Statistical Primer

Sections of this document:

• Interpreting Results
• Statistical Analysis
• Variable Names & Descriptions
• Technical Details
• References

Relative risk is a statistical method widely applied in human health reporting to summarize and compare the risk of developing an illness for a given set of factors. This approach has been adapted to summarize the effects of different stressors on the environmental health of streams. Because streams experience a variety of stressors (e.g., increased nutrients, loss of riparian habitat, sediment), resource managers need a method to identify which threats present the greatest risk in order to implement effective programs to protect them. Relative risk summarizes the strength of the association between a stressor and an indicator of stream condition.

This databrowser links relative risk calculations to the national Wadeable Streams Assessment data set which used benthic macroinvertebrates to assess stream condition. The databrowser allows users to compare the relative importance of various stressors across political or ecological regions.

The map below shows results for IBI in the eastern U.S. Individual sampling locations are coded on the map according to whether the IBI indicated good or poor condition.

The graph for relative risk shows that six of the eight stressors had a significant association between poor condition for stressors and poor condition for IBI (the black line denoting the confidence interval does not include 1.0). Salinity and total nitrogen had a similar value for relative risk, ~1.75. In other words, the risk of poor IBI was 1.75 times greater in streams with poor values for either salinity or total N.

To interpret this result for planning purposes, relative risk information must be paired with information on relative extent. Although relative risk values were similar, very few stream miles were affected by poor values for salinity (< 5%). In contrast, about 38% of stream miles had poor values for total N. Thus, a more protective management plan would emphasize reduction of nutrients rather than salinity.

Note: Click on the map to create a .pdf file.

Relative risk is based on categorical classification of all variables; therefore, continuous variables must be first recoded as indicating “good” or “poor” condition. Different coding criteria were used for each variable. For acidification, criteria from the National Acid Precipitation Assessment Program (NAPAP) were used to define acid mine drainage and acid rain deposition effects. For salinity, best professional judgment was used. All other measures of biological condition, nutrients and physical habitat used a reference condition approach (see figure). Reference condition was defined in each region using independent measures of site condition and human influence and values for sites in those areas were used to define the reference distribution. For most variables a category described as “marginal” was also defined. Values in this category were not included in any of the calculations of relative risk.

Relative risk is calculated as the ratio between the risk of poor indicator values given poor stressor values and the risk of good indicator values given poor stressor values. Example data are given to illustrate this calculation in the table below.

 
          Excess sed GOOD   Excess sed POOR
IBI GOOD  59                4
IBI POOR  18                19
Total     77                23

For the example, relative risk is calculated as the ratio of:

Poor IBI, given Poor Excess sediment (19/23 = 0.83) and the risk of Poor IBI, given Good Excess sediment (18/77 = 0.23).

RR = Pr(Poor IBI | Poor Excess sediment) / Pr(Poor IBI | Good Excess sediment)

   = 0.83/0.23

   = 3.6

We would conclude from these data that the risk of Poor IBI is 3.6 times greater in streams with Poor Excess sediment than in streams with Good Excess sediment. In other words, excess sediment looks like a potentially important stressor for macroinvertebrates.

The next question to ask relates to the relative extent of the stressor. If many of the stream miles in the area have values indicating poor condition for excess sediment, this stressor and the human activities that drive it should be addressed with management actions.

For more information regarding the derivation of indicators or stressors from raw data, see Appendix A of the Wadeable Stream Assessment Report ADD REPORT LINK.

Biological Indicators

IBI

multimetric index summarizing regionally appropriate metrics for benthic macroinvertebrate assemblages (e.g., taxa richness or relative abundance of key groups)

O/E

Measure of taxa loss derived from a ratio of taxa observed at a site over taxa expected for a particular habitat type

Stressors

Human disturbance

Tally of different human activities in riparian area e.g., mining, row-crop agriculture, roads, landfills, buildings, grazing, channel revetment, silviculture

Salinity

Specific conductance

Acidification

Derived from measures of acid neutralizing capacity, sulfate, and dissolved organic carbon

Woody vegetation cover

Amount of riparian woody cover including ground layer, woody shrubs, and canopy trees

Natural fish cover

Natural types of cover within the stream (e.g., boulders, undercut banks, large wood, overhanging vegetation); a measure of habitat complexity for fish

Excess fine sediment

Deviation of %fines from expected value (aka, excess fines)

Total N

Total nitrogen

Total P

Total phosphorus

The statistical calculation routines were developed using the statistical language R. The routines can be downloaded from EPA's Aquatic Resources Monitoring site. The graphical user interface for the databrowser is written in HTML and passes client queries for specific variables to EPA's web server. A Python based CGI script on the web server converts the client's requests into a series of R commands that run the statistical routines for the variables selected by the client at the interface. Then the output from R is passed back to the client in the form of graphics.

Wadeable Stream Assessment: a Collaborative Survey of the Nation’s Streams. EPA 841-B-06-002. December 2006. (report)

Van Sickle, J., J. L. Stoddard, S.G. Paulsen, and A.R. Olsen (2006). Using relative risk to compare the effects of aquatic stressors at a regional scale. Environmental Management 38:1020-1030.

Evaluating the Extent and Relative Risk of Aquatic Stressors in Wadeable Streams throughout the U.S.A. (powerpoint) Van Sickle, J., J. L. Stoddards, S. G. Paulsen. Paper presentation at the 2006 National Monitoring Conference, San Jose, California.

R software to calculate relative extent and relative risk. www.epa.gov/nheerl/arm/