P.Filzmoser et al.Computers Geosciences 31 (2005)579-587 587 former in more detailed studies.Unfortunately.the Banks.D.(Eds.).Encyclopedia of Statistical Sciences EDA approach is often misused for a detailed process Update,Vol.2.Wiley,New York.NY.pp.589-596. study,leading to questionable conclusions. Reimann,C.Ayras,M.,Chekushin,V.,Bogatyrev,I.,Boyd, We conclude that proper exploratory data analysis R.,Caritat,P.De.,Dutter,R.,Finne,T.E..Halleraker,J.H.. and outlier recognition plays an essential part in the Jager,.Kashulina,G.,Lehto,O.,Niskavaara.H.. interpretation of geochemical data,and we suggest,data Pavlov,V.,Raisanen,M.L.,Strand,T.,Volden,T.,1998 Environmental Geochemical Atlas of the Central Barents from other geoscience and physical science studies. Region.NGU-GTK-CKE Special Publication,Geological The method has been implemented in the free statistical Survey of Norway.Trondheim,Norway 745pp. software package R(see http://cran.r-project.org/).It is Reimann,C.,Banks,D.,Kashulina.G.,2000.Processes available as a contributed package called "mvoutlier", influencing the chemical composition of the O-horizon of and it contains all the programs to the proposed methods podzols along a 500 km north-south profile from the coast and additionally valuable data sets from geochemistry, of the Barents Sea to the Arctic Circle.Geoderma 95. like the Kola data (Reimann et al.,1998)and data from 113-139. Northern Europe(Reimann et al.,2003). Reimann,C..Filzmoser,P..Garrett,R.G.,2002.Factor analysis applied to regional geochemical data:problems and possibilities.Applied Geochemistry 17(2). 185-206. References Reimann,C..Filzmoser,P..Garrett.R.G..2005.Background and threshold:critical comparison of methods of determi- Chork.C.Y..1990.Unmasking multivariate anomalous ob- nation.Science of the Total Environment,in press. servations in exploration geochemical data from sheeted- Reimann,C..Siewers.U.,Tarvainen,T.,Bityukova,L.. vein tin mineralisation near Emmaville,N.S.W.,Australia. Eriksson,J.,Gilucis,A.,Gregorauskiene,V.,Lukashev, Journal of Geochemical Exploration 37(2),205-223. V.K.,Matinian,N.N.,Pasieczna,A.,2003.Agricultural Chork.C.Y.,Salminen,R..1993.Interpreting exploration soils in Northern Europe:a geochemical atlas.Geologisches geochemical data from Outukumpu,Finland:a Jahrbuch,Sonderhefte,Reihe D,Heft SD 5.2003. MVE-robust factor analysis.Journal of Geochemical Schweizerbart'sche Verlagsbuchhandlung. Stuttgart, Exploration 48(1),1-20. Germany,279pp. Csorgo,M.,Revesz,P.,1981.Strong Approximations in Rose.A.W..Hawkes.H.E..Webb.J.S..1979.Geochemistry in Probability and Statistics.Academic Press,New York. Mineral Exploration,second ed.Academic Press,London NY 284pP. 657pp. Garrett,R.G.,1989.The chi-square plot:a tool for multivariate Rousseeuw,P.J.,1984.Least median of squares regression. outlier recognition.Journal of Geochemical Exploration 32 Journal of the American Statistical Association 79 (388). (1/3),319-341. 871-880. Gervini.D..2003.A robust and efficient adaptive reweighted Rousseeuw,P.J.,1985.Multivariate estimation with high estimator of multivariate location and scatter.Journal of breakdown point.In:Grossmann,W.,Pflug,G.,Vincze, Multivariate Analysis 84,116-144. I..Wertz,W.(Eds.),Mathematical Statistics and Applica- Gnanadesikan,R..1977.Methods for the Statistical Data tions,vol.B.Akademiai Kiado,Budapest,Hungary, Analysis of Multivariate Observations.Wiley,New York, pp.283-297. NY 311PP. Rousseeuw,P.J..Van Driessen,K..1999.A fast algorithm for Hampel,F.R.,Ronchetti,E.M..Rousseeuw,P.J.,Stahel,W.. the minimum covariance determinant estimator.Techno- 1986.Robust Statistics.The Approach Based on Influence metrics 41,212-223. Functions.Wiley,New York,NY 502pp. Rousseeuw,P.J.,Van Zomeren,B.C.,1990.Unmasking multi- Maronna,R.A.,Yohai,V.J.,1998.Robust estimation of variate outliers and leverage points.Journal of the Amer- multivariate location and scatter.In:Kotz,S.,Read,C.. ican Statistical Association 85(411),633-651.former in more detailed studies. Unfortunately, the EDA approach is often misused for a detailed process study, leadingto questionable conclusions. We conclude that proper exploratory data analysis and outlier recognition plays an essential part in the interpretation of geochemical data, and we suggest, data from other geoscience and physical science studies. The method has been implemented in the free statistical software package R (see http://cran.r-project.org/). It is available as a contributed package called ‘‘mvoutlier’’, and it contains all the programs to the proposed methods and additionally valuable data sets from geochemistry, like the Kola data (Reimann et al., 1998) and data from Northern Europe (Reimann et al., 2003). References Chork, C.Y., 1990. Unmaskingmultivariate anomalous ob￾servations in exploration geochemical data from sheeted￾vein tin mineralisation near Emmaville, N.S.W., Australia. Journal of Geochemical Exploration 37 (2), 205–223. Chork, C.Y., Salminen, R., 1993. Interpretingexploration geochemical data from Outukumpu, Finland: a MVE-robust factor analysis. Journal of Geochemical Exploration 48 (1), 1–20. Cso¨rgo+, M., Re´ve´sz, P., 1981. StrongApproximations in Probability and Statistics. Academic Press, New York, NY 284pp. Garrett, R.G., 1989. The chi-square plot: a tool for multivariate outlier recognition. Journal of Geochemical Exploration 32 (1/3), 319–341. Gervini, D., 2003. A robust and efficient adaptive reweighted estimator of multivariate location and scatter. Journal of Multivariate Analysis 84, 116–144. Gnanadesikan, R., 1977. Methods for the Statistical Data Analysis of Multivariate Observations. Wiley, New York, NY 311pp. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W., 1986. Robust Statistics. The Approach Based on Influence Functions. Wiley, New York, NY 502pp. Maronna, R.A., Yohai, V.J., 1998. Robust estimation of multivariate location and scatter. In: Kotz, S., Read, C., Banks, D. (Eds.), Encyclopedia of Statistical Sciences Update, Vol. 2. Wiley, New York, NY, pp. 589–596. Reimann, C., A¨yra¨s, M., Chekushin, V., Bogatyrev, I., Boyd, R., Caritat, P.De., Dutter, R., Finne, T.E., Halleraker, J.H., Jæger, Ø., Kashulina, G., Lehto, O., Niskavaara, H., Pavlov, V., Ra¨isa¨nen, M.L., Strand, T., Volden, T., 1998. Environmental Geochemical Atlas of the Central Barents Region. NGU-GTK-CKE Special Publication, Geological Survey of Norway, Trondheim, Norway 745pp. Reimann, C., Banks, D., Kashulina, G., 2000. Processes influencingthe chemical composition of the O-horizon of podzols alonga 500 km north–south profile from the coast of the Barents Sea to the Arctic Circle. Geoderma 95, 113–139. Reimann, C., Filzmoser, P., Garrett, R.G., 2002. Factor analysis applied to regional geochemical data: problems and possibilities. Applied Geochemistry 17 (2), 185–206. Reimann, C., Filzmoser, P., Garrett, R.G., 2005. Background and threshold: critical comparison of methods of determi￾nation. Science of the Total Environment, in press. Reimann, C., Siewers, U., Tarvainen, T., Bityukova, L., Eriksson, J., Gilucis, A., Gregorauskiene, V., Lukashev, V.K., Matinian, N.N., Pasieczna, A., 2003. Agricultural soils in Northern Europe: a geochemical atlas. Geologisches Jahrbuch, Sonderhefte, Reihe D, Heft SD 5, 2003, Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, Germany, 279pp. Rose, A.W., Hawkes, H.E., Webb, J.S., 1979. Geochemistry in Mineral Exploration, second ed. Academic Press, London 657pp. Rousseeuw, P.J., 1984. Least median of squares regression. Journal of the American Statistical Association 79 (388), 871–880. Rousseeuw, P.J., 1985. Multivariate estimation with high breakdown point. In: Grossmann, W., Pflug, G., Vincze, I., Wertz, W. (Eds.), Mathematical Statistics and Applica￾tions, vol. B. Akade´miai Kiado´, Budapest, Hungary, pp. 283–297. Rousseeuw, P.J., Van Driessen, K., 1999. A fast algorithm for the minimum covariance determinant estimator. Techno￾metrics 41, 212–223. Rousseeuw, P.J., Van Zomeren, B.C., 1990. Unmaskingmulti￾variate outliers and leverage points. Journal of the Amer￾ican Statistical Association 85 (411), 633–651. ARTICLE IN PRESS P. Filzmoser et al. / Computers & Geosciences 31 (2005) 579–587 587