A Critical Evaluation of Correlation Methods in Climatology and Hydrology

Abstract

The sampling properties of three types of correlation coefficients are examined critically with reference to the practical problem of selecting a statistic optimally suited to correlation analyses in climatology and hydrology. Reasons are presented for concluding (1) that undue concern has been given the problem of non-normality of underlying frequency distributions, and (ii) that application of significance tests and determinations of confidence limits for the product-moment coefficient, r, are quite adequately achieved through simple use of the standard error of r. It is suggested that the growing tendency in climatology and hydrology to employ unnecessarily elaborate methods stems jointly from characteristic emphasis upon theoretical refinements found 1n most statistics references and from neglect on the part of users of statistics to examine the numerical magnitudes of these refinements in relation to basic data-precision and to desired precision of inference. The properties of a tetrachoric and a rank correlation coefficient are discussed, and it is concluded that in many geophysical applications, especially in cases of moderate sample sizes, the Spearman rank-difference coefficient should be regarded as the preferred correlation statistic. Em- . pirical comparison of these three coefficients are presented for a sample of precipitation data taken from a region (Arizona) where non-normality of precipitation frequency .distributions .. is known to be extreme. The rank difference coefficient is found to lie within one standard error of r for eleven of fourteen cases in this sample. The tetrachoric coefficient is found to be a much poorer estimate of r, yet in thirteen of fourteen cases it yields (on an approximation basis) the same inferences as does r with regard to existence of correlation.