 1.,6 3.3 1.,0 0.,6 1.0 2.4 1.,3 0. 8 1.0



62

BIOLOGICAL TRACE ELEMENT RESEARCH

Table III. Continued Analyte


Potassium

Rubidium

Selenium

Sodium

Strontium

Sulfur Thorium Uranium Vanadium Zinc

a

SRM Oyster Wheat F Rice F l Spinach Orchard

NIST concn 0..969H 0.,136H 0.,112H 3.,56 H 1.47 H

Tomato Pine Nd Bovn L i Oyster Spinach

4..46 H 0.,370H 0.,97 H 4.,45 M 12.,1 M

36 26 75 8 8

0.4 0.8 1.0 1.1 5.2

2.9 6.7 12 1.1 1.6

22 12 17 12 25

3 * 4 0 12 12

0 .2 1 .2 0 .0 0 .2 0 .2

1.7 1.8 1.5 0.9 0.7

4.2 4.6 3.3 0.9 1.7

Orchard Tomato Bovn L i Oyster Wheat F

12 16..5 18.,3 2.,1 1.,1

M M M M M

74 8 67 21 38

5.3 4.6 0.5 1.0 6.4

4.3 4.6 0.5 1.0 8.2

8 12 13 10 8

7 12 6 0 0

0 .8 0 .1 0 .5 1 .7 1 .2

1.0 1.4 0.6 0.7 0.5

1.0 1.4 0.9 0.8 0.7

Rice F l Orchard Bovn L i Oyster Orchard

400 80 1.,1 5100 82

B B M M M

34 107 187 12 65

5.0 1.2 0.9 2.9 8.5

4.3 2.5 O'.O 4.3 17

0 10 8 17 25

0 3 5 8 5

1 .4 0 .5 0 .6 1 .3 0 .9

0.7 0.5 0.5 1.0 2.0

0.7 0.8 0.6 1.4 4.1

Bovn L i Oyster Spinach Orchard Tomato

2430 M 10.,36M 87 M 37 M 44.,9 M

64 9 8 65 14

1.4 2.5 8.0 2.7 6.5

1.2 2.5 7.6 2.7 1.6

8 11 12 18 12

3 11 12 6 12

1 .1 0 .5 0 .3 0 .3 0 .1

1.7 0.6 0.8 0.9 1.3

2.1 0.7 0.8 1.5 2.0

Pine Nd Citrus Orchard Orchard Oyster

4.,8 4070 64 29 2.,3

9 11 16 23 9

4.2 0.2 9.4 0.0 17

17 0.7 16 0.7 13

22 36 19 9 11

11 0 0 4 0

0 .3 0,.5 0 .4 0 .6 0 .3

0.6 1.0 0.9 0.4 0.5

2.6 1.4 1.8 0.5 1.2

26 21 19 49 212

0.2 0.0 1.5 0.0 0.0

2.1 3.8 1.5 2.6 6.4

19 19 16 9 11

4 0 5 2 4

0 .3 0 .8 0,.5 0 .4 1 .2

0.5 0.3 0.3 0.9 0.8

1.0 1.0 0.5 1.4 1.3

M M B B M

Oyster Wheat F Rice F l Spinach Orchard

852 M 10.,6 M 19.,4 M 50 M 25 M

Tomato Bovn L i Bovn L i A

62 130 123

N

U

14 15 11 31 97

Difference, % CONS IUPAC 4.1 4.0 4.4 3.7 6.2 2.4 0.0 0.6 2.0 2.0

Outliers, % CONS IUPAC 14 14 7 20 18 0 19 10 14 1

NIST 0 .1 0 .5 0 .3 0 .8 0 .5

HORRAT CONS IUPAC 1.9 1.9 1.3 1.9 2.2 1.6 1.8 1.3 2.2 1.3

Concentration u n i t s :

1.3 0.8 0.0 20 5 1,.1 0.7 1.0 2 0.3 9 1 .3 7 0 0.4 0.6 0.8 0.8 -2 -6 p a r t s per hundred (10 ) , H; p a r t s p e r m i l l i o n (10 ) , M;

and p a r t s per b i l l i o n

(10 ) , B.

M M M

56 210 29

1.6 0.0 0.8

Wmber o f q u a n t i t a t i v e values l i s t e d i n c o m p i l a t i o n b e f o r e removal o f extreme values.


5.

HORWITZ & ALBERT


63

v a l u e f o r t h e consensus v a l u e s i s 0.8, s l i g h t l y b e t t e r t h a n e x p e c t e d from t h e H o r w i t z c u r v e (1.0) , r a n g i n g from 0.3 f o r s t r o n t i u m and r u b i d i u m t o 1.5 f o r p h o s p h o r u s . The number o f extreme v a l u e s removed by t h e c o m p i l e r s t o a c h i e v e t h e consensus v a l u e (from T a b l e IV) averaged 14%, r a n g i n g from 7% f o r s e l e n i u m t o 25% f o r chromium. The s c a t t e r o f v a l u e s w i t h i n a s p e c i f i c a n a l y t e o f i n t e r e s t c a n be d e t e r m i n e d from T a b l e I I I .


Discussion Our i n t e r e s t i n t h e NIST c e r t i f i e d v a l u e s l i e s n o t so much i n t h e i r absolute accuracy but i n the c l u e s that the use o f the c e r t i f i e d v a l u e statement can s u p p l y as t o t h e p r a c t i c a l r e l i a b i l i t y o f a n a l y t i c a l c h e m i s t r y as a measurement s c i e n c e . NIST i s c h a r g e d by law (11) t o p r e p a r e and d i s t r i b u t e s t a n d a r d samples, which a r e now c a l l e d S t a n d a r d R e f e r e n c e M a t e r i a l s (SRMs). C o n s e q u e n t l y , t h e c e r t i f i e d c o n c e n t r a t i o n v a l u e a s s i g n e d by NIST i s t h e " t r u e v a l u e " used i n t h e d e f i n i t i o n o f [ i n ] a c c u r a c y — t h e d i f f e r e n c e from t h e t r u e v a l u e . D e s c r i p t i o n s p u b l i s h e d by NIST o f t h e work t h a t has gone i n t o t h e c h o i c e and v a l i d a t i o n o f t h e c e r t i f i e d v a l u e , t h e i n f r e q u e n t appearance o f p a p e r s d i s p u t i n g an a s s i g n e d v a l u e , and t h e u s u a l c l o s e n e s s t o t h e c e r t i f i e d v a l u e s and the s i n g l e - p e a k d i s t r i b u t i o n o f s u b s e q u e n t l y p u b l i s h e d l i t e r a t u r e v a l u e s a t t e s t t o t h e s c i e n t i f i c soundness o f t h e NIST a s s i g n m e n t s . T h e r e i s l e s s a s s u r a n c e w i t h r e s p e c t t o t h e meaning o f t h e u n c e r t a i n t y statement a t t a c h e d t o t h e NIST c e r t i f i e d v a l u e s . Taylor (12) i n d i c a t e s t h a t t h e u n c e r t a i n t y l i m i t s accompanying c e r t i f i e d a n a l y t e s a r e f o r t h e "95% l e v e l o f c o n f i d e n c e and i n c l u d e a l l o w a n c e s f o r t h e u n c e r t a i n t i e s o f known s o u r c e s o f s y s t e m a t i c e r r o r as w e l l as t h e random e r r o r o f measurement." U n f o r t u n a t e l y t h i s d e f i n i t i o n does n o t p e r m i t a p r a c t i c a l i n t e r p r e t a t i o n o f t h e s t a t e d u n c e r t a i n t y s i n c e t h e q u o t e d statement r a i s e s more s t a t i s t i c a l q u e s t i o n s t h a n i t answers. F o r example, i f "95% l i m i t s o f c o n f i d e n c e " i s meant t o a p p l y t o "95% c o n f i d e n c e l i m i t s , " t h e s e depend on t h e number o f o b s e r v a t i o n s e n t e r i n g i n t o t h e mean, which i s n o t g i v e n f o r NIST values. F u r t h e r m o r e , u n c e r t a i n t i e s p r e s e n t e d as (± v a l u e s ) cannot p r o p e r l y d e p i c t u n s y m m e t r i c a l d i s t r i b u t i o n s , which would be formed i f s y s t e m a t i c e r r o r , which i s always o n e - s i d e d , i s i n c l u d e d . NIST a l s o has d i f f i c u l t i e s i n f o r m u l a t i n g a d e f i n i t i o n s i n c e d i f f e r e n t c e r t i f i c a t e s provide d i f f e r e n t d e f i n i t i o n s . Nevertheless, i n order t o a v o i d e x t e n s i v e e x p l o r a t i o n o f t h e meaning o f u n c e r t a i n t y as applied to c e r t i f i e d values, the uncertainty value given i n the c o m p i l a t i o n (5) f o r t h e NIST c e r t i f i e d v a l u e i s t r e a t e d as a s t a n d a r d d e v i a t i o n so t h a t o t h e r u s e r s may r e i n t e r p r e t t h e v a l u e a c c o r d i n g t o t h e i r own u n d e r s t a n d i n g . That these u n c e r t a i n t y v a l u e s attached t o t h e c e r t i f i e d values a p p r o x i m a t e s t a n d a r d d e v i a t i o n s i s s u g g e s t e d by F i g u r e 1, where t h e u n c e r t a i n t i e s , c o n s i d e r e d as s t a n d a r d d e v i a t i o n s , a r e t r a n s f o r m e d t o r e l a t i v e s t a n d a r d d e v i a t i o n s (by d i v i d i n g by t h e mean and m u l t i p l y i n g by 100) and p l o t t e d a g a i n s t (-log c o n c e n t r a t i o n ) . The s i m i l a r i t y o f F i g u r e 1 t o F i g u r e s 2 and 3 o f t h e p a p e r by Boyer e t a l . (10) i s s t r i k i n g . A l l t h e f i g u r e s u s e t h e same v a r i a b l e s and range o f r e l a t i v e s t a n d a r d d e v i a t i o n s between l a b o r a t o r i e s (RSD ) p l o t t e d a g a i n s t (-log c o n c e n t r a t i o n ) f o r many o f t h e same a n a l y t e s



64

BIOLOGICAL

TRACE ELEMENT

RESEARCH

T a b l e IV. Averages o f A b s o l u t e D i f f e r e n c e s Between NIST C e r t i f i e d V a l u e s and Consensus V a l u e s as Developed by C o m p i l e r s E x p r e s s e d as P e r c e n t a g e s o f NIST V a l u e s ( D e l t a s ) ; Average H o r w i t z R a t i o s (HORRATs) o f Consensus V a l u e s ; and Average P e r c e n t O u t l i e r s Removed t o A c h i e v e Consensus V a l u e s Element Arsenic Cadmium Calcium Chromium Copper

Concentration Range 10 300 M 0.034 M 0.013 H 0.092 M 2 200 M

Iron Lead Magnesium Manganese Phosphorus

9 700 0.3 - 45 0.060.6 10 700 0.1 0.6

Potassium Rubidium Selenium Sodium Strontium Zinc Av. d

4 4 0.010.015 10

0.1 18 2 0.5 90 900

Av. HORRAT 1.1 0.6 1.0 0.8 0.9

(5),

Av. % Outliers 11 11 14 25 12

No. Of Data S e t s 7 5 9 7 9

Av. Delta 2.9 5.5 3.0 8.7 1.8

M M H M H

9 6 3 9 4

6.9 2.2 2.3 2.2 3.2

0.9 0.7 0.8 0.5 1.5

15 12 11 11 12

H M M H M

8 5 5 3 5

2.4 2.4 2.9 4.3 4.8

0.5 0.3 1.1 1.1 0.3

17 14 7 17 15

M

8

0.5

0.8

14

3.5

0.8

O n l y elements w i t h a t l e a s t 3 c e r t i f i e d v a l u e s i n T a b l e I I I used f o r t h e c a l c u l a t i o n s .


14 were

5.

HORWITZ & ALBERT


65

i n comparable b i o l o g i c a l m a t r i c e s . The 2 s e t s o f f i g u r e s q u a l i t a t i v e l y show t h e same e x p a n s i o n o f RSD w i t h d e c r e a s i n g c o n c e n t r a t i o n ( i n c r e a s i n g - l o g C) and t h e same i n f r e q u e n t s c a t t e r o f v a l u e s above t h e upper l i m i t o f t w i c e t h e H o r w i t z c u r v e .


R

Comparison o f Consensus and IUPAC V a l u e s w i t h NIST V a l u e s . The r e l a t i o n s h i p between t h e NIST v a l u e s (both c e r t i f i e d and i n f o r m a t i o n a l ) and t h e consensus v a l u e s i s g i v e n i n F i g u r e 2. The n e g a t i v e l o g a r i t h m o f t h e consensus v a l u e s i s p l o t t e d a g a i n s t t h e n e g a t i v e l o g a r i t h m o f t h e NIST v a l u e s i n o r d e r t o p r e s e n t i n a s i n g l e p l o t t h e c o n c e n t r a t i o n range c o v e r e d by t h e SRM a n a l y t e v a l u e s o v e r 7 d e c a d e s . The absence o f s u b s t a n t i a l d e v i a t i o n s from l i n e a r i t y i n t h e 117 p a i r s o f v a l u e s from t h e d a t a b a s e s u p p o r t s t h e assumption o f t h e soundness o f t h e NIST v a l u e s . Figure 3 i s a s i m i l a r log-log p l o t of the analyte values c a l c u l a t e d by t h e extended IUPAC-1987 p r o t o c o l a g a i n s t t h e NIST v a l u e s . A t l e a s t 3 s u b s t a n t i a l d e v i a t i o n s from t h e s t r a i g h t l i n e r e l a t i o n s h i p o f t h e consensus v a l u e s a r e a p p a r e n t . F i g u r e s 2 and 3, c o v e r i n g 7 decades o f c o n c e n t r a t i o n v a l u e s on a l o g a r i t h m i c s c a l e , are not s e n s i t i v e t o the numerical d i f f e r e n c e s between t h e NIST v a l u e s and t h e consensus v a l u e s e s t a b l i s h e d by t h e c o m p i l e r s , o r t o t h e d i f f e r e n c e s between t h e NIST v a l u e s and t h e v a l u e s c a l c u l a t e d by IUPAC-1987. The a b s o l u t e n u m e r i c a l d i f f e r e n c e s between t h e NIST c e r t i f i e d v a l u e s and t h e consensus v a l u e s ( o r between t h e NIST c e r t i f i e d v a l u e s and t h e IUPAC-1987 v a l u e s ) as p e r c e n t a g e s o f t h e NIST v a l u e s a r e shown i n F i g u r e 4 f o r t h e 117 c e r t i f i e d a n a l y t e v a l u e s . The two h i s t o g r a m s a r e r o u g h l y comparable e x c e p t f o r a l o n g t a i l i n t h e IUPAC s e t , f o r which t h e 4 v a l u e s given numerically are o f f the s c a l e . A p p r o x i m a t e l y 2/3 o f b o t h s e t s o f v a l u e s (1 s t a n d a r d d e v i a t i o n ) show a d i f f e r e n c e o f l e s s t h a n 4.0% from t h e NIST v a l u e ; a p p r o x i m a t e l y 95% o f t h e consensus d i f f e r e n c e s and a p p r o x i m a t e l y 90% o f t h e IUPAC d i f f e r e n c e s a r e l e s s than 10%. A l l o f t h e h i g h e s t consensus d i f f e r e n c e s (maximum 31%) can be considered a n a l y t i c a l l y reasonable; the 3 highest d i f f e r e n c e s c a l c u l a t e d by t h e IUPAC p r o t o c o l a r e a n a l y t i c a l l y u n r e a s o n a b l e (64%, C r i n S p i n a c h ; 156%, Mo i n O r c h a r d L e a v e s ; and 364%, C r i n B o v i n e Liver). T h i s c o n f i r m s t h a t even t h e extended IUPAC-1987 o u t l i e r removal procedure i s inadequate t o t r i m t h e v a l u e s t o approach the NIST c e r t i f i e d v a l u e s , when compared w i t h t h e a n a l y t i c a l judgment e x e r c i s e d by t h e c o m p i l e r s . However, t h e IUPAC-1987 o u t l i e r r e m o v a l p r o t o c o l was n o t i n t e n d e d t o a p p l y t o d a t a g r o s s l y c o n t a m i n a t e d w i t h outliers. The p r o t o c o l was i n t e n d e d t o a p p l y t o " v a l i d d a t a " d e f i n e d (8; §3.1) as " t h o s e d a t a t h a t would be r e p o r t e d as r e s u l t i n g from t h e normal p e r f o r m a n c e o f l a b o r a t o r y a n a l y s e s ; t h e y a r e n o t marred by method d e v i a t i o n s , i n s t r u m e n t m a l f u n c t i o n s , unexpected o c c u r r e n c e s d u r i n g p e r f o r m a n c e , o r by c l e r i c a l o r t y p o g r a p h i c a l errors." Outliers. The mean (consensus) v a l u e s o b t a i n e d from t h e e x a m i n a t i o n of the data reported i n the l i t e r a t u r e f o r the c e r t i f i e d analytes can depend g r e a t l y on t h e p r o c e d u r e used t o remove extreme v a l u e s , a l t h o u g h i t becomes l e s s i n f l u e n t i a l as t h e number o f v a l u e s i n t h e s e t examined i n c r e a s e s , p a r t i c u l a r l y when t h e number o f v a l u e s exceeds 100. A l t h o u g h t h e c o m p i l e r s p u b l i s h e d a l l t h e d a t a w i t h o u t


66


RESEARCH

40

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i

MINUS LOG NIST CONCENTRATION

F i g u r e 1. The u n c e r t a i n t i e s o f t h e c e r t i f i e d a n a l y t e s o f t h e NIST b i o l o g i c a l SRMs t r a n s f o r m e d t o r e l a t i v e s t a n d a r d d e v i a t i o n s (RSDR) and p l o t t e d a g a i n s t (-log c e r t i f i e d c o n c e n t r a t i o n ) . The lower l i n e i s t h e H o r w i t z c u r v e and t h e upper l i n e i s t w i c e t h a t curve.

-LOG CONSENSUS CONCN VS -LOG NIST CONCN ( c e r t i f i e d )

2

4

6

8

MINUS LOG OF CERTIFIED NIST CONCN

F i g u r e 2. The n e g a t i v e l o g a r i t h m s o f t h e consensus mean v a l u e s of c e r t i f i e d analytes p l o t t e d against the negative logarithms of t h e NIST v a l u e s .


HORWITZ & ALBERT


67

-LOG IUPAC CONCN VS -LOG NIST CONCN ( c e r t i f i e d )


8

Qi

.

1

0

.

1

1

1

4

2

1

6

1

8

MINUS LOG OF CERTIFIED NIST CONCN

F i g u r e 3. The n e g a t i v e l o g a r i t h m s o f t h e a n a l y t e mean v a l u e s c a l c u l a t e d by t h e extended IUPAC-1987 p r o t o c o l p l o t t e d a g a i n s t t h e n e g a t i v e l o g a r i t h m s o f t h e NIST v a l u e s .

HISTOGRAMS OF RELATIVE ERRORS OF CONSENSUS AND IUPAC VALUES

0

10

20

30

F i g u r e 4. Upper h i s t o g r a m : The a b s o l u t e n u m e r i c a l d i f f e r e n c e s between t h e NIST c e r t i f i e d v a l u e s and t h e consensus mean v a l u e s as p e r c e n t a g e s o f t h e NIST v a l u e s f o r t h e 117 c e r t i f i e d a n a l y t e values. Lower h i s t o g r a m : Same as t h e upper h i s t o g r a m , b u t u s i n g mean v a l u e s g e n e r a t e d by t h e IUPAC-1987 p r o t o c o l i n p l a c e o f consensus mean v a l u e s . The v e r t i c a l s c a l e s a r e d i f f e r e n t i n t h e 2 h i s t o g r a m s , b u t t h e h o r i z o n t a l % s c a l e s a r e t h e same.



68


RESEARCH

c e n s o r i n g , t h e y used a r a t h e r l i b e r a l approach t o remove v a l u e s , i . e . , t h e y removed c l e a r l y u n a c c e p t a b l e v a l u e s on a n a l y t i c a l grounds as w e l l as v a l u e s o u t s i d e 2 s t a n d a r d d e v i a t i o n s from t h e mean o f t h e trimmed d a t a ; t h e n t h e mean and s t a n d a r d d e v i a t i o n o f t h e r e m a i n i n g v a l u e s were c a l c u l a t e d and p r e s e n t e d as t h e consensus mean and consensus s t a n d a r d d e v i a t i o n . T h i s p r o c e d u r e r e s u l t e d i n the removal o f some v a l u e s by t h e c o m p i l e r s from almost e v e r y d a t a s e t as shown i n t h e lower h i s t o g r a m o f F i g u r e 5 — frequency of o u t l i e r removal from an analyte-SRM d a t a s e t a g a i n s t p e r c e n t o u t l i e r s removed by t h e c o m p i l e r s . From the 117 c e r t i f i e d v a l u e s , 16 (13.7%) d a t a s e t s had more than 22.2% (maximum 39%) o f t h e v a l u e s removed by t h e c o m p i l e r s . The s i g n i f i c a n c e o f t h e 22.2% c u t o f f p o i n t i s t h a t the IUPAC-1987 p r o t o c o l abandons o u t l i e r removal i f more t h a n 2/9 (22.2%) o f t h e v a l u e s must be removed from method-performance ( c o l l a b o r a t i v e ) s t u d i e s . In such c a s e s , e i t h e r t h e e s t i m a t e o f t h e p r e c i s i o n p a r a m e t e r s must be c o n s i d e r e d a c c e p t a b l e w i t h fewer o u t l i e r s removed, as p r o v i d i n g a " c e i l i n g " parameter, o r t h e method must be improved. The d i s t r i b u t i o n o f t h e p e r c e n t o u t l i e r s removed by t h e IUPAC-1987 p r o t o c o l i s shown i n t h e upper h i s t o g r a m o f F i g u r e 5. The p a t t e r n i s c o m p l e t e l y d i f f e r e n t from t h e o u t l i e r removal p a t t e r n o f t h e consensus v a l u e s , as e x p e c t e d . A l t h o u g h d i f f e r e n t r e v i e w e r s p r o b a b l y would not s e l e c t t h e same v a l u e s from a l l analyte-SRM c o m b i n a t i o n s f o r removal, t h e c h o i c e s o f the c o m p i l e r s appear t o be r e a s o n a b l e and f a i r l y c o n s i s t e n t . A l t h o u g h we r e v i e w e d o n l y s u p e r f i c i a l l y t h e p a t t e r n o f o u t l i e r removal by t h e c o m p i l e r s , c e r t a i n v a l u e s , from t h e same or s i m i l a r s t u d i e s by t h e same t y p e o f method, f o r example, X-ray f l u o r e s c e n c e and o p t i c a l e m i s s i o n s p e c t r o s c o p y , a p p l i e d t o a number o f d i f f e r e n t elements i n t h e same SRM and t o t h e same element i n d i f f e r e n t SRMs always seemed t o appear near t h e extremes o f t h e distribution. F o r t h e p r e s e n t purpose, i t was not n e c e s s a r y t o r e v i e w t h e o r i g i n a l documents t o determine p o s s i b l e s o u r c e s o f t h e systematic e r r o r or t o determine i f the excursions are i n h e r e n t i n the methods t h e m s e l v e s . Undoubtedly some e x p l a n a t i o n s may be d i s c o v e r e d f o r s y s t e m a t i c e r r o r s o f a s i n g l e a n a l y t e i n an SRM — f o r example, i f d i f f e r e n t methods o f d i s s o l u t i o n o f an SRM were c o n s i d e r e d as independent o b s e r v a t i o n s when a c t u a l l y t h e same c a l i b r a t i o n c u r v e may have been used t o o b t a i n a l l o f t h e v a l u e s i n a study. In any c a s e , as shown i n t h e lower h i s t o g r a m o f F i g u r e 5, o n l y 1 d a t a s e t from t h e 117 c e r t i f i e d a n a l y t e - m a t r i x c o m b i n a t i o n s examined (of t h o s e h a v i n g a t l e a s t 8 v a l u e s ) had no o u t l i e r s removed by t h e c o m p i l e r s ; t h e average p r o p o r t i o n o f o u t l i e r s removed was 14% (mode, 1 1 % ) , w i t h a maximum o f 38% i n t h e c a s e o f chromium i n SRM Spinach. The e x i s t e n c e o f such a l a r g e p r o p o r t i o n o f o u t l i e r s i n a n a l y t i c a l work p u b l i s h e d i n p e e r - r e v i e w e d j o u r n a l s was not thought p o s s i b l e (13). The o u t l i e r removal p r o c e d u r e s o f ISO ( 2 ) , t h e IUPAC-1987 p r o t o c o l ( 8 ) , and t h e AOAC G u i d e l i n e s (14) remove extreme v a l u e s o n l y a t t h e a l p h a ( p r o b a b i l i t y o f f a l s e l y removing a good v a l u e ) = 0.01 l e v e l . Youden (15) , however, had no qualms r e g a r d i n g removal o f v a l u e s t h a t would d i s t o r t "the p i c t u r e t h a t would o c c u r from k e e p i n g a r e s u l t so f a r out o f l i n e t h a t t h e e s t i m a t e o f e r r o r does



5.

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69

not m i r r o r t h e r e a l m e r i t o f t h e a n a l y t i c a l method." C h e m i s t s have not been w i l l i n g t o admit t o t h e f r e q u e n t appearance o f extreme v a l u e s i n t h e i r o u t p u t d e s p i t e t h e e x i s t e n c e , i n t h e c l i n i c a l and drug t e s t i n g a r e a s , o f e r r o r s o f such a magnitude t h a t t h e y have a t t r a c t e d t h e a t t e n t i o n o f t h e p u b l i c media. One s c h o o l o f t h o u g h t w i t h r e s p e c t t o o u t l i e r removal h o l d s t h a t o u t l i e r s s h o u l d n o t be removed u n l e s s an e x p l a n a t i o n i s a v a i l a b l e f o r t h e extreme v a l u e s . Such a c o n c e p t i s u n t e n a b l e f o r the SRM d a t a s e t s because i t would l e a v e , as a c c e p t a b l e , v a l u e s t h a t would r e s u l t i n u n r e a l i s t i c p r e c i s i o n p a r a m e t e r s . A f t e r - t h e - f a c t e x a m i n a t i o n o f t h e v a l i d i t y o f v a l u e s from d e f u n c t l a b o r a t o r i e s and u n a v a i l a b l e a n a l y s t s i s n o t p r a c t i c a b l e . The o n l y e v i d e n c e o f t e n a v a i l a b l e must be i n h e r e n t i n t h e d a t a t h e m s e l v e s o r i n t h e accompanying d o c u m e n t a t i o n . Many o u t l i e r - r e m o v a l d e c i s i o n s must be a r b i t r a r y o r based on t h e r e c o g n i z a b l e d i s t r i b u t i o n p a t t e r n o f t h e r e m a i n i n g p o p u l a t i o n , o r on o t h e r a v a i l a b l e i n f o r m a t i o n o r inferences. A second s c h o o l o f t h o u g h t p e r m i t s r e t e n t i o n o f o u t l i e r s i n t h e d a t a s e t as l o n g as they do n o t a f f e c t t h e p r e c i s i o n p a r a m e t e r s s i g n i f i c a n t l y (10). " S i g n i f i c a n t l y " was found by e x p e r i e n c e t o be a r e d u c t i o n i n p r e c i s i o n p a r a m e t e r s by a t l e a s t 40%. T h i s p r o c e d u r e i s most e f f e c t i v e w i t h s m a l l numbers o f v a l u e s (fewer t h a n 2 0 ) . T h i s " d e l t a 40%" r u l e was found t o be r e l a t e d t o t h e Grubbs t e s t and c o u l d be abandoned when t h e IUPAC-1987 p r o t o c o l a d v o c a t e d r e p l a c i n g t h e p r e v i o u s l y used D i x o n o u t l i e r removal t e s t w i t h t h e Grubbs t e s t s , p a r t i c u l a r l y i f t h e Grubbs t e s t s a r e e x p r e s s e d i n terms o f p e r c e n t a g e r e d u c t i o n i n s t a n d a r d d e v i a t i o n caused by t h e extreme value removal. The IUPAC-1987 p r o t o c o l e x e m p l i f i e s a t h i r d a p p r o a c h i n which a r e a s o n a b l e , s c i e n t i f i c a l l y based s e t o f r u l e s i s u t i l i z e d i n t h e i n t e r e s t o f harmonization. A l l p r a c t i t i o n e r s a p p l y i n g t h e same p r o t o c o l s h o u l d o b t a i n t h e same answers. The p r o t o c o l recommends c a l c u l a t i o n o f t h e s t a t i s t i c a l p a r a m e t e r s o f mean and r e l a t i v e s t a n d a r d d e v i a t i o n b o t h (1) w i t h o u t o u t l i e r removal and (2) w i t h o u t l i e r removal by t h e Cochran t e s t , when r e p l i c a t i o n i s p r e s e n t , and t h e n by t h e Grubbs t e s t s , s i n g l e and p a i r e d , a t a c r i t i c a l 2 - t a i l p r o b a b i l i t y l e v e l o f 1%. I t a l s o p e r m i t s , p r i o r t o application of the prescribed o u t l i e r t e s t s , prescreening f o r i n v a l i d data. T h i s p r o c e d u r e has worked f a i r l y w e l l w i t h t h e s m a l l number o f l a b o r a t o r i e s ( u s u a l l y 8-12) t h a t a r e i n v o l v e d i n t h e v e r y w e l l - c o n t r o l l e d method-performance ( c o l l a b o r a t i v e ) s t u d i e s . B u t i t i s obvious t h a t t h i s procedure i s not s a t i s f a c t o r y i f a p p l i e d b l i n d l y t o m a t e r i a l - c e r t i f i c a t i o n s t u d i e s , where a " t r u e v a l u e " i s a v a i l a b l e a g a i n s t which any g i v e n v a l u e c a n be judged. Knowledge o f the t r u e v a l u e s e r v e s as a u s e f u l t o o l t o s c r e e n o u t i n v a l i d d a t a . A f o u r t h approach t o t h e removal o f extreme v a l u e s i s t h e c o m b i n a t i o n used by t h e c o m p i l e r s (3) — u s i n g a n a l y t i c a l judgment t o e l i m i n a t e o b v i o u s l y i n v a l i d r e s u l t s , removing v a l u e s o u t s i d e o f 2 s t a n d a r d d e v i a t i o n s from t h e mean o f t h e trimmed v a l u e s , and u s i n g t h e r e m a i n i n g v a l u e s f o r t h e c a l c u l a t i o n o f t h e consensus mean and s t a n d a r d d e v i a t i o n . The extreme v a l u e s t h u s removed a r e u s u a l l y v a l u e s t h a t a c a s u a l r e v i e w o f t h e d a t a would have e l i m i n a t e d anyway. The p r o c e d u r e i s used t o p r o v i d e a benchmark f o r j u d g i n g t h e a c c e p t a b i l i t y o f method p e r f o r m a n c e and l a b o r a t o r y p e r f o r m a n c e .


70


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As such, t h e p r o c e d u r e c a n a l s o p r o v i d e t h e r e f e r e n c e s t a n d a r d f o r the a c c e p t a b i l i t y o r r e j e c t i o n o f extreme v a l u e s . U n f o r t u n a t e l y , i n any d i s c u s s i o n o f r e l i a b i l i t y , o u t l i e r s must be g i v e n f a r g r e a t e r prominence than t h e y d e s e r v e . They a r e v e r y c o n s p i c u o u s i n any s e t o f d a t a and a u t o m a t i c a l l y a t t r a c t a t t e n t i o n . But t h i s v e r y v i s i b i l i t y s h o u l d c a u s e any a n a l y s t t o pause and reexamine t h e s u p p o r t f o r a b e r r a n t v a l u e s b e f o r e t h e y a r e r e p o r t e d . N e v e r t h e l e s s , t h e p e r s i s t e n t r e p o r t i n g o f extreme v a l u e s i n t h e f a c e of the a v a i l a b i l i t y of a true value i s d i s t u r b i n g . D i s t r i b u t i o n o f E s t i m a t e s o f P r e c i s i o n o f t h e Consensus V a l u e s o f the C e r t i f i e d A n a l y t e s . The d i s t r i b u t i o n o f t h e e s t i m a t e s o f t h e v a r i a b i l i t y o f t h e 117 v a l u e s accompanying t h e c e r t i f i e d v a l u e s f o r the 28 elements from 11 b i o l o g i c a l SRMs where a t l e a s t 8 q u a n t i t a t i v e v a l u e s a r e a v a i l a b l e c a n n o t be examined d i r e c t l y because o f t h e wide range o f c o n c e n t r a t i o n s d i s p l a y e d by t h e d a t a (from 5 ng/g t o 4 % ) . Removing t h e e f f e c t o f c o n c e n t r a t i o n by n o r m a l i z i n g t h e r e l a t i v e standard d e v i a t i o n s a g a i n s t t h e Horwitz c u r v e p e r m i t s an e x a m i n a t i o n o f t h e s p r e a d o f t h e consensus d a t a . The lower h i s t o g r a m o f F i g u r e 6 shows t h e HORRAT v a l u e s o f t h e 117 consensus analyte-SRM c o m b i n a t i o n s . Only 2 HORRAT v a l u e s a r e above 2.0 — c a l c i u m i n O y s t e r T i s s u e and i r o n i n Tomato L e a v e s . T h i s s u g g e s t s t h a t t h e c o m p i l e r s ' c h o i c e o f p r o t o c o l f o r removing extreme v a l u e s i n an u n c o n t r o l l e d m a t e r i a l s - p e r f o r m a n c e study r e s u l t s i n a d i s t r i b u t i o n of concentration-normalized precision v a l u e s t h a t c l o s e l y matches t h e p r e c i s i o n d i s t r i b u t i o n o f c l o s e l y c o n t r o l l e d methods-performance s t u d i e s . I f t h e same t y p e o f h i s t o g r a m (top p o r t i o n o f F i g u r e 6) i s p r e p a r e d f o r t h e HORRAT v a l u e s c a l c u l a t e d from t h e a p p l i c a t i o n o f t h e IUPAC-1987 p r o t o c o l t o the unscreened data, a f l a t t e r d i s t r i b u t i o n with a very long p o s i t i v e t a i l r e s u l t s , e x t e n d i n g up t o a HORRAT o f 8.1 f o r molybdenum i n O r c h a r d L e a v e s . I f t h e IUPAC p r o t o c o l i s a p p l i e d t o the d a t a p r e s c r e e n e d by t h e consensus p r o t o c o l , o n l y 3 a n a l y t e m a t e r i a l c o m b i n a t i o n s a r e a f f e c t e d . However, t h e e f f e c t i s i n c o n s e q u e n t i a l s i n c e t h e p r e c i s i o n s o f t h e a f f e c t e d a n a l y t e s were a l r e a d y a c c e p t a b l e by t h e consensus p r o t o c o l : cadmium i n Wheat F l o u r , HORRAT = 0.62; chromium i n Brewer's Y e a s t , HORRAT = 0.90; and l e a d i n S p i n a c h , HORRAT = 1.35. For these c a l c u l a t i o n s , t h e " u n c e r t a i n " u n c e r t a i n t y values a s s o c i a t e d w i t h t h e NIST c e r t i f i e d c o n c e n t r a t i o n s a r e n o t u s e d . T h e r e f o r e , t h e assumption t h a t t h e v a l u e s a r e s t a n d a r d d e v i a t i o n s i s immaterial f o r t h e d i s c u s s i o n o f t h e p r e c i s o n parameters o f the consensus v a l u e s , which we s u g g e s t r e f l e c t t h e b e s t c u r r e n t a n a l y t i c a l performance. Conclusion The 206 a n a l y t e - m a t r i x c o m b i n a t i o n s produce a remarkable a r r a y o f p r e c i s i o n v a r i a b i l i t y , even when n o r m a l i z e d f o r c o n c e n t r a t i o n by use o f t h e HORRAT r a t i o . D i r e c t a p p l i c a t i o n o f t h e IUPAC r u l e s t o t h e raw d a t a does n o t c h a r a c t e r i z e many o f t h e extreme v a l u e s as analytically unlikely. T h e r e f o r e , i t i s important t h a t a n a l y t i c a l judgment be a p p l i e d t o t h e r e p o r t e d v a l u e s t o remove i n v a l i d d a t a b e f o r e an o u t l i e r p r o c e d u r e i s u s e d .


5.

HORWITZ


& ALBERT


HISTOGRAMS OF PCT. OF LABS DROPPED

71

( c e r t i f i e d NIST and c o n s e n s u s )

F i g u r e 5. Upper h i s t o g r a m : The f r e q u e n c y o f o u t l i e r removal from the 117 d a t a s e t s o f t h e c e r t i f i e d a n a l y t e s a g a i n s t p e r c e n t o u t l i e r s removed by t h e IUPAC-1987 p r o t o c o l (8) u s i n g t h e Grubbs t a b l e s extended t o 325 v a l u e s . Lower h i s t o g r a m : Same as t h e upper h i s t o g r a m , b u t u s i n g t h e f r e q u e n c y o f o u t l i e r s removed by t h e c o m p i l e r s , Gladney e t a l . ( 5 ) . The v e r t i c a l s c a l e s a r e d i f f e r e n t i n the 2 histograms, but the h o r i z o n t a l % s c a l e s are t h e same. , •»

I HISTOGRAM OF IUPAC AND CONSENSUS HORRAT VALUES i

i

1

IUPAC HORRAT N0.PTS.=117

J 1

2

3

4

5

6

7

8

CONSEN HORRAT N0.PTS.=11?

F i g u r e 6. Upper h i s t o g r a m : HORRAT v a l u e s c a l c u l a t e d a f t e r removal o f o u t l i e r s by t h e IUPAC-1987 p r o t o c o l ( 8 ) . Lower h i s t o g r a m : Same as t h e upper h i s t o g r a m , but u s i n g t h e consensus mean and RSD v a l u e s g e n e r a t e d by t h e c o m p i l e r s , Gladney e t a l . (5). R



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RESEARCH

S t a t i s t i c i a n s balk at consecutive a p p l i c a t i o n of o u t l i e r t e s t s t o d a t a because once an o u t l i e r removal p r o c e d u r e has been a p p l i e d on t h e b a s i s o f p r o b a b i l i t y , t h e p r o b a b i l i t i e s f o r t h e o c c u r r e n c e o f a d d i t i o n a l o u t l i e r s change i n a complex way. Moreover, t h e b l i n d a p p l i c a t i o n o f s t a t i s t i c a l r u l e s f o r removal o f extreme v a l u e s i s often inappropriate. A p p l i c a t i o n of a r u l e of "inconsistency with the b u l k o f a p o p u l a t i o n " composed o f i n d e p e n d e n t v a l u e s o b t a i n e d i n numerous l a b o r a t o r i e s a t d i f f e r e n t t i m e s , by d i f f e r e n t t e c h n i q u e s , r e a s o n a b l y s c a t t e r e d about a c e r t i f i e d v a l u e , o r even an i n f o r m a t i o n a l v a l u e , i s s u f f i c i e n t r e a s o n f o r removal o f r e p o r t e d results. T h i s i s p a r t i c u l a r l y t r u e when a p a t t e r n o f c o n s i s t e n t d e v i a t i o n s a p p e a r s f o r a g i v e n a n a l y t e i n d i f f e r e n t SRMs. The c o n c e n t r a t i o n e s t i m a t e s o f t h e c o n s t i t u e n t s o f NIST SRMs as r e p o r t e d i n t h e l i t e r a t u r e have a l a r g e v a r i a b i l i t y . Part of t h i s v a r i a b i l i t y i s c l e a r l y due t o "sore-thumb" o u t l i e r s , g r o t e s q u e l y d e v i a n t v a l u e s , o b t a i n e d when t h e a n a l y s t unknowingly was o u t o f control. S i n c e no a p r i o r i d i s t r i b u t i o n i s c o n c e i v a b l e f o r such o u t l i e r s , i . e . , s i n c e t h e appearance o f such o u t l i e r s i s n o t based on any d e s c r i b a b l e p r o c e s s , no c o n v e n t i o n a l s t a t i s t i c a l t e s t s a r e p o s s i b l e f o r f l a g g i n g and removing them. The d a t a c o m p i l e r s (5) used t h e i r own common sense t o s c r e e n o u t t h e t r u l y o b v i o u s outliers. Then they r e f i n e d t h e d a t a f u r t h e r by removing from t h e reduced d a t a a l l v a l u e s more than 2 s t a n d a r d d e v i a t i o n s from t h e new a v e r a g e . T h i s approach i s q u i t e c l o s e i n s p i r i t and g i v e s r e s u l t s comparable t o t h o s e o b t a i n e d by t h e IUPAC p r o t o c o l which a p p l i e s a Grubbs t e s t (which, i n e f f e c t , removes as o u t l y i n g v a l u e s r e s u l t s t h a t a r e more t h a n a c e r t a i n number o f s t a n d a r d d e v i a t i o n s from t h e average) t o d a t a deemed t o be v a l i d (8, § 3 . 1 ; 14, §6.1) — i . e . , t o d a t a purged o f b l a t a n t o u t l i e r s f o r r e a s o n s a p p a r e n t i n t h e s u p p o r t i n g documentation o r f o r gross i n c o n s i s t e n c y with t h e t r u e o r assigned value. Even a f t e r o u t l i e r removal and t h e consequent n a r r o w i n g o f t h e v a r i a b i l i t y , no g u a r a n t e e as t o t h e a c c u r a c y o f t h e c o n c e n t r a t i o n estimates e x i s t s . F o r r e s u l t s t o be t a k e n s e r i o u s l y as v a l i d a d d i t i o n s t o t h e d a t a b a s e e s t i m a t e s o f c o n c e n t r a t i o n s , a u t h o r s must r e p o r t t h e i r q u a l i t y c o n t r o l p r o c e d u r e s and t h e i r e f f o r t s t o t r a c k down s o u r c e s o f extreme v a l u e s t h a t do n o t agree w i t h t h e c e r t i f i e d value. B u i l t - i n q u a l i t y c o n t r o l w i t h f r e q u e n t r e c o u r s e t o known o r f o r m u l a t e d r e f e r e n c e m a t e r i a l s must become t h e s t a n d a r d o p e r a t i n g p r o c e d u r e f o r a l l a n a l y t i c a l l a b o r a t o r i e s . An example o f a system t o e v a l u a t e a n a l y t i c a l r e s u l t s i s g i v e n by Holden e t a l . ( 1 6 ) .

Literature Cited 1. 2. 3. 4.

Currie, L. A. In Treatise on Analytical Chemistry Part I, 2nd Ed.; Kolthoff, I. M.; Elving, P. M., Eds.; Wiley: New York, 1978; Vol. 1, Chapter 4. ISO-5725-1986. Circulated proposed revision in 6 parts, International Organization for Standardization, Geneva, Switzerland. Available from national standards organizations. Iyengar, G. V. Elemental Analysis of Biological Systems; CRC Press: Boca Raton, FL, 1989; Vol. I, pp 200-29. Horwitz, W.; Kamps, L. R.; Boyer K. W. J . Assoc. Off. Anal. Chem. 1980, 63, 1344-54.


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HORWTTZ

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8. 9. 10. 11. 12. 13.

14. 15. 16.

& ALBERT


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Gladney, E. S.; O'Malley, B. T.; Roelandts, I.; Gills, T. E. Standard Reference Materials: Compilation of Elemental Concentration Data for NBS Clinical, Biological, Geological, and Environmental Standard Reference Materials, National Bureau of Standards Special Publication 260-111, Superintendent of Documents: Washington, DC 20402-9325, 1987. Byrne, F. P. In Accuracy in Trace Analysis, NBS Special Publication 422, Superintendent of Documents, Washington, DC 20402-9325, 1976. Thompson, M. In Proceedings Third International Symposium on the Harmonization of Quality Assurance Systems in Chemical Analysis, 19-20 April 1989, Washington, DC, Prepared by International Organization for Standardization as ISO/REMCO 184, 1989, pp 183-189. Horwitz, W. Pure Appl. Chem. 1988, 60, 855-64. Kelly, P. J . Assoc. Off. Anal. Chem. 1990, 62, 58-64. Boyer, K. W.; Horwitz, W.; Albert, R. Anal. Chem. 1985, 57, 454-9. Act of 22 July 1950; 64 Stat. 371 (Public Law 619, 81 Congress) Amending Sec. 2 of the Act of Mar. 3, 1901, establishing the National Bureau of Standards. Taylor, J . K. Standard Reference Materials: Handbook for SRM Users. US Government Printing Office: Washington DC 20402-9325, 1985; p 27. Unrecorded discussion at Third International Symposium on the Harmonization of Quality Assurance Systems in Chemical Analysis, 19-20 April 1989, Washington, DC; International Organization for Standardization, Geneva, Switzerland. Guidelines for Collaborative Study Procedure to Validate Characteristics of a Method of Analysis. J . Assoc. Off. Anal. Chem. 1989, 72, 694-704. Youden, W. J . Statistical Manual of the AOAC; AOAC: Arlington, VA 22201, 1975; p 30. Holden, J . M.; Schubert, A.; Wolf, W. R.; Beecher, G. R. In Food and Nutrition Bull. Supplement 12, Food Composition Data: A Users Perspective; W. M. Rand; C. T. Windham; R. W. Wyse; V. R. Young, Eds.; United Nations University: Tokyo, 1987; pp 177-93.

RECEIVED July 16,

1990


Biologically Related National Institute of Standards and Technology

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