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Separation coefficient for analysis of large environmental data sets: Ion concentrations of lake superior and lake huron
Author(s) -
Jensen A. L.
Publication year - 1991
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.3770020306
Subject(s) - statistics , separation (statistics) , statistic , sample size determination , sample (material) , mathematics , environmental science , coefficient of variation , chemistry , chromatography
When statistical hypotheses are tested with large environmental data sets, such as those available for ionic constituents of the Great Lakes, even small differences between means are detectable, and the usual result is that all or nearly all differences tested are statistically significant. In this situation, hypothesis testing is not useful. Differences between means also are not useful for comparisons because of differences in units of measurement and variances. The t ‐statistic is used to determine if two populations are significantly different, but the value of t is not useful for evaluating the degree of separation of two populations because the value of t is influenced by sample size, t has no lower or upper bound, and the value of t has no meaningful interpretation. A separation coefficient is developed that measures the proportion overlap of two normally distributed populations; it is not influenced by sample size, is easily calculated, and takes values between 0 and 1. The separation coefficient was applied to examine differences in ion concentrations between Lake Superior and Lake Huron. The sample sizes were large and all differences were statistically significant, but the coefficients of separation varied from 0.07 to 1, which indicates that concentrations of some ions in the lakes were more similar than others. The pattern in the coefficients of separation indicate meaningful differences between the lakes.