INTRODUCTION TO SAMPLING

1
INTRODUCTION TO SAMPLING
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Sampling

• Estimating population density
• / area
• (1995)

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Sampling

• Estimating population density
• / area
• (1995)

4
Sampling

• Estimating population density
• / area
• technique used is dependent on species and
  question
• Important to consider how animals are distributed
  in space
• (1995)

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x x x x x x x x x x x x x x x x x
Uniform
xx x xx x x x x x x x x x x
x x
Random
xxx xx xxx xx xx xx xxx xx
Aggregated
x x xx xxxx x xx xxxx x x x xx
xxx
Gradient
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Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density
• (1995)

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Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density, and what
  questions will that information answer?
• (1995)

8
Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density, and what
  questions will that information answer?
• Is absolute density required or will an index of
  density suffice?
• (1995)

9
Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density, and what
  questions will that information answer?
• Is absolute density required or will an index of
  density suffice?
• Will a rough estimate answer the question or is
  an accurate estimate required?
• (1995)

10
Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density, and what
  questions will that information answer?
• Is absolute density required or will an index of
  density suffice?
• Will a rough estimate answer the question or is
  an accurate estimate required?
• What is the most appropriate method biologically
  and statistically?
• (1995)

11
Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density, and what
  questions will that information answer?
• Is absolute density required or will an index of
  density suffice?
• Will a rough estimate answer the question or is
  an accurate estimate required?
• What is the most appropriate method biologically
  and statistically?
• How much will it cost?
• (1995)

12
Sampling

• Questions asked by wildlife/fisheries manager
• Do I need indication of density, and what
  questions will that information answer?
• Is absolute density required or will an index of
  density suffice?
• Will a rough estimate answer the question or is
  an accurate estimate required?
• What is the most appropriate method biologically
  and statistically?
• How much will it cost?
• Do we have that kind of money?
• Would that money be better spent on answering
  another question?

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Sampling

• Sampling with Replacement (SWR)
• Sampling units can be selected more than once
• Sampling without Replacement (SWOR)
• Sampling units cannot be selected more than once
• (Bluefish/ Menidia example)

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Sampling

• Total Counts vs Partial Counts
• Most direct way--Total counts (Atlantic salmon)
• But...Not always practical

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Sampling

• Sampling methods- Partial Counts
• Sampling is drawing a subset of sampling units

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Partial Count Sampling

• Sampling methods
• Sampling is drawing a subset of sampling units
• Quadrats, transects and mark-recapture (next
  week)
• Focus on Quadrats for lab

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Partial Count Sampling

• Sampling design
• Transects
• Using lines to sample

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Partial Count Sampling

• Sampling design
• Transects

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Partial Count Sampling

• Quadrats and transects
• Quadrats
• Sampling all individuals on quadrats of known size

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Partial Count Sampling

• Quadrats and transects
• Quadrats
• Reliability?
• The population of each quadrat examined must be
  determined exactly
• The area of each quadrat must be known

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Sampling

• Sampling design

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Sampling

• Sampling design
• Simple random design?

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Partial Count Sampling

• Sampling design
• Simple random design
• Every sample unit in population have similar
  chance of being drawn
• Selecting units is random

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Partial Count Sampling

• Sampling design
• Systematic sample?

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Partial Count Sampling

• Sampling design
• Systematic sample
• Selecting elements at regular intervals
• Similar variance as simple random, but
• Can be biased if distribution is non-random

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Partial Count Sampling

• Sampling design
• Populations often patchily distributed (Habitat
  quality)
• Stratified random sample
• Simple random sample of strata

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Partial Count Sampling

• Quadrats

1 m2 quadrats
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Partial Count Sampling

• Quadrats and transects

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Sampling

• Quadrats and transects

Atotal area aarea sampled ninumber of animals
counted in quadrat i
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Sampling

• Quadrats and transects

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Sampling

• Quadrats and transects

• How good is that estimate (162)?

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Sampling

• How good is that estimate (216)?
• Calculate a variance

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Sampling

• How good is that estimate (216)?
• Calculate a variance

Correction for SWOR
variance
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Sampling

• How good is that estimate (216)?
• Calculate a variance

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Sampling

• How good is that estimate (216)?
• Calculate a standard deviation

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Sampling

• How good is that estimate (216)?
• Calculate a coefficient of variation

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Sampling

• How good is that estimate (216)?
• Calculate a 95 confidence intervals

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Stratified Random Sampling

• Sampling design
• Stratified random sample-how to allocate?
• Proportional allocation
• Constant fraction in each stratum
• e.g. 10 of the area of each stratum

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Stratified Sampling

• Sampling design
• Stratified random sample-how to allocate?
• Proportional allocation vs Optimal allocation
• Minimizing cost of sampling
• Minimizing SE for a fixed cost
• Minimizing total cost for a specific SE
• CCO?chnh

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Stratified Sampling

• Calculate a mean and a variance for each strata
  sampled
• Calculate the overall mean per sampling unit for
  the entire population
• Weighted average
• Weight by area of strata sampled

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Weighted Average Yw
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Stratified Random Sampling

• 1) Calculate overall mean per sampling unit
  (weighted average ( ))
• Use size of stratum to weight

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Stratified Random Sampling

• 1) Calculate mean per sampling unit ( )

stratified population mean per sampling unit
Nh Size of stratum h h Stratum number
(1,2,3,.L) NTotal number of sampling units ( ?
Nh)
Observed mean of stratum h
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Stratified Random Sampling

• 1) Calculate weighted average ( )
• 2) Calculate total population size

Population total
N Size of statistical population (total number
of units)
Stratified mean per sampling unit
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Calculating a Variance(stratified random
sampling)
wh Stratum weight (whNh/N) s2h Observed
variance of stratum h nh Sample size in
stratum h fh Sampling fraction in stratum h
(nh/Nh)
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Calculating a Variance(stratified random
sampling)
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Calculate 95 CIs
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100 m2 Area
10 m
0
10 m
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GOOD HABITAT A
MARGINAL HABITAT B
POOR HABITAT C
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Proportional allocation of 10 of sampling
all Sampling units (n10) based on stratum
weights (wh)
nA5
nB3
nC3