STAT 110 LECTURE 48

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STAT 110LECTURE 48

• Janine Wright

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FURTHER EXAMPLES

• See notes p 436
• Dolphins in gillnets
• Mussel farms in the Marlborough Sounds
• Cockles at Papanui Inlet

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EXAMPLE Dolphins in Gillnets

• Design a research study to
• test the effectiveness of
• pingers in warning dolphins
• about the presence of
• gillnets.
• Pingers are attached to the
• nets and send out a sound signal to warn the
  dolphins of the presence of the nets.
• We want to know the reduction in dolphin bycatch
  that results from using pingers on gillnets.

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QUESTIONS TO BE ANSWERED

• Four questions
• 1. How will we measure the effect of the
  pingers?
• 2. How many nets do we need?
• 3. How do we decide which nets get pingers?
• 4. Do the nets possibly differ in some way
  before the pingers are added?

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QUESTION ONE

• How will we measure the
• effect of the pingers?
• Compare two groups of nets
• Group 1 - With pingers
• Group 2 - Without pingers
• Unit net
• Treatments with pingers without pingers
• Without pingers group called a CONTROL group

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QUESTION TWO

• How many nets do we need?
• We think that ten nets per group is enough.
• Is this justified?
• Revisit this soon
• calculating number of replicates

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QUESTION THREE

• How do we decide which nets get pingers?
• We could use an abitrary arrangement (see p447).
• Better to use a random arrangement
• e.g. number nets from one to ten and use a
  random number generator to select five nets to
  attach pingers to.
• Random assignment reduces bias from unfair
  assignment.

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QUESTION FOUR

• Do the nets possibly differ in some way before
  the pingers are added?
• Nets in some areas may be more likely to catch
  dolphins than nets in other areas dolphins may
  prefer different parts of the coastline.
• Before assigning pingers to nets we could first
  group the nets by area and then randomly assign
  pingers to half of the nets in each area (p448).
• Grouping units before treatment allocation
  BLOCKING

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EXAMPLE Proposed Mussel Farms in Marlborough
Sounds (p448)

• Environmental Impact Study for resource consent
  hearing
• Replicates 10 x 1 square metre quadrats
• Two areas
• Site 1 Near an existing
• mussel farm
• Site 2 Close to site of
• proposed farm
• Response number of
• brachiopods per quadrat

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RESULTS

• See p 448 in notes
• current farm site mean 1.9, s.d. 2.1 and
  for proposed site mean 11.2, s.d. 6.0.
• Brachiopod densities (number per square metre)
  were much lower at the site of the current mussel
  farm than at the proposed site
• 95 confidence intervals
• Site 1 1.9 2.262 x 2.1/v10 (0.4, 3.4)
• Site 2 11.2 2.262 x 6.0/v10 (6.9, 15.5)
• Clear evidence of a difference between the mean
  densities at these two sites.

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CONCLUSIONS

• We can not extrapolate this finding to conclude
  that we would expect this difference between any
  two sites of this type (one with a current farm
  and one without)
• the results only apply to this pair of
  sites.
• We can not conclude that if we introduced the
  proposed farm that the density at the site would
  fall to the level at the site of the current farm.

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PROBLEMS

• The observed difference may be due to mussel
  farming or may be caused by other differences
  between the two sites (we have confounding
  factors).
• We would require replicates to make a statement
  about the effects of mussel farms on brachiopod
  density.

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EXAMPLE Cockles at Papanui Inlet

• Estimate number and
• biomass of cockles in
• Waitati and Papanui
• Inlets.
• Results required for Ministry of Fisheries to use
  to set a quota for a local company.
• Sampling units 0.1 square metre quadrats

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TWO QUESTIONS TO ANSWER

• 1. How many quadrats to use?
• 2. Where to place the quadrats?

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QUESTION ONE

• How many quadrats to use?
• Need enough quadrats to estimate the natural
  (between-quadrat) variation in cockle density and
  biomass.
• Important for predicting the width of our
  confidence interval (details soon).

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QUESTION TWO

• Where to place the quadrats?
• Idea randomly place throughout the inlet,
  choosing a set of n random coordinates from a
  random number generator.
• But this could be quite time consuming.
• Simpler idea use a systematic grid pattern
  (p406).

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PROBLEM TO CONSIDER

• Some parts of the inlet are known to have a
  higher density of cockles than other parts
  (cockles occur in greater abundance close to
  channels).
• We need to overcome the problem of a random
  allocation placing our quadrats mostly in areas
  away from the channels.
• Solution Partition the inlet into areas where
  we expect the density of cockles to be more alike
  within areas than between areas (STRATA).
• Used 113 strata with 2 or 3 quadrats in each.
• Total 249 quadrats.

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RESULTS

• Page 451 in notes.
• 95 confidence intervals for the mean
• Total commercial biomass (tonnes)
• 1707 635
• Total number of cockles (millions)
• 540 110