Systematic and Stratified Sampling Designs In LongTerm Ecological Monitoring Studies

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Systematic and Stratified Sampling Designs In
Long-Term Ecological Monitoring Studies Trent L.
McDonald and Paul H. Geissler 22 March 2004 Draft
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• Introduction
• Probability sampling
• Unstratified, stratified, unequal probability
• Systematic or random selection
• We recommend either unstratified or stratified
  systematic sampling
• Numerical examples in paper
• Judgment haphazard designs are scientifically
  invalid never appropriate

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Hypothetical National Park (HYNP) used to
illustrate sampling designs.
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• Unstratified systematic (grid) samples
• Simple and straightforward
• Start with a random point
• Sample points are evenly spaced on a grid
• Spacing of grid points determines sample size
• Sometimes points are measured every nth year
  (rotating panel design)

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The hypothetic population overlaid with a
systematic sample of 16 points. One revisit
option calls for sites labeled 1 to be visited
year 1, sites labeled 2 to be visited year 2,
and so on.
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• Useful to draw extra contingency sites in case
  some sites cannot be measured or additional
  resources are available.
• Perhaps draw twice as many points and use every
  other one.
• Very important to only replace a site if it
  cannot be measured and not because it is
  inconvenient or atypical.
• Have a rule for selecting a nearby replacement
  site.
• Visit sites or clusters of sites in random order
  in case you cannot finish.

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• Characteristics of Unstratified Systematic Sample
  Designs
• More precise than a simple random sample (SRS)
  if spatial autocorrelation
• SRS tend to clump

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• Advantages of uniform coverage with systematic
  samples
• Increases precision
• Better for mapping
• Good for investigating spatial patterns
• Easier to find sites
• Looks better

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• Stratified and unequal probability sampling
  sample same areas at higher rates than others.
• Unstratified sampling samples all areas in
  proportion to their representation in the
  population.
• If you are primarily interested in common
  species and habitats or in park-wide estimates,
  choose an unstratified design with proportional
  allocation.

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• If you have equal interest in all habitat types,
  you should stratify and allocate about the same
  number of samples to each so that estimates for
  each habitat type will have about the same
  precision.
• If you are especially interested in rare
  habitats or in threatened or endangered species,
  you should stratify and allocate more samples to
  those strata.
• Remember that precision is primarily determined
  by the sample size in each habitat type and does
  not depend on the proportion of the area that is
  sampled.

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• Stratified and unequal probability sampling can
  increase sample size and precision by sampling
  accessible areas at a higher rate.
• When the population is very heterogeneous,,
  stratification can substantially reduce the
  variance by estimating the variance separately
  within homogenous units called strata. But you
  lose a degree of freedom (a sample point) for
  each stratum.

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• Cluster Sampling
• Reduces travel time by measuring a cluster of
  points, at a sample point (transect or
  subplots).
• Subplots are not independent, so use their mean
  as the observation for the sample point.
• Variance of that observation is reduced,
  because v(mean) v(observation)/m.
• Some people think that bird counts along a
  transect are independent if the counts are far
  enough apart so the observer cannot count the
  same bird twice.
• That is not true because habitat and bird
  populations are not independent.

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• Stratified Sampling
• The population is divided into strata without
  skips or duplicates, and a separate sample is
  selected in each stratum, often with different
  sampling intensities.
• Recommended if
• Estimates are needed for the strata.
• Need good estimates for less common habitat.
• Large differences in travel costs
• Large differences in response mean among strata

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HYNP stratified into 3 strata based on access and
less common habitats. Strata 1 is common habitat
in easily accessible terrain. Strata 2 is common
habitat in difficult to access terrain. Strata 3
is less common habitat whose location is known.
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• Strata should remain fixed forever, using
  unchanging features such as elevation, because it
  is difficult and complex to change strata.
• However, it the exact location of strata
  boundaries is usually not critical, as mistakes
  will not introduce any bias.
• Strata changes are almost never needed.
• What is important is that the strata increase
  the likelihood of including less common habitat,
  have major differences in travel costs, etc.

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• Strata Domains
• Strata are defined before the sample is drawn
  and are used primarily to distribute the sample
  points.
• Domains represent subpopulations of interest
  (e.g., habitat types) for which we want
  estimates.
• The points which belong to each domain are
  typically not known until after the sample is
  observed.

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Map of HYNP showing 3 strata, 16 sample points,
and a domain of estimation (hatched areas)
constructed after 2 points in stratum 1 were
discovered to be in less common habitat.