Environmental Sampling

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Environmental Sampling

• ESM 206
• April 29, 2003

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Outline

• Overview
• How to sample
• What is a sample?
• Types of sampling
• Sample unit
• How many to sample
• Types of error
• Statistical power

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Data Collection

• Many purposes
• Need to know what to find out
• Can you sample it directly?
• Is it a relationship between things? (what kind)
• Need to know how how much to sample
• Technique
• Efficiency in sampling
• Sampling desired parameter
• Power
• Precision to estimate parameter to answer question

Overview - How to sample - How
many to sample
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Example

• Oysters in a creek contaminated with PCT
  (polychlorinated terphenyls)

Overview - How to sample - How
many to sample
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Sampling

• Cant sample everything
• Sample enough to be representative (n)
• Sample (subset of all oysters in creek)
• Sample entire population (N)
• Census (all oysters in creek maybe more
  realistic with employees, etc.)

Overview - How to sample - How
many to sample
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Sampling Objectives

• Unbiased estimate of population mean
• (mean PCT concentration)
• Assess precision of estimate
• Calculate standard error of mean
• Obtain as precise an estimate of parameters as
  possible for time money

Overview - How to sample - How
many to sample
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Sampling Methods

• Point samples
• Transects
• Line intercepts
• Plots
• Circular, quadrats, nested quadrats
• Permanent or temporary sites

Overview - How to sample - How
many to sample
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Sampling Methods

• Systematic
• Simple random
• Stratified random
• Random sampling within blocks
• Cluster sampling
• Two-stage sampling

Overview - How to sample - How
many to sample
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Subjective vs. Random

• Haphazard sampling
• Capricious selection by investigator without
  conscious bias
• Judgment sampling
• Select representative or politically desirable
  units
• Convenience sampling
• Select sites that are easy to reach

NOT random
Overview - How to sample - How
many to sample
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Systematic Sampling

• Samples selected systematically according to
  pre-determined plan
• Grid, every kth individual from finite population
• OK as long as sampling frequency doesnt match
  frequency of some repeating pattern
• Can use same formulas as for random samples

Overview - How to sample - How
many to sample
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Systematic
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Systematic Sampling Assumptions

• No spatial or temporal trends in variable
• No natural strata
• No correlations among individual samples

Overview - How to sample - How
many to sample
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Simple Random Sampling

• Each sample in population has equal chance of
  selection
• Prior selection doesnt affect chance that
  another is selected
• Unbiased estimate of mean variance

Overview - How to sample - How
many to sample
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To Do Random Sampling

• Either enumerate all units in population use
  random numbers to select units
• Or, if population is infinite, use random numbers
  to select locations

Overview - How to sample - How
many to sample
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Simple Random
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Stratified Random Sampling

• Use if environment is heterogeneous
• Use existing information to guide sampling
• Good when easy to divide environment into
  different types
• Strata
• Each strata sampled independently
• Can compare between strata
• Or, combine statistics taking into account number
  of samples per stratum

Overview - How to sample - How
many to sample
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Simple Stratified Random
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Stratified Random Area Weighted
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Formula for Stratified Random

• For K strata, with jth stratum covering fraction
  j of population, estimated mean of stratum j is
  xj(bar), P is proportion of total study area in
  jth stratum.

Overview - How to sample - How
many to sample
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Random Sampling within Blocks

• Combination of systematic random sampling
• Gives coverage of an area with some protection
  from bias

Overview - How to sample - How
many to sample
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Cluster Sampling

• Clusters of individuals chosen at random
• All units within cluster sampled

Overview - How to sample - How
many to sample
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Multi-Stage Sampling

• Select 1o and 2o units
• 2o units are subset
• Randomly sample both

2o unit
1o unit
Details in Gilbert 1987 Statistical Methods in
Environmental Pollution Monitoring.
Overview - How to sample - How
many to sample
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Summary of Sampling Methods

• Systematic
• Simple random
• Stratified random
• Random sample within blocks
• Cluster sampling
• Two-stage sampling

stratum
1o unit
2o unit
Overview - How to sample - How
many to sample
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Selecting Sample Units

• Increasing sample size decreases variance
• Need to know 3 things
• How should sample units be selected?
• What should sample unit be?
• 1 oyster or 1 cluster of oysters
• How many samples should be taken (1 - 8)?

Overview - How to sample - How
many to sample
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Kinds of Sample Units

• Sometimes very clearly defined
• 1 organism, 1 liter water, 1 product, 1 person
• Other times context or location of samples is
  more complicated
• Homogenous vs. heterogeneous environment

Overview - How to sample - How
many to sample
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Heterogeneity

• In heterogeneous environment, want sample units
  large enough to encompass heterogeneity
• Within each observation rather than between
  observations
• Ex. What is average PCT concentration in oysters
  in 10 creeks?
• - Get different variance if choose sampling unit
  as single oysters vs. all oysters in each creek

Overview - How to sample - How
many to sample
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Compositing Samples

• Aggregate smaller units to encompass
  heterogeneity
• Enlarges sampling unit (entire creek vs. single
  oyster)
• Composite sampling important when lab analysis
  costs are high compared to collecting samples
• Collect several physical samples, mix well, and
  analyze as single observation

Overview - How to sample - How
many to sample
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Compositing Samples

• Some considerations
• Larger sample units can be more expensive (and
  time consuming)

Overview - How to sample - How
many to sample
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Kinds of Uncertainty

• Epistemic
• Inherent environmental variation
• Imperfect knowledge
• Measurement error
• Ignorance
• Semantic
• Ambiguity (multiple interpretations)
• Vagueness (under-specification)

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many to sample
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Measurement Error

• Measured variation composed of
• Natural variation
• Measurement error
• Measurement error can be reduced
• Improve sampling protocols
• Improve instrumentation
• Will increase precision without increasing number
  of samples

Overview - How to sample - How
many to sample
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Components of Measurement Error

• Systematic
• Certain assumptions
• Instrument error
• Operator error
• Random
• Instrument error
• Operator error
• Extrinsic factors

Overview - How to sample - How
many to sample
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Types of Error

• Type I error (a)
• Incorrectly accepting alternative hypothesis
  (there is an effect)
• - P-value
• Type II error (ß)
• Incorrectly accepting null hypothesis (there is
  no effect)
• - Tradeoff between a and ß Power is 1- ß

Overview - How to sample - How
many to sample
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Power of the test

• Probability of detecting effect if it exists
• Probability of rejecting incorrect Ho
• 1-ß (Type II error)

Overview - How to sample - How
many to sample
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Statistical Power depends on

• Effect Size (ES)
• Magnitude of difference between treatments
• Larger effects easier to detect
• Background variation
• Variation between sample units (est. by s2)
• Greater background variation, less likely to
  detect effects
• Increasing sample size makes effects easier to
  detect

Overview - How to sample - How
many to sample
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Power Analysis

• As a decreases, ß increases, power decreases
• Exact formula depends on statistical test
• n is number of samples, s is standard deviation,
  ES is effect size, a is significance level

Overview - How to sample - How
many to sample
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A priori Power Analysis

• Determine sample size
• Need to know
• What power wanted
• Background variation (pilot study, previous lit.)
• What ES want to detect if effect occurs

Overview - How to sample - How
many to sample
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Post-hoc Power Analysis

• If conclusion is non-significant, solve power
  equation for specific ES
• _at_ a 0.05

Overview - How to sample - How
many to sample
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Example Power Analysis

• Want to know what our power to detect change is
  if
• n 50 oysters
• s 30 ppt
• ES 30 ppt or 10 ppt
• a 0.05 or 0.10

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Example Power Analysis
Overview - How to sample - How
many to sample
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Oysters in a creek