Areal Variation and Statistical Correlation
Correlations introduced between pairs of otherwise statistically independent and uncorrelated variates by similarity in their areal map patterns can be evaluated by partitioning the observed variance-covariance matrices into a trend component and a residual. If the original variates are correlated and have areal trends as well, the problem becomes complicated for sedimentological studies in which only one sample can be taken at any given map point. The situation becomes even more complicated when initially open data are closed, as by taking percentages.
This paper reviews the topic in terms of as yet unpublished work in the past two years. Several possible sources of covariance in sedimentary data are discussed, and it is emphasized that although the effect of map trends can be satisfactorily estimated, some other covariance components are confounded with residual effects. The general conclusion is reached that sedimentological correlation studies of environmental areas need to be supplemented by trend analysis to detect situations in which a seeming correlation is simply the result of similar areal responses by a given pair of variates to a common set of environmental conditions.
KeywordsStatistical Correlation Point Correlation Covariance Component Trend Component Areal Pattern
Unable to display preview. Download preview PDF.
- Chayes, F., 1960, On correlation between variables of constant sum: Jour. Geophysical Res., v. 65, no. 12, p. 4185–4193.Google Scholar
- Chayes, F., 1971, Ratio correlation: Univ. Chicago Press, Chicago, 99 p.Google Scholar
- Krumbein, W. C., 1972, Areal variation and statistical correlation in open and closed number systems: Intern. Assoc. Stat., Phys. Sci., Proc. (in press).Google Scholar
- Krumbein, W. C., and Jones, T. A., 1970, The influence of areal trends on correlation of sedimentary attributes: Jour. Sed. Pet., v. 40, no. 2, p. 656–665.Google Scholar
- Krumbein, W. C., and Watson, G. S., 1972, The effect of trends on correlation in open and closed three-component systems: Jour. Intern. Assoc. Math. Geol. (in preparation).Google Scholar
- Mirchink, M. F., and Bukhartsev, V. P., 1960, The possibility of a statistical study of structural correlations: Dokl. Earth Sci. Sect., v$1126, no$15, p. 1062–1065 (English Translation, p. 495–497 ).Google Scholar