ESM 206A: Data analysis for environmental science and management

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ESM 206A Data analysis for environmental science
and management

• Fall 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).
• Has the power plant increased the water
  temperature? If so, is the increase enough to
  have ecological effects?

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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
• 7 altogether through year
• 2 this quarter
• Solutions provided
• Covers concepts techniques
• Work as many as you need

• Labs
• 1 per week. T.A. Marion Wittmann.
• 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 6

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RESOURCES

• Costello Kendall, Data Analysis for
  Environmental Science Management (on the class
  web page Bren Library)
• Texts in Bren Library
• Fox Applied Regression Analysis by John Fox
• Manly Statistics for Environmental Science and
  Management by Brian Manly
• Moore Introduction to the Practice of Statistics
  by David Moore and George McCabe
• Zar Biostatistical Analysis by J. H. Zar

• 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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The plan for the year

• Fall (ESM 206A) 3 weeks
• How to draw inferences about statistical
  populations (the truth) from statistical
  samples (the data)
• Making decisions using data
• Assessing the effectiveness of management
• Assessing impacts of anthropogenic activities
• Incorporating prior information into analyses
• Tools include
• Probability theory
• Hypothesis testing (t-tests and ANOVA)
• Resampling techniques

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The plan for the year

• Winter (ESM 206B) 3 weeks
• Understanding the relationships between
  continuous variables
• CO2 emissions vs. gas price
• Eutrophication vs. nitrogen fertilizer input
• Using these relationships to predict the effects
  of policy interventions
• Using these relationships to rank the
  effectiveness of various policy interventions
• Primary tool is Ordinary Least Squares (OLS)
  regression
• Spring (ESM 206C) 4 weeks
• Various advanced topics, including other types of
  regression, survey design and analysis,
  multi-criteria prioritization

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Environmental challenge

• The problem California gold miners in the 19th
  century used mercury to help extract gold from
  placer deposits. Much of this mercury was not
  recovered, leading to substantial mercury
  contamination of sediments near historic mine
  sites. This mercury bioaccumulates in animals,
  ultimately threatening ecosystems and (through
  fish contamination) human health.Your job
  Characterize the level of mercury contamination
  in the soils at a former mine site.

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Populations and samples
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Heres some data

• 0.853511661, 0.391905707, 0.143344303,
  0.198267857, 0.266572367, 0.327306702,
  0.834747834, 5.32261822, 0.817037696,
  0.157247167, 0.328456677, 3.793153524,
  0.513433215, 0.502938253, 0.733454663,
  0.279345254, 0.95247347, 0.742740502,
  0.178309271, 0.469049646, 0.764546106,
  1.819858816, 0.830187557, 0.369993886,
  0.644729374, 0.841576129, 0.734056277,
  0.773035692, 0.810722543, 0.357449318
• The mean of the data is 0.858 the standard
  deviation is 1.08 the sample size is 30.

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Look at the data
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The problem with histograms
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Dot-plot
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Cumulative density function
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How well does the sample statistic estimate the
population parameter? Insights from Resampling
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Distribution of sample means