Geology - Use of Nonparametric Statistical Tests in the Interpretation of Geological Data

Nonparametric statistical tests have practical application to many geological problems because, unlike the standard statistical tests, they do not require assumptions regarding the form of the population frequency distribution. Many of them do not even require that the variable be susceptible to numerical measurement. These tests are useful either 1) for geological data representing population distributions of unknown form, or otherwise not meeting the requirements for standard parametric tests; or 2) for sample attributes that cannot be measured but only ranked in order of relative magnitude. The application of two such tests will be illustrated. The Kolmogorov-Smimov test will be used to test for significant differences in copper distribution in samples of two rock types; the Spearman rank-correlation method will be used to determine whether there is a significant association between intensity of rock alteration and copper content of the rock. Nonparametric tests are, in general, quicker and easier to perform than the corresponding parametric tests, and they may be applied to a greater variety of data. They are not as powerful as the standard tests if used on data to which the latter are applicable, and computer programs utilizing them are not generally available. The use of standard or parametric statistical procedures for the interpretation of measured geological data is familiar to most mining engineers and explora- tion geologists. The computation of product moment correlation coefficients on sample assays for more-than one component is already standard procedure in some company operations, as is the use of Student's F test and Snedecor's F test for the comparison of means and variances of sample groups. The application of these three tests is limited by the prerequisites that the samples must be random, independent representatives of normally distributed populations and that the variables involved must be measurable. If such tests are applied to data which fall short of fulfilling these prerequisites, then the probability level attributed to the computed statistic is invalid and the conclusions based thereon may be erroneous. A number of nonparametric, or distribution free, statistical tests have been developed for use with data which are not amenable to standard parametric procedures. These tests have been widely used in the behavioral sciences such as psychology and sociology for some time, but their application to geologic problems is relatively new. Nonparametric tests may be grouped into two main categories: those which test for significant differences in a single variable by comparing either sample values with a standard value or representative values between two or more groups of samples; and those which test for significant association between pairs of variables in a single group of samples. The versatile chi square test, the Kolmogorov-Smirnov one and two sample tests, the Wilcox matched pairs signed ranks test, the median test, the Mann-Whitney U test and the Cochran Q test are examples of nonparametric tests with demonstrated or potential geological applications that belong in the first category. The contingency coefficient, Spearman rank correlation coefficient, Kendall rank correlation coefficient and the