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GRAPHICAL COMPARISON OF GEOCHEMICAL RESULTS

L. Paul BEDARD

Groupe de Recherche sur le Magmatisme Terrestre, Dkpartement de Gkologie, Universitk de Montrkal, C.P. 6128, Succ. A, Montrkal, QuCbec, Canada H3C 357

Comparison of analytical results obtained for geo- chemical reference samples with accepted results is tedious and error prone. Graphical representation fa- cilitates comparison. Nevertheless, currently used dia- grams lack representativeness when a wide range of concentrations are studied. A newly designed graph representing normalized results against concentrations is proposed. It allows comparison of a wide range of concentrations and helps detect analytical problems for particular ranges of concentrations.

Once concentrations have been determined for a geo- chemical reference sample, they are compared with other results (another laboratory, accepted values, etc.) in tables or through “XY” or 1 : 1 diagrams: determined concentra- tion against a reference result (Figure 1). Although tables are necessary, diagrams can provide a better framework to compare geochemical reference samples or analytical re- sults. “XY” diagrams do not help make realistic compari- sons of results for concentrations of different magnitude. Moreover, in current geochemistry journals, comparative geochemical diagrams for geochemical reference samples do not seem to be widely used. In this article, a normalized diagram is proposed to help the comparison of geochemical results with expected results.

The common way for graphical comparison of two data sets is a XY diagram in which determinations are plotted against a reference value (Figure 1). If analytical errors or standard deviations are plotted, they are difficult to com- pare graphically for samples of different concentrations.

It is proposed that a redesigned diagram be used to emphasize the comparison of results. In order that it be useful, thediagram should: 1- allow comparison of concen- trations of different magnitudes; 2- show analytical errors

0.3 1.0 10 100 1c Accepted Value (ppm)

Figure 1. “X-Y diagram” showing the results of determina- tions for a geochemical reference Sample (MAG-1) com- pared with accepted results. Determinations taken from (1) and reference values from (2) and (4)

(or standard deviations on multiple determinations), and any systematic variations; and 3- maximize data-to-ink ratio (3).

TERMINOLOGY

To make the text clearer, a few terms are defined:

1 - determination is the result of a single analysis on a sample.

2 - accepted value is the concentration of an element for a reference sample from multiple determinations (2).

Geostandards Newsletter, Vol. 18, No I , Avril 1994, p. 101 d 103

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3 - reference value is a value to which it is wished to compare; it can be an accepted or a working value.

4 - result is used as a general term for a determination or a value.

THE DIAGRAM

The proposed diagram shows concentrations on the horizontal axis and normalized results on the vertical axis (Figures 2 and 3). A normalized result is a determination divided by a reference value minus one. Aperfect match of two values produces a normalized result of zero (0). Abso- lute analytical errors have been added in this case and are calculated as follows:

[ (Ro+Er)/Rr 1 - 1 ; { (Ro-Er)/Rr } + 1

where Ro is the obtained result, Er is the absolute analytical error and Rr reference or normalizing value. Either ele- ments or samples may be plotted on the horizontal axis. This diagram also helps to identify analytical problems that can happen at high or low concentrations. A logarithmic scale for concentration (horizontal axis) is preferred because it more evenly distributes the data. In the case of monitoring an internal standard, the horizontal axis becomes the date, determination number, or user, and is then linear (Figure 4).

To be practical, it must be possible to computerize the drafting of such diagrams and a spreadsheet and graphics program does make drafting relatively quick.

ADVANTAGES

The proposed diagrams allows comparison of elements of different concentrations on a common basis because results are normalized. In a standard "XY" diagram (Figure l), precision and/or accuracy for high and low concentrations are difficult to compare (e.g., compare Ba and Lu in Figures 1 and2).

Accuracy of results can be easily visualized by their departure from the 0 line of the normalized axis (Figures 2, 3 and 4). Positive and negative signs will help identify if the results are over or below reference values.

An analytical problem in a particular range of concentra- tion should be easy to identify. In the case of Sc determined by neutron activation (l), this redesigned graph emphasizes the loss of precision and accuracy for low Sc concentrations (Figure 3). This loss is interpreted as the result of detection limit for Sc using this technique.

F

3 4 . 1 5 3 - 3 +0.1

4 .05 2 s o 5 -0.05 al

0 - $ -0.1 - -0.15

-0.2 Y

L, 1 1 1 1 . 1 1 I I 1 1 1 1 1 1 1 I 1 I t 1 1 1 . 1 ' I I I

0.3 1.0 10 100 5( Reference Value (ppm)

Figure 2. Proposed normalized comparison diagram show- ing the same data as in Figure 1. Horizontal ticks are the normalized results with errors shown as vertical bars. De- terminations are from (1 )

Figure 3. Normalized comparison diagram of Sc for differ- ent geochemical reference samples. Determinations are from (1)

Internal Standard Monitoring I Sc(INAA) %

CI)

111 s o

D m - 1 1

-0.05 2 4 6 8 10 12 14 16 18 20 22 24 e Analysis Number

Figure 4. Normalized comparison diagram used to monitor an internal standard. Different determinations are num- bered on the horizontal axis. Data are from determinations on an internal standard. Analytical errors are approximately the size of sample markers (black rectangles) or smaller

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USES

This diagram may be used to compare:

1 - different elements of a sample (Figure 2) in order to verify that a method is valid for a sample type.

2 - concentrations of an element in different samples (Figure 3) to check method validity over an element for different sample types.

valeurs acceptCes est une tiiche ardue ou des erreurs peuvent facilement se glisser. Une reprksentation graphique facilite la comparaison. NCanmoins, les graphiques utilisCs manquent de reprkentativit6 si la gamme de variation est grande. Un nouveau diagramme est propod, prCsentant les rksultats normalis& en fonction des concentrations. I1 permet la comparaison de gammes de teneurs ktendues et facilife la dbtection de problhmes analytiques pour des gammes de teneurs particulihres.

3 - results of an internal reference sample used in every batch (Figure 4) to monitor variations.

REFERENCES CONCLUSION

Comparison of geochemical results by the proposed normalized diagram may help visualize analytical prob- lems. It is less tedious than comparing results in tables, although tables are necessary.

ACKNOWLEDGEMENT

Gilles Gauthier and Cecilia Jenkins made many useful comments on the manuscript. Drs. Brian L. Cousens and John Stix are thanked for their critical comments of an earlier version of the manuscript and Pierre Btdard made useful suggestions on the technicalities of computer graphic. The author acknowledge Le Prkt d’Honneur and NSERC post-doctoral fellowships and support from FCAR funds to John Ludden.

RESUME

La comparaison des rksultats analytiques obtenus pour des khantillom gkochimiques de rCfCrence avec les

(1) L.P. Btdard and S.-J. Barnes (1 990) Instrumental neutron activation analysis by collecting only one spectrum: results for international geochemical refer- ence samples, Geostandards Newsletter, 14: 479-484.

(2) K. Govindaraju (1 989) 1989 Compilation of working values and sample descrip- tion for 272 geostandards, Geostandards Newsletter, 13: Special issue, July 1989, 11 3 p.

(3) E.R. Tufte (1 983) The visuaI display of quantitative information, Graphic Press, Sheshire, Connecticut, U.S.A., 197 p.

(4) E.S. Gladney and I. Roelandts (1988) 1987 compilation of elemental concentration data for USGS

1 and STM-1, Geostandards Newsletter, 12: 253-362. BHVO- 1, MAG- 1, QLO- 1, RGM- 1, SCO- 1, SDC- 1, SGR-