Transcript 50_Analysis & interpretation

Steps 3 & 4:
Analysis & interpretation of evidence
Hypothesis testing: a simple scenario
SCENARIO 1
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DO measured upstream &
downstream over 9 months
SCENARIO 2
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Upstream = 9.3 mg/L
— Downstream = 8.4 mg/L
Upstream = 7.9 mg/L
— Downstream = 4.2 mg/L
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Difference significant at
P<0.05
DO measured upstream &
downstream over 3 months
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Difference not significant at
P<0.05
Which scenario presents a stronger case for DO
causing impairment?
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Using statistics responsibly
Use caution in interpreting differences
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Look at magnitude & consistency of differences, rather
than statistical significance
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Statistical significance detects differences exceeding
natural variance
— Does not detect stressor effects
— Does not equal biological significance
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Can use statistics, but also use your head
— Consider relationship between minimum detectable
difference (power) & biologically relevant difference
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That said, graphs & statistics can help a lot…
STEP 2
STEP 3
STEP 4
List candidate
causes
Evaluate data
from case
Evaluate data
from elsewhere
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Regression analysis
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Predicting environmental
condition from biological
observations (PECBO)
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Scatterplots
Boxplots
Correlation analysis
Conditional probability analysis
Classification & regression tree
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Species sensitivity distributions
(SSDs)
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Quantile regression
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Sampling/data collection issues
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Want to collect candidate cause & biological response
variables at same sites, at same times
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Want to time sampling to accurately assess exposures
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For continuous exposures, try to catch sensitive life
stages & conditions that enhance exposure or effects
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For episodic exposures, try to characterize episodes
through continuous, event, and post-event sampling
Want to collect good reference comparisons, in space
& time
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At unimpaired sites, at same times you sample impaired
sites
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Data analysis tools
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Species sensitivity distribution (SSD) generator
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Tool that calculates & plots proportion of species affected at
different levels of exposure in laboratory toxicity tests
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Data analysis tools
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Species sensitivity distribution (SSD) generator
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Command-line R scripts
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Tool that calculates & plots proportion of species affected at
different levels of exposure in laboratory toxicity tests
Powerful and free statistical package [http://www.r-project.org/]
R scripts provided for PECBO (predicting environmental
conditions from biological observations)
CADStat
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Menu-driven package of data visualization & statistical
techniques, based on JGR (Java GUI for R)
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R
R is a powerful and free statistical package…
[http://www.r-project.org/]
…but it’s run at the command line, so there’s a steep learning curve
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JGR/CADStat: a gentler introduction to R
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JGR provides point-and-click tools for
basic R functions
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Loading data
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Scatterplots
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Setting up a workspace
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Boxplots
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Managing data in your workspace
Correlation analysis
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Installing packages
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Linear regression
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Quantile regression
CADStat adds several tools to JGR
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Point-and-click interfaces for tools useful
in causal analysis
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Conditional
probability analysis
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Rendering of analysis results in browser
window
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PECBO
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Additional help files
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Load your data into CADStat, or use example data…
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Where are we?
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Step 1 
— Biological effects of interest defined
— Impaired & reference sites identified
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Step 2 
— Map completed
— Conceptual model developed
— Candidate causes identified
— Data identified & collected
Now we’re ready to analyze available data &
use results as evidence in Steps 3 & 4
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Begin with data exploration
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Want to examine relationships between different
variables
— Linear & more complex
— Expected & unexpected
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1st step is visualizing data
— Scatterplots & boxplots
— No statistics, hypotheses, or p-values
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Looking at your data…
examples from exercise
PC1 – reference PC2 – impaired
Dissolved oxygen (mg/L)
7.3
7.9
Canopy cover
moderate
low
EPT taxa richness over time
2004
2005
2006
2007
PC1
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PC2
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9
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In Fall 2004, an unpermitted industrial
discharge with high metal concentrations
was discovered and removed, just
upstream of PC2.
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Which candidate cause do the data relate to?
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Do the data support or weaken the case for the candidate cause?
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What type of evidence do the data represent?
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Boxplots
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Depict distribution of
observations
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Center box indicates spread of 50%
of observations
Whiskers indicate either max & min
values, or 1.5X the interquartile
range
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Good data exploration &
visualization tool
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Can be used to evaluate data from
case & data from elsewhere
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Spatial/temporal co-occurrence
Stressor-response relationships
from the field or from other field
studies
Causal pathway
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Scatterplots
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% Non-insects
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H
G
D
E
C
B F
200
400
600
800
A
1000
Conductivity (uS/cm)
Good data exploration & visualization
tool
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Dependent variable (y-axis) vs. independent
variable (x-axis)
Often dependent variable is biological
response, independent variable is measure of
candidate cause
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Graphical displays of matched data
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EPT Richness
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Can view several at once in
scatterplot matrix
Can be used to evaluate data from
case & from elsewhere
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Stressor-response relationships from
the field, from other field studies, &
from laboratory studies
Causal pathway
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Examples from exercise: scatterplots
EPT taxa richness
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PC1
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PC2
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Maximum summer water temperature (˚C)
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Do the data support or weaken the case for temperature as a
candidate cause?
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What type(s) of evidence do these data provide?
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EPT taxa richness
Examples from exercise: scatterplots
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Log [Zn], ug/L
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1
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Log [Cu], ug/L
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Do the data support or weaken the cases for copper & zinc as
candidate causes?
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What type(s) of evidence do these data provide?
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Correlation analysis
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Method for measuring degree of association between 2 variables
in a matched data set
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Correlation coefficient provides quantitative measure of degree to which 2
variables co-vary
Elevation
Water
Temp
Air
Temp
Log
Conductivity
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-0.75
-0.25
-0.02
Water Temp
-0.75
1
0.64
0.07
Air Temp
-0.25
0.64
1
0.39
Log
Conductivity
-0.02
0.07
0.39
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Elevation
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Good data exploration tool
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Can be used to evaluate data from case
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Stressor-response relationships from the field
Causal pathway
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Regression analysis
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Method for quantifying relationship
between dependent & independent
variable
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Can have ≥ 1 independent variables
Models can be used to:
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Predict value of response
variable for new values of
explanatory variable
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Estimate value of explanatory
variable needed to account for
change in response variable
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Model natural variation in
stressors, to define reference
expectations
90th percentile prediction limits
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Quantile regression
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Models relationship between
specified quantile of response
variable and explanatory
variable (stressor)
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50th quantile gives median
line, under which 50% of
observed responses occur
90th quantile gives line under
which 90% of observed
responses occur
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Provides means of estimating location of upper boundary on
scatterplot
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Used to evaluate stressor-response relationships from other field
studies (Step 4: Evaluating data from elsewhere)
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Applying quantile regression
SUPPORTS
WEAKENS
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Predicting environmental conditions from
biological observations (PECBO)
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Uses taxa list & niche characteristics to predict environmental
conditions at site
Maximum likelihood
inference based on taxonenvironment relationships
Predicted temperature if
both Ameletus & Diphetor
are present at site
Ameletus
Diphetor
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Useful when environmental
data not available
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Using PECBO to verify predictions
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Biologically-based predictions can provide valuable
supporting evidence, under “Verified predictions”
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If stressor elevated at site,
can test hypothesis that
biologically-based
prediction should also be
elevated
Tools for calculating taxonenvironmental relationships
& PECBO available on CADDIS
R2 = 0.67
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Species sensitivity distributions (SSDs)
An SSD is a statistical distribution describing the variation of responses
of a set of species to a stressor; it can be used to estimate the
proportion of species adversely affected at a given stressor intensity.
SSD plot showing LC50s for arthropods
exposed to dissolved cadmium
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Now where are we?
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Step 1 
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Biological effects of interest defined
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Impaired & reference sites identified
Step 2 
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Map completed
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Conceptual model developed
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Candidate causes identified
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Data identified & collected
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Steps 3 & 4 
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Available data examined &
analyzed
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Available data organized into
types of evidence
Now we’re ready to evaluate & score the evidence
across candidate causes
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