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Correlation
description | simple example | MAIA example | diatom example | how it works | caveats
Description: You give correlation 2 variables that you suspect are related and the model tells you how closely associated the 2 variables are. The test returns r-values that range from 0 to 1. A value of 1 (or -1) indicates a perfect linear correlation; 0 indicates no linear relationship.
Simple example: You would like to test whether large organic debris and canopy cover increase together for stream sites. Correlation is the appropriate test if you expect an approximately linear relationship.
MAIA example: For the development of a fish multimetric index, candidate fish metrics were tested against 15 different stressors, such as acidic condition, percent fines and riparian vegetation, and 1 measure of natural variability, stream slope (Stoddard, pers. comm. and McCormick, et al. in review). Fish metrics that were significantly correlated with multiple measures of disturbance (and not strongly correlated with stream slope) were selected as metrics.
Figure
Figure: Correlation of intolerant taxa richness (fish) with multiple measures of human disturbance. Significant correlations are outlined in red. Stream slope was strongly associated with some fish metrics but not related to human disturbance, rather it was a natural feature of streams. Strong correlation with slope resulted in a candidate metric not being selected for the index.
Diatom example: Diatom metrics and human disturbance - Biological metrics must be tested for their association with human disturbance before they are used to assess water resources.
To summarize the intensity of human disturbance in a watershed, Bryce et al. (1999) used topographic maps, aerial photos, and field information to develop an index of human disturbance in each watershed. The index grouped sites into five categories ranging from 1 (indicating minimal risk of impairment) to 5 (indicating very high risk of impairment).
Several diatom metrics were significantly correlated with the risk index, three are pictured at right. The percentage of diatom valves belonging to salt tolerant species increased with disturbance, possibly due to the chloride in treated wastewater, the chemicals used to remove road ice in winter, or other industrial sources. The percentage of valves belonging to intolerant species declined steadily as disturbance increased. The percentage of valves belonging to very motile genera increased with disturbance. Motile diatoms can move and avoid being buried by sediment associated with erosion.
How the method works: The correlation coefficient, r, is calculated by multiplying the pairs of values for the 2 variables being considered. The values are summed for all cases and divided by the square of the sum of the values for each variable. Thus, r is a measure of the closeness of association between the 2 variables.
Assumptions/alternatives: Be aware that larger sample sizes are more likely to show statistical significance even when the strength of the correlation is very low; this is true of most tests. Always consider the size of the r-value when evaluating results.
The relationship between the variables is assumed to be linear, so the test may not detect a strongly curvilinear relationship as significant. Always plot your data.
Correlation and regression are very similar and will typically give you the same answer as to whether the relationship between 2 variables is statistically significant. Results from significance testing are most likely to differ when large outliers are present and significance is marginal, that is, the extreme values determine significance.