CADDIS Volume 4: Data Analysis
Selecting an Analysis Approach
 How Can I Use My Data?
 Establishing Differences From Expectations
 Estimating StressorResponse Relationships
Estimating StressorResponse Relationships from Field Data
 Author: L.L. Yuan
Estimating StressorResponse Relationships from Field Data
StressorResponse relationships estimated from field data can potentially inform two types of evidence: stressorresponse from the case and stressorresponse from other field studies.
Stressorresponse from the case
For this type of evidence, an association in which the magnitude of the biological response decreases as stressor levels decrease in measurements collected from the same stream would be consistent with a causal relationship. This relationship between stressor and response can be shown simply with a scatterplot. In cases in which the variability in the measured response data is too high to discern a response, a regression fit to the data may help assess whether biological response changes as hypothesized.
Analytical tools used to support this type of evidence:
Stressorresponse from other field studies
For this type of evidence, we use data collected from a larger study area to quantify the effects of the stressor on the biological response. Accurate estimates of effects can be difficult to obtain because of the strong possibility of covarying factors in fieldcollected data. In many cases, a more attainable analysis goal may be to simply determine whether the stressor of interest causes effects in the biological response.
A methodical approach to analysis can be helpful, including the following steps:

Explore associations between variables in the data set.
Identify extreme observations and autocorrelation that may influence estimates of relationships.
Calculate correlations and view scatterplots to reveal relationships between pairs of variables.
Use multivariate approaches to reveal relationships among groups of variables
Identify variables that may confound the estimated relationship.
Estimate effects.
Classification and regression trees can suggest possible discontinuities in relationships of interest.

Regression analysis provides an estimate of the mean relationship between the biological response and stressor of interest. In some cases, the effects of possible confounding variables can be controlled by including them in the regression model, but estimates of effect may be unreliable when variables covary too strongly.

Quantile regression provides a way to estimate the upper bound of the relationship between a stressor and a biological response. Under certain assumptions, this upper bound may provide a reasonably accurate estimate of the stressorresponse relationship.

Propensity score analysis provides a powerful means of controlling for the effects of covarying variables, and accurately estimating effects.
Interpret results.
 Have most potential confounders been treated in the analysis?
 What do the significance test results mean?