ESM 206: Data analysis for environmental science and management

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ESM 206 Data analysis for environmental science
and management

• Spring 2006

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Ecological Effects of Nuclear Power Plants

• Nuclear reactors require cooling water to take
  heat away from the fission reaction.
• The San Onofre power plant discharges its cooling
  water to the ocean.
• An environmental defense group claims that if the
  plant increases the local water temperature above
  56 ?F, certain sensitive species will die.
• Historical data reveals that the mean water
  temperature in July is 50 ?F, with a standard
  deviation of 3 ?F.
• You take samples each day, for six consecutive
  days in mid-July, with the following results
  (52, 58, 57, 60, 62, 51).

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Acidification of Norwegian lakes

• The year is 1979. Concern is growing in Norway
  about acidification of its lakes, and the
  Norwegian government asks Britain and Germany to
  reduce emissions of sulphur dioxide from their
  power plants. In response, Britain demands proof
  that their emissions are acidifying Norwegian
  lakes.

• As science advisor to the Norwegian government,
  you are asked to design a study to produce this
  proof.
• What questions do you need to answer?
• What data should you request be collected?
• How should you analyze those data?

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What is statistics good for?
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Enhance understanding
Make predictions
Estimate parameters
Describe patterns and relationships in data
Select models
Test statistical hypotheses
Test theories
Make decisions
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COURSE OBJECTIVES

• To formulate qualitative questions about and
  decision criteria for ESM as testable
  quantitative models.
• To select and use analytical tools to estimate
  parameters of these models from data.

• To use the fitted models to answer the
  qualitative questions.
• To explain the results of the analysis in a way
  that does justice to both unpredictability
  (natural variability) and uncertainty (the limits
  of the data).

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COURSE FORMAT

• Lectures
• 2 per week
• Expected to attend all lectures
• Lecture material applied and motivated with real
  environmental problems
• Problem sets
• 8 altogether
• Solutions provided
• Covers concepts techniques
• Work as many as you need

• Labs
• 1 per week. T.A. Lisa Berry.
• In GIS lab.
• Instruction on using software discussion
  clarification of lecture, homework assignments
• Micro-Exams
• One with each problem set
• Open book, but once you start, no consultation
  with other humans
• Grade based on best 7

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RESOURCES

• Costello Kendall, Data Analysis for
  Environmental Science Management (on the class
  web page at Grafikart)

• Class web page www.bren.ucsb.edu/academics/
  course.asp?number206
• Class email list esm206_at_bren.ucsb.edu
• Software JMP, PopTools
• Installed on Bren computers
• Student edition of JMP may be available from
  bookstore
• PopTools available at http//www.cse.csiro.au/popt
  ools/

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EXPECTATIONS

• Of You
• Participate in class/lab
• Do readings
• Submit assignments on time
• Do your own work
• Be in class on time

• Of Ourselves
• Keep it interesting
• Introduce techniques with real-world examples
• Make ourselves accessible
• Make lecture notes available
• Provide solutions when work is turned in
• End class on time

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WHAT YOU SHOULD ALREADY KNOW

• Simple data summaries
• Basic probability theory
• Properties of random variables
• The normal probability distribution
• Confidence intervals what they are, and how to
  calculate them for means
• Hypothesis testing
• T-tests

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A SYSTEMATIC APPROACH TO STATISTICAL ANALYSIS

• Clearly formulate the problem, question, or
  decision that you are facing
• What are the quantities that you need to
  estimate?
• Write down a statistical model that relates the
  quantities of interest to the data you will
  collect (or have collected)
• This model will include a random component that
  represents natural variability or sampling error

• Estimate the parameters of the statistical model
• In addition to the estimate of the most likely
  value, quantify your uncertainty in that estimate
• Use the results to address your problem,
  question, or decision
• Your report should include a quantification of
  the probability that your answer is incorrect

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Statistics Decision Making EPAs Data Quality
Objectives (DQOs)

• What are DQOs? DQOs are qualitative and
  quantitative statements, developed using the DQO
  Process, that clarify study objectives, define
  the appropriate type of data, and specify
  tolerable levels of potential decision errors
  that will be used as the basis for establishing
  the quality and quantity of data needed to
  support decisions. DQOs define the performance
  criteria that limit the probabilities of making
  decision errors by considering the purpose of
  collecting the data defining the appropriate
  type of data needed and specifying tolerable
  probabilities of making decision errors.
• See link on class website

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The DQO process

• State the Problem
• Define the problem identify the planning team
  examine budget, schedule.
• Identify the Decision
• State decision identify study question define
  alternative actions.
• Identify the Inputs to the Decision
• Identify information needed for the decision
  (information sources, basis for Action Level,
  sampling/analysis method).
• Define the Boundaries of the Study
• Specify sample characteristics define
  spatial/temporal limits, units of decision making.

• Develop a Decision Rule
• Define statistical parameter (mean, median)
  specify Action Level develop logic for action.
• Specify Tolerable Limits on Decision Errors
• Set acceptable limits for decision errors
  relative to consequences (health effects, costs).
• Optimize the Design for Obtaining Data
• Select resource-effective sampling and analysis
  plan that meets the performance criteria.

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Models in statistics

• The heart of classical statistics Ordinary least
  squares
• ANOVA t-test
• Regression
• Factors enter the model linearly
• Residual variation is normally distributed
• Observations are independent

• Modern statistics
• Nonlinear least squares (NLS)
• Generalized linear model (GLM)
• Logistic regression
• Other probability distributions for residuals
• Generalized least squares (GLS)
• Account for correlation in observations

Other topics Contingency tables, multivariate
statistics