Abstract
In the context of analysis of variance, Box and Cox (1964) developed a generalized technique for power transformation of frequency distributions to normality. It is here applied to geochemical data, based on the nonlinear optimization of skewness and kurtosis. The transform appears to be particularly well suited to the preprocessing of geochemical data prior to multivariate analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahrens, L. H., 1954, The lognormal distribution of the elements: Geochem. Cosmochim. Acta, Part 1, v. 5, p. 49–73; Part 2, v. 6, p. 121–131.
Andrews, D. F., 1971, A note on the selection of data transformations: Biometrika, v. 58, p. 249–254.
Bartlett, M. S., 1947, The use of transformations: Biometrics, v. 3, p. 39–52.
Box, G. E. P. and Cox, D. R., 1964, An analysis of transformations: J. Roy. Stat. Soc., Ser. B., v. 26, p. 211–243.
Chapman, R. P., 1976, Some consequences of applying lognormal theory to pseudolognormal distributions: Math. Geol., v. 8, p. 209–214.
Chapman, R. P., 1977, Log transformations in exploration geochemistry: Math. Geol., v. 9, p. 194–198.
Draper, N. R. and Cox, D. R., 1969, On distributions and their transformation to normality: J. Roy. Stat. Soc., Ser. B., v. 31, p. 472–476.
Draper, N. R. and Hunter, W. G., 1969, Transformations: Some examples revisited: Technometrics, v. 11, p. 23–40.
Dunlap, W. P. and Duffy, J. A., 1974, A computer program for determining optimal data transformations minimizing skew: Behav. Res. Meth. Instru., v. 6, p. 46–48.
Hinkley, D. V., 1975, On power transformations to symmetry: Biometrika, v. 62, p. 101–111.
Himmleblau, D. M., 1972, Applied nonlinear programming (1st ed.): McGraw-Hill Book Co., New York, 498 p.
Hoyle, M. H., 1973, Transformations—an introduction and bibliography: Int. Stat. Rev., v. 41, p. 203–223.
Krumbein, W. C. and Graybill, F. A., 1965, An introduction to statistical models in geology (1st ed.): McGraw-Hill Book Co., New York, 475 p.
Kuester, J. L. and Mize, J. H., 1973, Optimization techniques with Fortran (1st ed.): McGraw Hill, New York, 500 p.
Lindqvist, L., 1976, SELLO, a Fortran IV program for the transformation of skewed distributions to normality: Comput. Geosci. v. 1, p. 129–145.
Link, R. F. and Koch, G. S., 1975, Some consequences of applying lognormal theory to pseudolognormal distributions: Math. Geol., v. 7, p. 117–128.
Maclean, C. J., Morton, N. E., Elston, R. C., and Yee, S., 1976, Skewness in commingled distributions: Biometrics, v. 32, p. 695–699.
Miesch, A. T., 1977, Log transformations in geochemistry: Math. Geol. v. 9, p. 191–194.
Miller, R. L. and Kahn, J. S., 1962, Statistical analysis in the geological sciences (1st ed.): John Wiley & Sons Inc., New York, 483 p.
Nichol, I., Thornton, I., Webb, J. S., Fletcher, W. K., Horsnail, R. J., Khaleelee, J., and Taylor, D., 1970, Regional geochemical reconnaissance of the Denbighshire area: Rep. Inst. Geol. Sci. (London). no. 70/8, 40p.
Shaw, D. M., 1961, Element distribution laws in geochemistry: Geochem. Cosmochim. Acta, v. 23, p. 116–134.
Sinclair, A. J., 1976, Applications of probability graphs in mineral exploration: Association of Exploration Geochemists, Special Vol. no. 4, 96 p.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Howarth, R.J., Earle, S.A.M. Application of a generalized power transformation to geochemical data. Mathematical Geology 11, 45–62 (1979). https://doi.org/10.1007/BF01043245
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01043245