From Star Charts to Stoneflies: Detecting Relationships in Continuous Bivariate Data
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Date
1998
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Abstract
Within many ecological systems, relationships between controlling factors
and associated response variables are complex. In many cases, the response should vary
little when the controlling factor exerts strong effects. Conversely, when the effect of the
controlling factor is weak or absent, the response may vary greatly with effects of other
factors. Correlation or regression analyses often may not be appropriate for testing these
relationships, because variance of the response changes with values of the controlling factor.
We suggest using a technique from the astronomy literature, a two-dimensional Kolmogorov-
Smirnov (2DKS) test, to detect relationships in bivariate data with these patterns of
variance. This technique successfully identified simulated bivariate data composed of paired
independent values as having nonsignificant relationships and simulated bivariate data in
which mean and variance of y was constrained at high levels of x as having significant
relationships. Using these simulations and examples from aquatic and terrestrial systems,
we demonstrate that the 2DKS is a robust test for detecting nonrandom patterns in bivariate distributions that commonly arise in many ecological systems.
Description
Keywords
bivariate distributions, correlation, limiting factors, nonparametric test, statistical test, two-dimensional Kolmogorov-Smirnov test (2DKS), variance, ecological systems
Citation
Garvey, James E.; Marschall, Elizabeth A.; Wright, Russell A. "From Star Charts to Stoneflies: Detecting Relationships in Continuous Bivariate Data," Ecology, v. 79, no. 2, 1998, pp. 442-447.