Van Sickle, J. 2003. Analyzing correlations between stream and watershed attributes. J. Am. Water Resources Assn. 39(3):717-726. WED-02-183
Bivariate correlation analysis has been widely used to explore relationships between stream and watershed attributes that have all been measured on the same set of watersheds or sampling locations. Researchers routinely test H0: ρ=0 for each correlation in a large table and then go on to discuss only those that are declared “significant.” Such test results are inaccurate because no allowance is made for multiple testing, and also because the tests are not mutually independent. I review the Bonferroni approach to controlling the overall error rate in ultiple testing and show how the approach becomes impractical for large correlation tables. The Hotelling/Williams test is introduced for comparing two dependent correlations that share a variable, and numerical constraints for two such correlations are illustrated. References are also given for testing other hypothesized patterns among dependent correlations, and links to dependent-correlation software are provided. The methods are illustrated for watershed and stream variables sampled in 23 small agricultural watersheds of the Willamette Valley, Oregon.